CN1809170A

CN1809170A - Discrete cosine transform method and apparatus applicable to image coding and video coding

Info

Publication number: CN1809170A
Application number: CN 200610048984
Authority: CN
Inventors: 虞露; 张赐勋
Original assignee: Zhejiang University ZJU
Current assignee: XFusion Digital Technologies Co Ltd
Priority date: 2006-01-11
Filing date: 2006-01-11
Publication date: 2006-07-26
Anticipated expiration: 2026-01-11
Also published as: CN100490539C

Abstract

The invention discloses a discrete cosine transform method and device for image coding and video coding. It obtains higher precision with lower implementation complexity, and can control the implementation complexity more conveniently. The coefficients of the transformation matrix adopted are closer to the coefficients of the theoretical discrete cosine transform matrix, and therefore closer to the result of the theoretical discrete cosine transform, and the precision is higher than that of the prior art with considerable implementation complexity. At the same time, in the prior art, multiple coefficients need to be adjusted when adjusting the complexity and precision of the implementation, but the present invention allows one, two or more coefficients to be adjusted, and the adjustment method is more convenient and comprehensive. The present invention can be used in fields related to image coding and video coding. The discrete cosine transform device in the present invention fully realizes the discrete cosine transform method in the present invention.

Description

Method and device for discrete cosine transform applied to image coding and video coding

技术领域technical field

本发明涉及电数字数据处理技术领域，特别是一种运用于图像编码和视频编码的离散余弦变换的方法与装置。The invention relates to the technical field of electrical digital data processing, in particular to a discrete cosine transform method and device for image coding and video coding.

背景技术Background technique

传统的视频编码标准如ITU制定的H.261，H.263标准以及ISO的MPEG组织制定的MEPG-1，MPEG-2，MPEG-4等都是基于混合编码。所谓混合编码框架是综合考虑预测，变换以及熵编码的方法的编码框架，有以下主要特点：Traditional video coding standards such as H.261 and H.263 standards formulated by ITU and MEPG-1, MPEG-2, and MPEG-4 formulated by ISO's MPEG organization are all based on hybrid coding. The so-called hybrid coding framework is a coding framework that comprehensively considers prediction, transformation and entropy coding methods, and has the following main features:

1)利用预测去除时间域的冗余度；1) Use prediction to remove redundancy in the time domain;

2)利用变换去除空间域的冗余度；2) Use transformation to remove redundancy in the spatial domain;

3)而用熵编码去除统计上的冗余度；3) and remove statistical redundancy with entropy coding;

上述视频编码标准都具有帧内编码帧，即I帧，和帧间编码帧，即P帧，I帧和P帧采用不同的编码方法。I帧的编码过程如下：对原始图像数据或帧内预测得到的残差块进行二维变换；然后在变换域中对变换系数进行量化；最后进行熵编码，即Huffman编码或者算术编码等。P帧的编码过程如下：采用运动估计得到运动矢量，然后采用基于运动补偿的帧间预测，接着对帧间预测得到的残差块进行二维变换，再对变换域系数进行量化，最后进行熵编码。The above-mentioned video coding standards all have intra-coded frames, namely I frames, and inter-frame coded frames, namely P frames, and I frames and P frames adopt different coding methods. The coding process of the I frame is as follows: perform two-dimensional transformation on the original image data or the residual block obtained by intra-frame prediction; then quantize the transformation coefficients in the transformation domain; finally perform entropy coding, that is, Huffman coding or arithmetic coding, etc. The encoding process of the P frame is as follows: use motion estimation to obtain the motion vector, then use inter-frame prediction based on motion compensation, then perform two-dimensional transformation on the residual block obtained by inter-frame prediction, quantize the transform domain coefficients, and finally perform entropy coding.

传统的图像编码标准，如JPEG标准，与视频编码标准有着相近之处，对原始图像数据或图像内预测得到的残差块进行二维变换；然后在变换域中对变换系数进行量化；最后进行熵编码。Traditional image coding standards, such as the JPEG standard, are similar to video coding standards, performing two-dimensional transformation on the original image data or the residual block obtained by intra-image prediction; then quantizing the transform coefficients in the transform domain; finally performing Entropy coding.

由于视频数据和图像数据在空间域上较强的相关性，二维变换是提高编码增益的关键因素，因此二维变换是视频编码和图像编码的很重要的部分。Due to the strong correlation between video data and image data in the spatial domain, two-dimensional transformation is a key factor to improve coding gain, so two-dimensional transformation is a very important part of video coding and image coding.

离散余弦变换(DCT)变换通常用于图像数据和视频数据的块变换编码，这是因为对于各种信号，离散余弦变换非常近似于统计最佳的K-L变换。离散余弦变换被广泛应用于各种视频/图像编码标准中。离散余弦变换的一个缺点是矩阵中的部分系数是无理数，所以在数字计算机上用迭代的方法进行变换和反变换后，不能得到一模一样的初始值。在解码端，由于没有定义具体的反离散余弦变换(IDCT)的具体过程，所以不同的解码器解码的结果可能不同，导致了解码器失配(decoder mismatch)的问题。因此，符合标准的解码器必须达到一定的精度要求。但是高的精度通常要求高的实现复杂度。在设计和实现时要根据不同需要对精度和实现复杂度两者进行权衡。The Discrete Cosine Transform (DCT) transform is commonly used for block transform coding of image data and video data, since it closely approximates the statistically optimal K-L transform for various signals. Discrete cosine transform is widely used in various video/image coding standards. One disadvantage of discrete cosine transform is that some coefficients in the matrix are irrational numbers, so after transforming and inverse transforming with iterative method on a digital computer, the same initial value cannot be obtained. At the decoding end, since the specific process of the inverse discrete cosine transform (IDCT) is not defined, the decoding results of different decoders may be different, resulting in the problem of decoder mismatch. Therefore, a standard-compliant decoder must meet certain precision requirements. But high precision usually requires high implementation complexity. When designing and implementing, it is necessary to balance the accuracy and implementation complexity according to different needs.

发明内容Contents of the invention

本发明的目的是提供一种运用于图像编码和视频编码的离散余弦变换的方法和装置。The object of the present invention is to provide a discrete cosine transform method and device for image coding and video coding.

本发明解决其技术问题所采用的技术方案是：The technical solution adopted by the present invention to solve its technical problems is:

1、一种运用于图像编码和视频编码的离散余弦变换的方法，对于正变换：根据下式选取N×N正变换矩阵FDCT_fpN：1. A method of discrete cosine transform applied to image coding and video coding, for forward transform: select N×N forward transform matrix FDCT _fpN according to the following formula:

${FDCT FDCT}_{fpN f} = = round round ((\sqrt{N N} {g g 22}^{{SCALE SCALE}_{f f}} gFDCT wxya)) / / 22^{{SCALE SCALE}_{f f}};;$

其中FDCT为理论的N×N离散余弦正变换矩阵；SCALE_f为预先指定的非负整数，用于获得N×N正变换矩阵；round(g)为普通的四舍五入操作；对于正变换采用或调整SCALE_f达到不同的精度和不同的实现复杂度；Among them, FDCT is the theoretical N×N discrete cosine positive transformation matrix; SCALE _f is a pre-specified non-negative integer used to obtain the N×N positive transformation matrix; round (g) is an ordinary rounding operation; for positive transformation, use or adjust SCALE _f achieves different precision and different implementation complexity;

根据所选取的N×N正变换矩阵，进行相应的正变换过程：According to the selected N×N forward transformation matrix, perform the corresponding forward transformation process:

在正变换前先左移FS0位，在一维正变换后右移FS1位，在二维正变换后右移FS2位；其中FS0，FS1，FS2为整数，值为零时表示不进行移位操作，值为正整数时表示进行上所述方向的移位操作，值为负整数表示进行和上述方向相反的移位操作；对于正变换，采用或调整FS0，FS1，FS2中的一个、两个或三个达到不同的精度和不同的实现复杂度。Shift the FS0 bits to the left before the forward transformation, shift the FS1 bits to the right after the one-dimensional forward transformation, and shift the FS2 bits to the right after the two-dimensional forward transformation; where FS0, FS1, and FS2 are integers, and when the value is zero, it means no shifting Operation, when the value is a positive integer, it means to perform the shift operation in the above direction, and when the value is a negative integer, it means to perform the shift operation opposite to the above direction; for positive transformation, use or adjust one or both of FS0, FS1, and FS2 One or three achieve different precision and different implementation complexity.

采用或调整N×N正变换矩阵FDCT_fpN中的系数达到不同的精度和不同的实现复杂度，即用FDCT_fpNr代替FDCT_fpN，满足：Use or adjust the coefficients in the N×N forward transformation matrix FDCT _fpN to achieve different precision and different implementation complexity, that is, replace FDCT _fpN with FDCT _fpNr , satisfying:

|(FDCT_fpNr(i，j)-FDCT_fpN(i，j))/FDCT_fpN(i，j)|≤1％ 0≤i≤N-1，0≤j≤N-1；|(FDCT _fpNr (i, j)-FDCT _fpN (i, j))/FDCT _fpN (i, j)|≤1% 0≤i≤N-1, 0≤j≤N-1;

其中FDCT_fpNr(i，j)和FDC_fpN(i，j)分别表示FDCT_fpN和FDCT_fpN中位置为(i，j)的系数。where FDCT _fpNr (i, j) and FDC _fpN (i, j) represent FDCT _fpN and the coefficient at position (i, j) in FDCT _fpN , respectively.

所说的选取N×N正变换矩阵的方法具体应用到8×8正变换矩阵如下：The method of selecting the N×N positive transformation matrix is specifically applied to the 8×8 positive transformation matrix as follows:

采用如下的8×8正变换矩阵FDCT_fp8：The following 8×8 forward transformation matrix FDCT _fp8 is adopted:

${FDCT FDCT}_{fp fp 88} = = round round ((\sqrt{88} {g g 22}^{{SCALE SCALE}_{f f}} gFDCT wxya)) / / 22^{{SCALE SCALE}_{f f}} = = [\begin{matrix} {G G}_{f f} & {G G}_{f f} & {G G}_{f f} & {G G}_{f f} & {G G}_{f f} & {G G}_{f f} & {G G}_{f f} & {G G}_{f f} \\ {A A}_{f f} & {B B}_{f f} & {C C}_{f f} & {D D.}_{f f} & - - {D D.}_{f f} & - - {C C}_{f f} & - - {B B}_{f f} & - - {A A}_{f f} \\ {E E.}_{f f} & {F f}_{f f} & - - {F f}_{f f} & - - {E E.}_{f f} & - - {E E.}_{f f} & - - {F f}_{f f} & {F f}_{f f} & {E E.}_{f f} \\ {B B}_{f f} & - - {D D.}_{f f} & - - {A A}_{f f} & - - {C C}_{f f} & {C C}_{f f} & {A A}_{f f} & {D D.}_{f f} & {- - B B}_{f f} \\ {G G}_{f f} & {- - G G}_{f f} & - - {G G}_{f f} & {G G}_{f f} & {G G}_{f f} & - - {G G}_{f f} & {G G}_{f f} & {G G}_{f f} \\ {C C}_{f f} & - - {A A}_{f f} & {D D.}_{f f} & {B B}_{f f} & - - {B B}_{f f} & - - {D D.}_{f f} & {A A}_{f f} & {- - C C}_{f f} \\ {F f}_{f f} & - - {E E.}_{f f} & {E E.}_{f f} & - - {F f}_{f f} & - - {F f}_{f f} & {E E.}_{f f} & - - {E E.}_{f f} & {F f}_{f f} \\ {D D.}_{f f} & - - {C C}_{f f} & {B B}_{f f} & - - {A A}_{f f} & {A A}_{f f} & - - {B B}_{f f} & {C C}_{f f} & - - {D D.}_{f f} \end{matrix}] / / 22^{{SCALE SCALE}_{f f}}$

其中FDCT为理论的8×8离散余弦正变换矩阵；SCALE_f为预先指定的非负整数，用于获得8×8正变换矩阵；round(g)为普通的四舍五入操作；A_f，B_f，C_f，D_f，E_f，F_f，G_f表示8×8正变换矩阵中的系数，且均为整数；Among them, FDCT is the theoretical 8×8 discrete cosine positive transformation matrix; SCALE _f is a pre-specified non-negative integer used to obtain the 8×8 positive transformation matrix; round(g) is an ordinary rounding operation; A _f , B _f , C _f , D _f , E _f , F _f , G _f represent the coefficients in the 8×8 forward transformation matrix, and they are all integers;

特别地，还包括以下四组正变换矩阵系数：In particular, the following four sets of positive transformation matrix coefficients are also included:

(1)A_f＝2841，B_f＝2408，C_f＝1609，D_f＝565，E_f＝2676，F_f＝1108，G_f＝2408，SCALE_f＝11；(1) A _f =2841, B _f =2408, C _f =1609, D _f =565, E _f =2676, F _f =1108, G _f =2408, SCALE _f =11;

(2)A_f＝5681，B_f＝4816，C_f＝3218，D_f＝1130，E_f＝5352，F_f＝2217，G_f＝4096，SCALE_f＝12；(2) A _f =5681, B _f =4816, C _f =3218, D _f =1130, E _f =5352, F _f =2217, G _f =4096, SCALE _f =12;

(3)A_f＝11363，B_f＝9633，C_f＝6436，D_f＝2260，E_f＝10703，F_f＝4433，G_f＝8192，SCALE_f＝13；(3) A _f =11363, B _f =9633, C _f =6436, D _f =2260, E _f =10703, F _f =4433, G _f =8192, SCALE _f =13;

(4)A_f＝22725，B_f＝19266，C_f＝12873，D_f＝4520，E_f＝21407，F_f＝8867，G_f＝16384，SCALE_f＝14。(4) A _f =22725, B _f =19266, C _f =12873, D _f =4520, E _f =21407, F _f =8867, G _f =16384, SCALE _f =14.

2、一种运用于图像编码和视频编码的离散余弦变换的方法，对于反变换：根据下面两式选取N×N反变换矩阵IDCT_fpN：2. A method of discrete cosine transform applied to image coding and video coding, for inverse transform: select N×N inverse transform matrix IDCT _fpN according to the following two formulas:

${IDCT IDCT}_{fpN f} = = round round ((\sqrt{N N} {g g 22}^{{SCALE SCALE}_{i i}} gIDCT gIDCT)) / / 22^{{SCALE SCALE}_{i i}};;$

其中IDCT为理论的N×N离散余弦反变换矩阵；SCALE_i为预先指定的非负整数，用于获得N×N反变换矩阵；round(g)为普通的四舍五入操作；对于反变换采用或调整SCALE_i达到不同的精度和不同的实现复杂度；Among them, IDCT is the theoretical N×N discrete cosine inverse transformation matrix; SCALE _i is a pre-specified non-negative integer used to obtain the N×N inverse transformation matrix; round (g) is an ordinary rounding operation; for inverse transformation, use or adjust SCALE _i achieves different precisions and different implementation complexities;

根据所选取的N×N反变换矩阵，进行相应的反变换过程：According to the selected N×N inverse transformation matrix, perform the corresponding inverse transformation process:

在变换前先左移IS0位，在一维变换后右移IS1位，在二维变换后右移IS2位；其中IS0，IS1，IS2为整数，值为零时表示不进行移位操作，值为正整数时表示进行上所述方向的移位操作，值为负整数表示进行和上述方向相反的移位操作；对于反变换，采用或调整IS0，IS1，IS2中的一个、两个或三个达到不同的精度和不同的实现复杂度。Shift the IS0 bit to the left before the transformation, shift the IS1 bit to the right after the one-dimensional transformation, and shift the IS2 bit to the right after the two-dimensional transformation; among them, IS0, IS1, and IS2 are integers, and when the value is zero, it means no shift operation, and the value When it is a positive integer, it means to perform the shift operation in the above direction, and when the value is a negative integer, it means to perform the shift operation opposite to the above direction; for the inverse transformation, use or adjust one, two or three of IS0, IS1, IS2 Each achieves different precision and different implementation complexity.

采用或调整N×N反变换矩阵IDCT_fpN中的系数达到不同的精度和不同的实现复杂度，即用IDCT_fpNr代替IDCT_fpN，满足：Use or adjust the coefficients in the N×N inverse transformation matrix IDCT _fpN to achieve different precision and different implementation complexity, that is, use IDCT _fpNr instead of IDCT _fpN to satisfy:

|(IDCT_fpNr(i，j)-IDCT_fpN(i，j))/IDCT_fpN(i，j)|≤1％ 0≤i≤N-1，0≤j≤N-1；|(IDCT _fpNr (i, j)-IDCT _fpN (i, j))/IDCT _fpN (i, j)|≤1% 0≤i≤N-1, 0≤j≤N-1;

其中IDCT_fpNr(i，j)和IDCT_fpN(i，j)分别表示FDCT_fpN和FDCT_fpN中位置为(i，j)的系数。where IDCT _fpNr (i, j) and IDCT _fpN (i, j) represent FDCT _fpN and the coefficient at position (i, j) in FDCT _fpN , respectively.

所说的选取N×N反变换矩阵的方法具体应用到8×8反变换矩阵如下：The method for selecting the N×N inverse transformation matrix is specifically applied to the 8×8 inverse transformation matrix as follows:

采用如下8×8反变换矩阵IDCT_fp8：Use the following 8×8 inverse transformation matrix IDCT _fp8 :

${IDCT IDCT}_{fp fp 88} = = round round ((\sqrt{88} {g g 22}^{{SCALE SCALE}_{i i}} gIDCT gIDCT)) / / 22^{{SCALE SCALE}_{i i}} = = [\begin{matrix} {G G}_{i i} & {A A}_{i i} & {E E.}_{i i} & {B B}_{i i} & {G G}_{i i} & {C C}_{i i} & {F f}_{i i} & {D D.}_{i i} \\ {G G}_{i i} & {B B}_{i i} & {F f}_{i i} & {- - D D.}_{i i} & - - {G G}_{i i} & - - {A A}_{i i} & - - {E E.}_{i i} & - - {C C}_{i i} \\ {G G}_{i i} & {C C}_{i i} & - - {F f}_{i i} & - - {A A}_{i i} & - - {G G}_{i i} & - - {D D.}_{i i} & {E E.}_{i i} & {B B}_{i i} \\ {G G}_{i i} & {D D.}_{i i} & - - {E E.}_{i i} & - - {C C}_{i i} & {G G}_{i i} & {B B}_{i i} & {- - F f}_{i i} & {- - A A}_{i i} \\ {G G}_{i i} & {- - D D.}_{i i} & - - {E E.}_{i i} & {C C}_{i i} & {G G}_{i i} & - - {B B}_{i i} & {- - F f}_{i i} & {A A}_{i i} \\ {G G}_{i i} & - - {C C}_{i i} & {- - F f}_{i i} & {A A}_{i i} & - - {G G}_{i i} & - - {D D.}_{i i} & {E E.}_{i i} & {- - B B}_{i i} \\ {G G}_{i i} & - - {B B}_{i i} & {F f}_{i i} & {D D.}_{i i} & - - {G G}_{i i} & {A A}_{i i} & - - {E E.}_{i i} & {C C}_{i i} \\ {G G}_{i i} & - - {A A}_{i i} & {E E.}_{i i} & - - {B B}_{i i} & {G G}_{i i} & - - {C C}_{i i} & {F f}_{i i} & - - {D D.}_{i i} \end{matrix}] / / 22^{{SCALE SCALE}_{f f}}$

其中IDCT为理论的8×8离散余弦反变换矩阵；SCALE_i为预先指定的非负整数，用于获得8×8反变换矩阵；round(g)为普通的四舍五入操作；A_i，B_i，C_i，D_i，E_i，F_i，G_i表示8×8反变换矩阵中的系数，且均为整数；特别地，还包括以下四组正变换矩阵系数和反变换矩阵系数：Among them, IDCT is the theoretical 8×8 inverse discrete cosine transform matrix; SCALE _i is a pre-specified non-negative integer used to obtain the 8×8 inverse transform matrix; round(g) is an ordinary rounding operation; A _i , B _i , C _i , D _i , E _i , F _i , G _i represent the coefficients in the 8×8 inverse transformation matrix, and they are all integers; in particular, the following four groups of forward transformation matrix coefficients and inverse transformation matrix coefficients are also included:

(1)A_i＝2841，B_i＝2408，C_i＝1609，D_i＝565，E_i＝2676，F_i＝1108，G_i＝2408，SCALE_i＝11；(1) A _i =2841, B _i =2408, C _i =1609, D _i =565, E _i =2676, F _i =1108, G _i =2408, SCALE _i =11;

(2)A_i＝5681，B_i＝4816，C_i＝3218，D_i＝1130，E_i＝5352，F_i＝2217，G_i＝4096，SCALE_i＝12；(2) A _i =5681, B _i =4816, C _i =3218, D _i =1130, E _i =5352, F _i =2217, G _i =4096, SCALE _i =12;

(3)A_i＝11363，B_i＝9633，C_i＝6436，D_i＝2260，E_i＝10703，F_i＝4433，G_i＝8192，SCALE_i＝13；(3) A _i =11363, B _i =9633, C _i =6436, D _i =2260, E _i =10703, F _i =4433, G _i =8192, SCALE _i =13;

(4)A_i＝22725，B_i＝19266，C_i＝12873，D_i＝4520，E_i＝21407，F_i＝8867，G_i＝16384，SCALE_i＝14。(4) A _i =22725, B _i =19266, C _i =12873, D _i =4520, E _i =21407, F _i =8867, G _i =16384, SCALE _i =14.

3、一种运用于图像编码和视频编码的离散余弦变换的装置：3. A device for discrete cosine transform applied to image coding and video coding:

正变换装置包括预移位装置，第一维正变换装置，第一维正变换后移位装置，第二维正变换装置，第二维正变换后移位装置；预移位装置的输入端与变换前的输入数据相连，预移位装置的输出端和第一维正变换装置的输入端相连，第一维正变换装置的输出端和第一维正变换后移位装置的输入端相连，第一维正变换后移位装置的输出端和第二维正变换装置输入端相连，第二维正变换装置输出端和第二维正变换后移位装置输入端相连，第二维正变换后移位装置输出端和变换输出数据相连。The forward transform device comprises a pre-shift device, a first-dimensional forward transform device, a shift device after the first-dimensional forward transform, a second-dimensional forward transform device, and a shift device after the second-dimensional forward transform; the input terminal of the pre-shift device It is connected with the input data before transformation, the output end of the pre-shift device is connected with the input end of the first-dimensional forward transform device, and the output end of the first-dimensional forward transform device is connected with the input end of the shift device after the first-dimensional forward transform , the output end of the shifting device after the first-dimensional forward transformation is connected to the input end of the second-dimensional forward transforming device, the output end of the second-dimensional forward transforming device is connected to the input end of the shifting device after the second-dimensional forward transformation, and the second-dimensional forward transforming device The output terminal of the transformed shifting device is connected to the transformed output data.

对于正变换装置，还包括正变换精度复杂度控制装置；正变换精度复杂度控制装置通过开关和预移位装置，第一维正变换装置，第一维正变换后移位装置，第二维正变换装置，第二维正变换后移位装置相连；For the forward transformation device, it also includes a forward transformation precision complexity control device; the forward transformation precision complexity control device passes through the switch and the pre-shift device, the first-dimensional forward transformation device, the first-dimensional forward transformation post-shift device, and the second dimension The forward transformation device is connected to the displacement device after the second dimension forward transformation;

4、一种运用于图像编码和视频编码的离散余弦变换的装置：4. A device for discrete cosine transform applied to image coding and video coding:

反变换装置包括预移位装置，第一维反变换装置，第一维反变换后移位装置，第二维反变换装置，第二维反变换后移位装置；预移位装置的输入端与变换前的输入数据相连，预移位装置的输出端和第一维反变换装置的输入端相连，第一维反变换装置的输出端和第一维反变换后移位装置的输入端相连，第一维反变换后移位装置的输出端和第二维反变换装置输入端相连，第二维反变换装置输出端和第二维反变换后移位装置输入端相连，第二维反变换后移位装置输出端和变换输出数据相连。The inverse transformation device comprises a pre-shift device, a first-dimensional inverse transformation device, a shift device after the first-dimensional inverse transformation, a second-dimensional inverse transformation device, and a shift device after the second-dimensional inverse transformation; the input terminal of the pre-shift device It is connected with the input data before transformation, the output terminal of the pre-shifting device is connected with the input terminal of the first-dimensional inverse transformation device, and the output terminal of the first-dimensional inverse transformation device is connected with the input terminal of the shifting device after the first-dimensional inverse transformation , the output end of the shifting device after the first-dimensional inverse transformation is connected to the input end of the second-dimensional inverse transformation device, the output end of the second-dimensional inverse transformation device is connected to the input end of the shifting device after the second-dimensional inverse transformation, and the second-dimensional inversion The output terminal of the transformed shifting device is connected to the transformed output data.

对于反变换装置，还包括反变换精度复杂度控制装置；反变换精度复杂度控制装置通过开关和预移位装置，第一维反变换装置，第一维反变换后移位装置，第二维反变换装置，第二维反变换后移位装置相连。For the inverse transformation device, it also includes an inverse transformation precision complexity control device; the inverse transformation precision complexity control device passes through the switch and the pre-shift device, the first dimension inverse transformation device, the first dimension inverse transformation post-shift device, the second dimension The inverse transformation device is connected with the displacement device after the second dimension inverse transformation.

本发明与背景技术相比，具有有益的效果：可以用较低的实现复杂度得到较高的精度，并且可以较方便的控制实现的复杂度。它所采用的变换矩阵的系数和理论的离散余弦变换矩阵的系数更加接近，因此和理论的离散余弦变换的结果更加接近，精度比现有技术在相当的实现复杂度下高。同时，现有技术在调整实现的复杂度和精度时需要调整多个系数，本发明允许可以调整一个、两个或多个系数，调整方法更加方便和全面。本发明可以用于图像编码和视频编码相关的领域中。Compared with the background technology, the present invention has beneficial effects: higher precision can be obtained with lower implementation complexity, and the implementation complexity can be controlled more conveniently. The coefficients of the transformation matrix adopted by it are closer to the coefficients of the theoretical discrete cosine transform matrix, and therefore closer to the result of the theoretical discrete cosine transform, and the accuracy is higher than that of the prior art with considerable implementation complexity. At the same time, in the prior art, multiple coefficients need to be adjusted when adjusting the complexity and precision of the implementation, but the present invention allows one, two or more coefficients to be adjusted, and the adjustment method is more convenient and comprehensive. The present invention can be used in fields related to image coding and video coding.

附图说明Description of drawings

图1是本发明实施例1、2、3、4、5、6的正变换蝶形图；Fig. 1 is the forward transformation butterfly diagram of embodiment 1, 2, 3, 4, 5, 6 of the present invention;

图2是本发明实施例1、2、3、4、5、6的反变换蝶形图；Fig. 2 is the inverse transformation butterfly diagram of embodiment 1, 2, 3, 4, 5, 6 of the present invention;

图3是本发明实施例7的正变换装置；Fig. 3 is the forward transformation device of embodiment 7 of the present invention;

图4是本发明实施例7的反变换装置；Fig. 4 is the reverse conversion device of embodiment 7 of the present invention;

图5是本发明实施例8的正变换装置；Fig. 5 is the forward conversion device of embodiment 8 of the present invention;

图6是本发明实施例8的反变换装置。Fig. 6 is an inverse transformation device according to Embodiment 8 of the present invention.

具体实施方式Detailed ways

实施例1Example 1

采用的正变换蝶形图和反变换蝶形图如图1、图2所示。(实际实现时可以根据需要采用不同的蝶形结构和实现方法。)图1中x0，x1，x2，x3，x4，x5，x6，x7为一维正变换输入数据，y0，y1，y2，y3，y4，y5，y6，y7为一维正变换输出数据，SCALE_f为选取正变换矩阵时确定的参数，e₀，e₁，e₂，d₀，d₁，d₂，d₃，d₄，d₅，d₆，d₇，d₈为根据所选取的正变换矩阵确定的参数，r为正变换后四舍五入参数；图2中y0，y1，y2，y3，y4，y5，y6，y7为一维反变换输入数据，x0，x1，x2，x3，x4，x5，x6，x7为一维反变换输出数据，SCALE_i为选取反变换矩阵时确定的参数，e₀，e₁，e₂，d₀，d₁，d₂，d₃，d₄，d₅，d₆，d₇，d₈为根据所选取的反变换矩阵确定的参数，r为反变换后四舍五入参数。The forward transformation butterfly diagram and the inverse transformation butterfly diagram are shown in Figure 1 and Figure 2. (During actual implementation, different butterfly structures and implementation methods can be adopted as required.) x0, x1, x2, x3, x4, x5, x6, and x7 in Fig. 1 are one-dimensional forward transformation input data, y0, y1, y2, y3, y4, y5, y6, y7 are one-dimensional forward transformation output data, SCALE _f is the parameter determined when selecting the forward transformation matrix, e ₀ , e ₁ , e ₂ , d ₀ , d ₁ , d ₂ , d ₃ , d ₄ , d ₅ , d ₆ , d ₇ , d ₈ are parameters determined according to the selected forward transformation matrix, and r is the rounding parameter after forward transformation; y0, y1, y2, y3, y4, y5, y6 in Figure 2 , y7 is the input data of one-dimensional inverse transformation, x0, x1, x2, x3, x4, x5, x6, x7 are the output data of one-dimensional inverse transformation, SCALE _i is the parameter determined when selecting the inverse transformation matrix, e ₀ , e ₁ , e ₂ , d ₀ , d ₁ , d ₂ , d ₃ , d ₄ , d ₅ , d ₆ , d ₇ , d ₈ are parameters determined according to the selected inverse transformation matrix, and r is the rounding parameter after inverse transformation.

采用的正变换矩阵为：The positive transformation matrix used is:

${FDCT FDCT}_{fp fp} = = [\begin{matrix} 81928192 & 81928192 & 81928192 & 81928192 & 81928192 & 81928192 & 81928192 & 81928192 \\ 1136311363 & 96339633 & 64366436 & 22602260 & - - 22602260 & - - 64366436 & - - 96339633 & - - 1136311363 \\ 1070310703 & 44334433 & - - 44334433 & - - 1070310703 & - - 1070310703 & - - 44334433 & 44334433 & 1070310703 \\ 96339633 & - - 22602260 & - - 1136311363 & - - 64366436 & 64366436 & 1136311363 & 22602260 & - - 96339633 \\ 81928192 & - - 81928192 & - - 81928192 & 81928192 & 81928192 & - - 81928192 & - - 81928192 & 81928192 \\ 64366436 & - - 1136311363 & 22602260 & 96339633 & - - 96339633 & - - 22602260 & 1136311363 & - - 64366436 \\ 44334433 & - - 1070310703 & 1070310703 & - - 44334433 & - - 44334433 & 1070310703 & - - 1070310703 & 44334433 \\ 22602260 & - - 64366436 & 96339633 & - - 1136311363 & 1136311363 & - - 96339633 & 64366436 & - - 22602260 \end{matrix}] / / 81928192$

正变换过程如下：在进行正变换过程前，对输入数据先左移6位，一维变换后不移位，二维变换后右移9位：The forward transformation process is as follows: before the forward transformation process, the input data is first shifted to the left by 6 bits, not shifted after the one-dimensional transformation, and shifted to the right by 9 bits after the two-dimensional transformation:

FS0＝6，FS1＝0，FS2＝9 FS0＝6, FS1＝0, FS2＝9

采用的反变换矩阵为正变换矩阵的转置：The inverse transformation matrix used is the transpose of the forward transformation matrix:

IDCT_fp＝(FDCT_fp)^T IDCT _fp = (FDCT _fp ) ^T

反变换过程如下：在进行反变换过程前，对输入数据先左移10位，一维变换后不移位，二维变换后右移13位：The inverse transformation process is as follows: Before the inverse transformation process, the input data is first shifted to the left by 10 bits, not shifted after one-dimensional transformation, and shifted to the right by 13 bits after two-dimensional transformation:

IS0＝10，IS1＝0，IS2＝13IS0＝10, IS1＝0, IS2＝13

图1、图2中的参数由下式计算得到：The parameters in Figure 1 and Figure 2 are calculated by the following formula:

e₀＝(-E-F)/2^SCALE e ₀ =(-EF)/2 ^SCALE

e₁＝F/2^SCALE e ₁ =F/2 ^SCALE

e₂＝(E-F)/2^SCALE e ₂ =(EF)/2 ^SCALE

d₀＝(-A+B+C-D)/2^SCALE d ₀ ＝(-A+B+CD)/2 ^SCALE

d₁＝(A+B-C+D)/2^SCALE d ₁ =(A+B-C+D)/2 ^SCALE

d₂＝(A+B+C-D)/2^SCALE d ₂ =(A+B+CD)/2 ^SCALE

d₃＝(A+B-C-D)/2^SCALE d ₃ =(A+BCD)/2 ^SCALE

d₄＝(-B+D)/2^SCALE d ₄ ＝(-B+D)/2 ^SCALE

d₅＝(-A-B)/2^SCALE d ₅ =(-AB)/2 ^SCALE

d₆＝(-B-C)/2^SCALE d ₆ =(-BC)/2 ^SCALE

d₇＝(-B+C)/2^SCALE d ₇ =(-B+C)/2 ^SCALE

d₈＝B/2^SCALE d ₈ =B/2 ^SCALE

具体参数如下：The specific parameters are as follows:

SCALE_f＝SCALE_i＝13SCALE _f =SCALE _i =13

e₀＝-15136/8192 e₁＝4433/8192 e₂＝6270/8192e ₀ =-15136/8192 e ₁ =4433/8192 e ₂ =6270/8192

d₀＝2446/8192 d₁＝16820/8192 d₂＝25172/8192d ₀ =2446/8192 d ₁ =16820/8192 d ₂ =25172/8192

d₃＝12300/8192 d₄＝-7373/8192 d₅＝-20996/8192d ₃ =12300/8192 d ₄ =-7373/8192 d ₅ =-20996/8192

d₆＝-16069/8192 d₇＝-3197/8192 d₈＝9633/8192d ₆ =-16069/8192 d ₇ =-3197/8192 d ₈ =9633/8192

实施例2Example 2

采用的正变换矩阵为：The positive transformation matrix used is:

FS0＝6，FS1＝0，FS2＝9 FS0＝6, FS1＝0, FS2＝9

IDCT_fp＝(FDCT_fp)^T IDCT _fp = (FDCT _fp ) ^T

反变换过程如下：在进行反变换过程前，对输入数据先左移8位，一维变换后不移位，二维变换后右移11位：The inverse transformation process is as follows: Before the inverse transformation process, the input data is first shifted to the left by 8 bits, not shifted after the one-dimensional transformation, and shifted to the right by 11 bits after the two-dimensional transformation:

IS0＝8，IS1＝0，IS2＝11IS0＝8, IS1＝0, IS2＝11

e₀＝(-E-F)/2^SCALE e ₀ =(-EF)/2 ^SCALE

e₁＝F/2^SCALE e ₁ =F/2 ^SCALE

e₂＝(E-F)/2^SCALE e ₂ =(EF)/2 ^SCALE

d₀＝(-A+B+C-D)/2^SCALE d ₀ ＝(-A+B+CD)/2 ^SCALE

d₁＝(A+B-C+D)/2^SCALE d ₁ =(A+B-C+D)/2 ^SCALE

d₂＝(A+B+C-D)/2^SCALE d ₂ =(A+B+CD)/2 ^SCALE

d₃＝(A+B-C-D)/2^SCALE d ₃ =(A+BCD)/2 ^SCALE

d₄＝(-B+D)/2^SCALE d ₄ ＝(-B+D)/2 ^SCALE

d₅＝(-A-B)/2^SCALE d ₅ =(-AB)/2 ^SCALE

d₆＝(-B-C)/2^SCALE d ₆ =(-BC)/2 ^SCALE

d₇＝(-B+C)/2^SCALE d ₇ =(-B+C)/2 ^SCALE

d₈＝B/2^SCALE d ₈ =B/2 ^SCALE

具体参数如下：The specific parameters are as follows:

SCALE_f＝SCALE_i＝13SCALE _f =SCALE _i =13

实施例3Example 3

采用的正变换矩阵为：The positive transformation matrix used is:

${FDCT FDCT}_{tp tp} = = [\begin{matrix} 20482048 & 20482048 & 20482048 & 20482048 & 20482048 & 20482048 & 20482048 & 20482048 \\ 28412841 & 24082408 & 16091609 & 565565 & - - 565565 & - - 16091609 & - - 24082408 & - - 28412841 \\ 26762676 & 11081108 & - - 11081108 & - - 26762676 & - - 26762676 & - - 11081108 & 11081108 & 26762676 \\ 24082408 & - - 565565 & - - 28412841 & - - 16091609 & 16091609 & 28412841 & 565565 & - - 24812481 \\ 20482048 & - - 20482048 & - - 20482048 & 20482048 & 20482048 & - - 20482048 & - - 20482048 & 20482048 \\ 16091609 & - - 28412841 & 565565 & 24082408 & - - 24082408 & - - 565565 & 28412841 & - - 16091609 \\ 11081108 & - - 26762676 & 26762676 & - - 11081108 & - - 11081108 & 26762676 & - - 26762676 & 11081108 \\ 565565 & - - 16091609 & 24082408 & - - 28412841 & 28412841 & - - 24082408 & 16091609 & - - 565565 \end{matrix}] / / 20482048$

正变换过程如下：在进行正变换过程前，对输入数据先左移5位，一维变换后不移位，二维变换后右移8位：The forward transformation process is as follows: Before the forward transformation process, the input data is first shifted to the left by 5 bits, not shifted after the one-dimensional transformation, and shifted to the right by 8 bits after the two-dimensional transformation:

FS0＝5，FS1＝0，FS2＝8 FS0＝5, FS1＝0, FS2＝8

IDCT_fp＝(FDCT_fp)^T IDCT _fp = (FDCT _fp ) ^T

IS0＝8，IS1＝0，IS2＝11IS0＝8, IS1＝0, IS2＝11

e₀＝(-E-F)/2^SCALE e ₀ =(-EF)/2 ^SCALE

e₁＝F/2^SCALE e ₁ =F/2 ^SCALE

e₂＝(E-F)/2^SCALE e ₂ =(EF)/2 ^SCALE

d₀＝(-A+B+C-D)/2^SCALE d ₀ ＝(-A+B+CD)/2 ^SCALE

d₁＝(A+B-C+D)/2^SCALE d ₁ =(A+B-C+D)/2 ^SCALE

d₂＝(A+B+C-D)/2^SCALE d ₂ =(A+B+CD)/2 ^SCALE

d₃＝(A+B-C-D)/2^SCALE d ₃ =(A+BCD)/2 ^SCALE

d₄＝(-B+D)/2^SCALE d ₄ ＝(-B+D)/2 ^SCALE

d₅＝(-A-B)/2^SCALE d ₅ =(-AB)/2 ^SCALE

d₆＝(-B-C)/2^SCALE d ₆ =(-BC)/2 ^SCALE

d₇＝(-B+C)/2^SCALE d ₇ =(-B+C)/2 ^SCALE

d₈＝B/2^SCALE d ₈ =B/2 ^SCALE

具体参数如下：The specific parameters are as follows:

SCALE_f＝SCALE_i＝11SCALE _f =SCALE _i =11

e₀＝-3784/2048 e₁＝1108/2048 e₂＝1568/2048e ₀ =-3784/2048 e ₁ =1108/2048 e ₂ =1568/2048

d₀＝611/2048 d₁＝4205/2048 d₂＝6293/2048d ₀ =611/2048 d ₁ =4205/2048 d ₂ =6293/2048

d₃＝3075/2048 d₄＝-1843/2048 d₅＝-5249/2048d ₃ =3075/2048 d ₄ =-1843/2048 d ₅ =-5249/2048

d₆＝-4017/2048 d₇＝-799/2048 d₈＝2408/2048d ₆ =-4017/2048 d ₇ =-799/2048 d ₈ =2408/2048

实施例4Example 4

采用的正变换矩阵为：The positive transformation matrix used is:

${FDCT FDCT}_{fp fp} = = [\begin{matrix} 1638416384 & 1638416384 & 1638416384 & 1638416384 & 1638416384 & 1638416384 & 1638416384 & 1638416384 \\ 2272522725 & 1926619266 & 1287312873 & 45204520 & - - 45204520 & - - 1287312873 & - - 1926619266 & - - 2272522725 \\ 2140721407 & 88678867 & - - 88678867 & - - 2140721407 & - - 2140721407 & - - 88678867 & 88678867 & 2140721407 \\ 1926619266 & - - 45204520 & - - 2272522725 & - - 1287312873 & 1287312873 & 2272522725 & 45204520 & - - 1926619266 \\ 1638416384 & - - 1638416384 & - - 1638416384 & 1638416384 & 1638416384 & - - 1638416384 & - - 1638416384 & 1638416384 \\ 1287312873 & - - 2272522725 & 45204520 & 1926619266 & - - 1926619266 & - - 45204520 & 2272522725 & - - 1287312873 \\ 88678867 & - - 2140721407 & 2140721407 & - - 88678867 & - - 88678867 & 2140721407 & - - 2140721407 & 88678867 \\ 45204520 & - - 1287312873 & 1926619266 & - - 2272522725 & 2272522725 & - - 1926619266 & 1287312873 & - - 45204520 \end{matrix}] / / 1638416384$

FS0＝6，FS1＝0，FS2＝9 FS0＝6, FS1＝0, FS2＝9

IDCT_fp＝(FDCT_fp)^T IDCT _fp = (FDCT _fp ) ^T

反变换过程如下：在进行反变换过程前，对输入数据先左移12位，一维变换后不移位，二维变换后右移15位：The inverse transformation process is as follows: Before the inverse transformation process, the input data is first shifted to the left by 12 bits, not shifted after the one-dimensional transformation, and shifted to the right by 15 bits after the two-dimensional transformation:

IS0＝12，IS1＝0，IS2＝15IS0＝12, IS1＝0, IS2＝15

e₀＝(-E-F)/2^SCALE e ₀ =(-EF)/2 ^SCALE

e₁＝F/2^SCALE e ₁ =F/2 ^SCALE

e₂＝(E-F)/2^SCALE e ₂ =(EF)/2 ^SCALE

d₀＝(-A+B+C-D)/2^SCALE d ₀ ＝(-A+B+CD)/2 ^SCALE

d₁＝(A+B-C+D)/2^SCALE d ₁ =(A+B-C+D)/2 ^SCALE

d₂＝(A+B+C-D)/2^SCALE d ₂ =(A+B+CD)/2 ^SCALE

d₃＝(A+B-C-D)/2^SCALE d ₃ =(A+BCD)/2 ^SCALE

d₄＝(-B+D)/2^SCALE d ₄ ＝(-B+D)/2 ^SCALE

d₅＝(-A-B)/2^SCALE d ₅ =(-AB)/2 ^SCALE

d₆＝(-B-C)/2^SCALE d ₆ =(-BC)/2 ^SCALE

d₇＝(-B+C)/2^SCALE d ₇ =(-B+C)/2 ^SCALE

d₈＝B/2^SCALE d ₈ =B/2 ^SCALE

具体参数如下：The specific parameters are as follows:

SCALE_f＝SCALE_i＝14SCALE _f =SCALE _i =14

e₀＝-30274/16384 e₁＝8867/16384 e₂＝12540/16384e ₀ =-30274/16384 e ₁ =8867/16384 e ₂ =12540/16384

d₀＝4894/16384 d₁＝33638/16384 d₂＝50344/16384d ₀ =4894/16384 d ₁ =33638/16384 d ₂ =50344/16384

d₃＝24598/16384 d₄＝-14746/16384 d₅＝-41991/16384d ₃ =24598/16384 d ₄ =-14746/16384 d ₅ =-41991/16384

d₆＝-32139/16384 d₇＝-6393/16384 d₈＝19266/16384d ₆ =-32139/16384 d ₇ =-6393/16384 d ₈ =19266/16384

实施例5Example 5

采用的正变换矩阵为：The positive transformation matrix used is:

${FDCT FDCT}_{fp fp} = = [\begin{matrix} 81928192 & 81928192 & 81928192 & 81928192 & 81928192 & 81928192 & 81928192 & 81928192 \\ 1136311363 & 96339633 & 64366436 & 22612261 & - - 22612261 & - - 64376437 & - - 96339633 & - - 1136311363 \\ 1070410704 & 44334433 & - - 44334433 & - - 1070410704 & - - 1070410704 & - - 44334433 & 44334433 & 1070410704 \\ 96339633 & - - 22612261 & - - 1136311363 & - - 64376437 & 64376437 & 1136311363 & 22612261 & - - 96339633 \\ 81928192 & - - 81928192 & - - 81928192 & 81928192 & 81928192 & - - 81928192 & - - 81928192 & 81928192 \\ 64376437 & - - 1136311363 & 22612261 & 96339633 & - - 96339633 & - - 22612261 & 1136311363 & - - 64376437 \\ 44334433 & - - 1070410704 & 1070410704 & - - 44334433 & - - 44334433 & 1070410704 & - - 1070410704 & 44334433 \\ 22612261 & - - 64376437 & 96339633 & - - 1136311363 & 1136311363 & - - 96339633 & 64376437 & - - 22612261 \end{matrix}] / / 81928192$

FS0＝6，FS1＝0，FS2＝9 FS0＝6, FS1＝0, FS2＝9

IDCT_fp＝(FDCT_fp)^T IDCT _fp = (FDCT _fp ) ^T

IS0＝10，IS1＝0，IS2＝13IS0＝10, IS1＝0, IS2＝13

e₀＝(-E-F)/2^SCALE e ₀ =(-EF)/2 ^SCALE

e₁＝F/2^SCALE e ₁ =F/2 ^SCALE

e₂＝(E-F)/2^SCALE e ₂ =(EF)/2 ^SCALE

d₀＝(-A+B+C-D)/2^SCALE d ₀ ＝(-A+B+CD)/2 ^SCALE

d₁＝(A+B-C+D)/2^SCALE d ₁ =(A+B-C+D)/2 ^SCALE

d₂＝(A+B+C-D)/2^SCALE d ₂ =(A+B+CD)/2 ^SCALE

d₃＝(A+B-C-D)/2^SCALE d ₃ =(A+BCD)/2 ^SCALE

d₄＝(-B+D)/2^SCALE d ₄ ＝(-B+D)/2 ^SCALE

d₅＝(-A-B)/2^SCALE d ₅ =(-AB)/2 ^SCALE

d₆＝(-B-C)/2^SCALE d ₆ =(-BC)/2 ^SCALE

d₇＝(-B+C)/2^SCALE d ₇ =(-B+C)/2 ^SCALE

d₈＝B/2^SCALE d ₈ =B/2 ^SCALE

具体参数如下：The specific parameters are as follows:

SCALE_f＝SCALE_i＝13SCALE _f =SCALE _i =13

e₀＝-15137/8192 e₁＝4433/8192 e₂＝6271/8192e ₀ =-15137/8192 e ₁ =4433/8192 e ₂ =6271/8192

d₃＝12298/8192 d₄＝-7372/8192 d₅＝-20996/8192d ₃ =12298/8192 d ₄ =-7372/8192 d ₅ =-20996/8192

d₆＝-16070/8192 d₇＝-3196/8192 d₈＝9633/8192d ₆ =-16070/8192 d ₇ =-3196/8192 d ₈ =9633/8192

实施例6Example 6

采用的正变换矩阵为：The positive transformation matrix used is:

FS0＝6，FS1＝0，FS2＝9 FS0＝6, FS1＝0, FS2＝9

图1中的参数由下式计算得到：The parameters in Figure 1 are calculated by the following formula:

${e e}_{00} = = (({- - E E.}_{f f} - - {F f}_{f f})) / / 22^{{SCALE SCALE}_{f f}}$

${e e}_{11} = = {F f}_{f f} / / 22^{{SCALE SCALE}_{f f}}$

${e e}_{22} = = {(({E E.}_{f f} - - {F f}_{f f})) / / 22}^{{SCALE SCALE}_{f f}}$

${d d}_{00} = = (({- - A A}_{f f} + + {B B}_{f f} + + {C C}_{f f} - - {D D.}_{f f})) / / 22^{{SCALE SCALE}_{f f}}$

${d d}_{11} = = (({A A}_{f f} + + {B B}_{f f} - - {C C}_{f f} + + {D D.}_{f f})) / / 22^{{SCALE SCALE}_{f f}}$

${d d}_{22} = = (({A A}_{f f} + + {B B}_{f f} + + {C C}_{f f} - - {D D.}_{f f})) / / 22^{{SCALE SCALE}_{f f}}$

${d d}_{33} = = (({A A}_{f f} + + {B B}_{f f} - - {C C}_{f f} - - {D D.}_{f f})) / / 22^{{SCALE SCALE}_{f f}}$

${d d}_{44} = = (({- - B B}_{f f} + + {D D.}_{f f})) / / 22^{{SCALE SCALE}_{f f}}$

${d d}_{55} = = (({- - A A}_{f f} - - {B B}_{f f})) / / 22^{{SCALE SCALE}_{f f}}$

${d d}_{66} = = (({- - B B}_{f f} - - {C C}_{f f})) / / 22^{{SCALE SCALE}_{f f}}$

${d d}_{77} = = (({- - B B}_{f f} + + {D D.}_{f f})) / / 22^{{SCALE SCALE}_{f f}}$

${d d}_{88} = = {B B}_{f f} / / 22^{{SCALE SCALE}_{f f}}$

具体参数如下：The specific parameters are as follows:

SCALE_f＝13SCALE _f = 13

采用的反变换矩阵为：The inverse transformation matrix used is:

反变换过程如下：在进行反变换过程前，对输入数据先左移12位，一维变换后不移位，二维变换后右移15位：The inverse transformation process is as follows: Before the inverse transformation process, the input data is first shifted to the left by 12 bits, not shifted after one-dimensional transformation, and shifted to the right by 15 bits after two-dimensional transformation:

IS0＝12，IS1＝0，IS2＝15IS0＝12, IS1＝0, IS2＝15

图2中的参数由下式计算得到：The parameters in Figure 2 are calculated by the following formula:

${e e}_{00} = = (({- - E E.}_{i i} - - {F f}_{i i})) / / 22^{{SCALE SCALE}_{i i}}$

${e e}_{11} = = {F f}_{i i} / / 22^{{SCALE SCALE}_{i i}}$

${e e}_{22} = = {(({E E.}_{i i} - - {F f}_{i i})) / / 22}^{{SCALE SCALE}_{i i}}$

${d d}_{00} = = (({- - A A}_{i i} + + {B B}_{i i} + + {C C}_{i i} - - {D D.}_{i i})) / / 22^{{SCALE SCALE}_{i i}}$

${d d}_{11} = = (({A A}_{i i} + + {B B}_{i i} - - {C C}_{i i} + + {D D.}_{i i})) / / 22^{{SCALE SCALE}_{i i}}$

${d d}_{22} = = (({A A}_{i i} + + {B B}_{i i} + + {C C}_{i i} - - {D D.}_{i i})) / / 22^{{SCALE SCALE}_{i i}}$

${d d}_{33} = = (({A A}_{i i} + + {B B}_{i i} - - {C C}_{i i} - - {D D.}_{i i})) / / 22^{{SCALE SCALE}_{i i}}$

${d d}_{44} = = (({- - B B}_{i i} + + {D D.}_{i i})) / / 22^{{SCALE SCALE}_{i i}}$

${d d}_{55} = = (({- - A A}_{i i} - - {B B}_{i i})) / / 22^{{SCALE SCALE}_{i i}}$

${d d}_{66} = = (({- - B B}_{i i} - - {C C}_{i i})) / / 22^{{SCALE SCALE}_{i i}}$

${d d}_{77} = = (({- - B B}_{i i} + + {D D.}_{i i})) / / 22^{{SCALE SCALE}_{i i}}$

${d d}_{88} = = {B B}_{i i} / / 22^{{SCALE SCALE}_{i i}}$

具体参数如下：The specific parameters are as follows:

SCALE_i＝14SCALE _i = 14

实施例7Example 7

一种运用于图像编码和视频编码的离散余弦变换的装置，它包括正变换装置(图3)和反变换装置(图4)两大部分：A device for discrete cosine transform applied to image coding and video coding, which includes two parts: a forward transform device (Fig. 3) and an inverse transform device (Fig. 4):

正变换装置包括预移位装置，第一维正变换装置，第一维正变换后移位装置，第二维正变换装置，第二维正变换后移位装置；预移位装置的输入端与变换前的输入数据相连，预移位装置的输出端和第一维正变换装置的输入端相连，第一维正变换装置的输出端和第一维正变换后移位装置的输入端相连，第一维正变换后移位装置的输出端和第二维正变换装置输入端相连，第二维正变换装置输出端和第二维正变换后移位装置输入端相连，第二维正变换后移位装置输出端和变换输出数据相连；The forward transform device comprises a pre-shift device, a first-dimensional forward transform device, a shift device after the first-dimensional forward transform, a second-dimensional forward transform device, and a shift device after the second-dimensional forward transform; the input terminal of the pre-shift device It is connected with the input data before transformation, the output end of the pre-shift device is connected with the input end of the first-dimensional forward transform device, and the output end of the first-dimensional forward transform device is connected with the input end of the shift device after the first-dimensional forward transform , the output end of the shifting device after the first-dimensional forward transformation is connected to the input end of the second-dimensional forward transforming device, the output end of the second-dimensional forward transforming device is connected to the input end of the shifting device after the second-dimensional forward transformation, and the second-dimensional forward transforming device The output end of the shifting device after transformation is connected with the transformed output data;

变换前输入数据首先经过预移位装置进行移位，其输出送到第一维正(反)变换装置进行变换，其输出送到第一维正(反)变换后移位装置进行移位，其输出送到第二维正(反)变换装置进行变换，其输出送到第二维正(反)变换后移位装置进行移位，其输出为变换后输出数据。Before the transformation, the input data is first shifted by the pre-shift device, and its output is sent to the first-dimensional forward (reverse) transformation device for transformation, and its output is sent to the first-dimensional forward (reverse) transformation and then shifted by the shifting device. Its output is sent to the second-dimensional forward (reverse) transformation device for transformation, and its output is sent to the second-dimensional forward (reverse) transformation shift device for shifting, and its output is the transformed output data.

第一维正(反)变换装置和第二维正(反)变换装置为图1、图2所示的正(反)变换蝶形结构。The first-dimensional forward (reverse) transformation device and the second-dimensional forward (reverse) transformation device are forward (reverse) transformation butterfly structures shown in FIG. 1 and FIG. 2 .

采用的正变换矩阵为：The positive transformation matrix used is:

正变换过程如下：在进行正变换过程前，预移位装置对输入数据先左移6位，第一维正变换后移位装置对一维变换后的数据不移位，第二维正变换后移位装置对二维变换后的数据右移9位：The forward transformation process is as follows: before the forward transformation process, the pre-shift device first shifts the input data by 6 bits to the left, after the first-dimensional forward transformation, the shift device does not shift the data after the one-dimensional transformation, and the second-dimensional forward transformation The rear shift device shifts the two-dimensionally transformed data to the right by 9 bits:

FS0＝6，FS1＝0，FS2＝9 FS0＝6, FS1＝0, FS2＝9

IDCT_fp＝(FDCT_fp)^T IDCT _fp = (FDCT _fp ) ^T

反变换过程如下：在进行反变换过程前，预移位装置对输入数据先左移10位，第一维反变换后移位装置对一维变换后的数据不移位，第二维反变换后移位装置对二维变换后的数据右移13位：The inverse transformation process is as follows: before the inverse transformation process, the pre-shift device first shifts the input data by 10 bits to the left, the shift device after the first-dimensional inverse transformation does not shift the data after the one-dimensional transformation, and the second-dimensional inverse transformation The post-shift device shifts the two-dimensionally transformed data to the right by 13 bits:

IS0＝10，IS1＝0，IS2＝13IS0＝10, IS1＝0, IS2＝13

e₀＝(-E-F)/2^SCALE e ₀ =(-EF)/2 ^SCALE

e₁＝F/2^SCALE e ₁ =F/2 ^SCALE

e₂＝(E-F)/2^SCALE e ₂ =(EF)/2 ^SCALE

d₀＝(-A+B+C-D)/2^SCALE d ₀ ＝(-A+B+CD)/2 ^SCALE

d₁＝(A+B-C+D)/2^SCALE d ₁ =(A+B-C+D)/2 ^SCALE

d₂＝(A+B+C-D)/2^SCALE d ₂ =(A+B+CD)/2 ^SCALE

d₃＝(A+B-C-D)/2^SCALE d ₃ =(A+BCD)/2 ^SCALE

d₄＝(-B+D)/2^SCALE d ₄ ＝(-B+D)/2 ^SCALE

d₅＝(-A-B)/2^SCALE d ₅ =(-AB)/2 ^SCALE

d₆＝(-B-C)/2^SCALE d ₆ =(-BC)/2 ^SCALE

d₇＝(-B+C)/2^SCALE d ₇ =(-B+C)/2 ^SCALE

d₈＝B/2^SCALE d ₈ =B/2 ^SCALE

具体参数如下：The specific parameters are as follows:

SCALE_f＝SCALE_i＝13SCALE _f =SCALE _i =13

实施例8Example 8

一种运用于图像编码和视频编码的离散余弦变换的装置，它包括正变换装置(图5)和反变换(图6)装置两大部分：A device for discrete cosine transform applied to image coding and video coding, which includes two parts: a forward transform device (Fig. 5) and an inverse transform (Fig. 6) device:

正变换装置包括预移位装置，第一维正变换装置，第一维正变换后移位装置，第二维正变换装置，第二维正变换后移位装置，正变换精度和复杂度控制器；预移位装置的输入端与变换前的输入数据相连，预移位装置的输出端和第一维正变换装置的输入端相连，第一维正变换装置的输出端和第一维正变换后移位装置的输入端相连，第一维正变换后移位装置的输出端和第二维正变换装置输入端相连，第二维正变换装置输出端和第二维正变换后移位装置输入端相连，第二维正变换后移位装置输出端和变换输出数据相连，正变换精度和复杂度控制器通过开关和预移位装置，第一维正变换装置，第一维正变换后移位装置，第二维正变换装置，第二维正变换后移位装置相连；The forward transform device includes a pre-shift device, a first-dimensional forward transform device, a shift device after the first-dimensional forward transform, a second-dimensional forward transform device, a shift device after the second-dimensional forward transform, and forward transform accuracy and complexity control device; the input end of the pre-shift device is connected to the input data before transformation, the output end of the pre-shift device is connected to the input end of the first-dimensional forward transform device, and the output end of the first-dimensional forward transform device is connected to the first-dimensional positive transform device The input end of the shifting device after transformation is connected, the output end of the shifting device after the first-dimensional forward transformation is connected with the input end of the second-dimensional forward transforming device, and the output end of the second-dimensional forward transforming device is connected to the shifting device after the second-dimensional forward transforming The input terminal of the device is connected, the output terminal of the shifting device after the second-dimensional forward transformation is connected with the transformed output data, the precision and complexity controller of the forward transformation passes through the switch and the pre-shifting device, the first-dimensional forward transformation device, The rear shifting device, the second-dimensional forward transforming device, and the second-dimensional forward transforming rear shifting device are connected;

反变换装置包括预移位装置，第一维反变换装置，第一维反变换后移位装置，第二维反变换装置，第二维反变换后移位装置；预移位装置的输入端与变换前的输入数据相连，预移位装置的输出端和第一维反变换装置的输入端相连，第一维反变换装置的输出端和第一维反变换后移位装置的输入端相连，第一维反变换后移位装置的输出端和第二维反变换装置输入端相连，第二维反变换装置输出端和第二维反变换后移位装置输入端相连，第二维反变换后移位装置输出端和变换输出数据相连，反变换精度和复杂度控制器通过开关和预移位装置，第一维反变换装置，第一维反变换后移位装置，第二维反变换装置，第二维反变换后移位装置相连。The inverse transformation device comprises a pre-shift device, a first-dimensional inverse transformation device, a shift device after the first-dimensional inverse transformation, a second-dimensional inverse transformation device, and a shift device after the second-dimensional inverse transformation; the input terminal of the pre-shift device It is connected with the input data before transformation, the output terminal of the pre-shifting device is connected with the input terminal of the first-dimensional inverse transformation device, and the output terminal of the first-dimensional inverse transformation device is connected with the input terminal of the shifting device after the first-dimensional inverse transformation , the output end of the shifting device after the first-dimensional inverse transformation is connected to the input end of the second-dimensional inverse transformation device, the output end of the second-dimensional inverse transformation device is connected to the input end of the shifting device after the second-dimensional inverse transformation, and the second-dimensional inversion The output end of the shifting device after transformation is connected with the transformation output data, the inverse transformation accuracy and complexity controller passes through the switch and the pre-shifting device, the first-dimensional inverse transformation device, the first-dimensional inverse transformation post-shifting device, and the second-dimensional inverse The transformation device is connected with the displacement device after the second dimension inverse transformation.

变换前输入数据首先经过预移位装置进行移位，其输出送到第一维正(反)变换装置进行变换，其输出送到第一维正(反)变换后移位装置进行移位，其输出送到第二维正(反)变换装置进行变换，其输出送到第二维正(反)变换后移位装置进行移位，其输出为变换后输出数据。正(反)变换精度和复杂度控制器通过开关控制和调整预移位装置，第一维正(反)变换装置，第一维正(反)变换后移位装置，第二维正(反)变换装置，第二维正(反)变换后移位装置中的相关参数，从而达到不同的精度和不同的实现复杂度。Before the transformation, the input data is first shifted by the pre-shift device, and its output is sent to the first-dimensional forward (reverse) transformation device for transformation, and its output is sent to the first-dimensional forward (reverse) transformation and then shifted by the shifting device. Its output is sent to the second-dimensional forward (reverse) transformation device for transformation, and its output is sent to the second-dimensional forward (reverse) transformation shift device for shifting, and its output is the transformed output data. The precision and complexity controller of the forward (reverse) transformation controls and adjusts the pre-shift device through the switch, the first-dimensional forward (reverse) transformation device, the first-dimensional forward (reverse) transformation post-shift device, the second-dimensional forward (reverse) ) transformation device, the relevant parameters in the displacement device after the second-dimensional forward (inverse) transformation, so as to achieve different precision and different implementation complexity.

采用的正变换矩阵为：The positive transformation matrix used is:

正变换过程如下：在进行正变换过程前，预移位装置对输入数据先左移6位，第一维正变换后移位装置对一维变换后的数据不移位，第二维正变换后移位装置对二维变换后的数据右移9位：The forward transformation process is as follows: before the forward transformation process, the pre-shift device first shifts the input data by 6 bits to the left, after the first-dimensional forward transformation, the shifting device does not shift the data after the one-dimensional transformation, and the second-dimensional forward transformation The rear shift device shifts the two-dimensionally transformed data to the right by 9 bits:

FS0＝6，FS1＝0，FS2＝9 FS0＝6, FS1＝0, FS2＝9

IDCT_fp＝(FDCT_fp)^T IDCT _fp = (FDCT _fp ) ^T

IS0＝10，IS1＝0，IS2＝13IS0＝10, IS1＝0, IS2＝13

e₀＝(-E-F)/2^SCALE e ₀ =(-EF)/2 ^SCALE

e₁＝F/2^SCALE e ₁ =F/2 ^SCALE

e₂＝(E-F)/2^SCALE e ₂ =(EF)/2 ^SCALE

d₀＝(-A+B+C-D)/2^SCALE d ₀ ＝(-A+B+CD)/2 ^SCALE

d₁＝(A+B-C+D)/2^SCALE d ₁ =(A+B-C+D)/2 ^SCALE

d₂＝(A+B+C-D)/2^SCALE d ₂ =(A+B+CD)/2 ^SCALE

d₃＝(A+B-C-D)/2^SCALE d ₃ =(A+BCD)/2 ^SCALE

d₄＝(-B+D)/2^SCALE d ₄ ＝(-B+D)/2 ^SCALE

d₅＝(-A-B)/2^SCALE d ₅ =(-AB)/2 ^SCALE

d₆＝(-B-C)/2^SCALE d ₆ =(-BC)/2 ^SCALE

d₇＝(-B+C)/2^SCALE d ₇ =(-B+C)/2 ^SCALE

d₈＝B/2^SCALE d ₈ =B/2 ^SCALE

具体参数如下：The specific parameters are as follows:

SCALE_f＝SCALE_i＝13SCALE _f =SCALE _i =13

正变换精度和复杂度控制器通过控制第一维正变换装置、第二维正变换装置达到不同的精度和实现复杂度，采用的正变换矩阵调整为：The forward transformation accuracy and complexity controller achieves different precision and complexity by controlling the first-dimensional forward transformation device and the second-dimensional forward transformation device, and the adopted forward transformation matrix is adjusted to:

${FDCT FDCT}_{fpr fpr} = = [\begin{matrix} 1638416384 & 1638416384 & 1638416384 & 1638416384 & 1638416384 & 1638416384 & 1638416384 & 1638416384 \\ 2272522725 & 1926619266 & 1287312873 & 45204520 & - - 45204520 & - - 1287312873 & - - 1926619266 & - - 2272522725 \\ 2140721407 & 88678867 & - - 88678867 & - - 2140721407 & - - 2140721407 & - - 88678867 & 88678867 & 2140721407 \\ 1926619266 & - - 45204520 & - - 2272522725 & - - 1287312873 & 1287312873 & 2272522725 & 45204520 & - - 1926619266 \\ 1638416384 & - - 1638416384 & - - 1638416384 & 1638416384 & 1638416384 & - - 1638416384 & - - 1638416384 & 1638416384 \\ 1287312873 & - - 2272522725 & 45204520 & 1926619266 & - - 1926619266 & - - 45204520 & 2272522725 & - - 1287312873 \\ 88678867 & - - 2140721407 & 2140721407 & - - 88678867 & - - 88678867 & 2140721407 & - - 2140721407 & 88678867 \\ 45204520 & - - 1287312873 & 1926619266 & - - 2272522725 & 2272522725 & - - 1926619266 & 1287312873 & - - 45204520 \end{matrix}] / / 1638416384$

图1、图2中的调整后的参数由下式计算得到：The adjusted parameters in Figure 1 and Figure 2 are calculated by the following formula:

e₀＝(-E-F)/2^SCALE e ₀ =(-EF)/2 ^SCALE

e₁＝F/2^SCALE e ₁ =F/2 ^SCALE

e₂＝(E-F)/2^SCALE e ₂ =(EF)/2 ^SCALE

d₀＝(-A+B+C-D)/2^SCALE d ₀ ＝(-A+B+CD)/2 ^SCALE

d₁＝(A+B-C+D)/2^SCALE d ₁ =(A+B-C+D)/2 ^SCALE

d₂＝(A+B+C-D)/2^SCALE d ₂ =(A+B+CD)/2 ^SCALE

d₃＝(A+B-C-D)/2^SCALE d ₃ =(A+BCD)/2 ^SCALE

d₄＝(-B+D)/2^SCALE d ₄ ＝(-B+D)/2 ^SCALE

d₅＝(-A-B)/2^SCALE d ₅ =(-AB)/2 ^SCALE

d₆＝(-B-C)/2^SCALE d ₆ =(-BC)/2 ^SCALE

d₇＝(-B+C)/2^SCALE d ₇ =(-B+C)/2 ^SCALE

d₈＝B/2^SCALE d ₈ =B/2 ^SCALE

具体的调整后的参数如下：The specific adjusted parameters are as follows:

SCALE_f＝14SCALE _f = 14

反变换精度和复杂度控制器通过控制预移位装置，第一维反变换装置，第一维反变换后移位装置、第二维反变换装置和第二维反变换后移位装置达到不同的精度和实现复杂度，采用的反变换矩阵调整为：The inverse transformation accuracy and complexity controller achieves different The accuracy and implementation complexity of , the inverse transformation matrix used is adjusted to:

IDCT_fpr＝(FDCT_fpr)^T IDCT _fpr ＝(FDCT _fpr ) ^T

e₀＝(-E-F)/2^SCALE e ₀ =(-EF)/2 ^SCALE

e₁＝F/2^SCALE e ₁ =F/2 ^SCALE

e₂＝(E-F)/2^SCALE e ₂ =(EF)/2 ^SCALE

d₀＝(-A+B+C-D)/2^SCALE d ₀ ＝(-A+B+CD)/2 ^SCALE

d₁＝(A+B-C+D)/2^SCALE d ₁ =(A+B-C+D)/2 ^SCALE

d₂＝(A+B+C-D)/2^SCALE d ₂ =(A+B+CD)/2 ^SCALE

d₃＝(A+B-C-D)/2^SCALE d ₃ =(A+BCD)/2 ^SCALE

d₄＝(-B+D)/2^SCALE d ₄ ＝(-B+D)/2 ^SCALE

d₅＝(-A-B)/2^SCALE d ₅ =(-AB)/2 ^SCALE

d₆＝(-B-C)/2^SCALE d ₆ =(-BC)/2 ^SCALE

d₇＝(-B+C)/2^SCALE d ₇ =(-B+C)/2 ^SCALE

d₈＝B/2^SCALE d ₈ =B/2 ^SCALE

SCALE_f＝14SCALE _f = 14

预移位装置对输入数据调整为先左移12位，第一维正(反)变换后移位装置对一维变换后的数据不移位，第二维正(反)变换后移位装置对二维变换后的数据调整为右移15位：The pre-shift device adjusts the input data to shift left by 12 bits first, the shift device after the first-dimensional forward (reverse) transformation does not shift the data after one-dimensional transformation, and the shift device after the second-dimensional forward (reverse) transformation The data after two-dimensional transformation is adjusted to be shifted to the right by 15 bits:

IS0＝12，IS1＝0，IS2＝15IS0＝12, IS1＝0, IS2＝15

上述实施例用来解释说明本发明，而不是对本发明进行限制，在本发明的精神和权利要求的保护范围内，对本发明作出的任何修改和改变，都落入本发明的保护范围。The above-mentioned embodiments are used to illustrate the present invention, rather than to limit the present invention. Within the spirit of the present invention and the protection scope of the claims, any modification and change made to the present invention will fall into the protection scope of the present invention.

Claims

1, a kind of method that applies to the discrete cosine transform of image encoding and video coding is characterized in that: for direct transform, choose N * N direct transform matrix F DCT according to following formula _FpN:

{FDCT}_{fpN} = round (\sqrt{N} {g 2}^{{SCALE}_{f}} gFDCT) / 2^{{SCALE}_{f}};

Wherein FDCT is theoretical N * N forward discrete cosine transform matrix; SCALE _fBe preassigned nonnegative integer, be used to obtain N * N direct transform matrix; Round (g) is the common operation that rounds up; Adopt or adjust SCALE for direct transform _fReach different precision and different implementation complexity;

According to selected N * N direct transform matrix, carry out corresponding direct transform process:

The FS0 position that before direct transform, moves to left earlier, the FS1 position that after the one dimension direct transform, moves to right, the FS2 position moves to right after two-dimentional direct transform; FS0 wherein, FS1, FS2 are integer, represent not carry out shifting function when value is zero, represent to carry out the shifting function of the above direction when being worth for positive integer, are worth for negative integer and represent to carry out the shifting function opposite with above-mentioned direction; For direct transform, adopt or adjust FS0, FS1, among the FS2 one, two or three reach different precision and different implementation complexity.

2, according to the method for the discrete cosine transform that applies to image encoding and video coding described in the claim 1, it is characterized in that, adopt or adjust N * N direct transform matrix F DCT _FpNIn coefficient reach different precision and different implementation complexity, promptly use FDCT _FpNrReplace FDCT _FpN, satisfy:

| (FDCT _FpNr(i, j)-FDCT _FpN(i, j))/FDCT _FpN(i, j) |≤1%0≤i≤N-1,0≤j≤N-1; FDCT wherein _FpNr(i, j) and FDCT _FpN(i j) represents FDCT respectively _FpNAnd FDCT _FpNMeta is changed to (i, coefficient j).

3, according to the method for the discrete cosine transform that applies to image encoding and video coding described in claim 1 or 2, it is as follows that the method that it is characterized in that the said N of choosing * N direct transform matrix specifically is applied to 8 * 8 direct transform matrixes:

Adopt 8 * 8 following direct transform matrix F DCT _Fp8:

{FDCT}_{fp 8} = round (\sqrt{8} {g 2}^{{SCALE}_{f}} gFDCT) / 2^{{SCALE}_{f}} = [\begin{matrix} G_{f} & G_{f} & G_{f} & G_{f} & G_{f} & G_{f} & G_{f} & G_{f} \\ A_{f} & B_{f} & C_{f} & D_{f} & {- D}_{f} & {- C}_{f} & {- B}_{f} & - A_{f} \\ E_{f} & F_{f} & {- F}_{f} & - E_{f} & {- E}_{f} & {- F}_{f} & F_{f} & E_{f} \\ B_{f} & {- D}_{f} & - A_{f} & - C_{f} & C_{f} & A_{f} & D_{f} & - B_{f} \\ G_{f} & - G_{f} & - G_{f} & G_{f} & G_{f} & - G_{f} & G_{f} & G_{f} \\ C_{f} & {- A}_{f} & D_{f} & B_{f} & - B_{f} & - D_{f} & A_{f} & {- C}_{f} \\ F_{f} & {- E}_{f} & E_{f} & - F_{f} & - F_{f} & E_{f} & - E_{f} & F_{f} \\ D_{f} & - C_{f} & B_{f} & {- A}_{f} & A_{f} & - B_{f} & C_{f} & - D_{f} \end{matrix}] / 2^{{SCALE}_{f}}

Wherein FDCT is 8 * 8 theoretical forward discrete cosine transform matrixes; SCALE _fBe preassigned nonnegative integer, be used to obtain 8 * 8 direct transform matrixes; Round (g) is the common operation that rounds up;

A _f, B _f, C _f, D _f, E _f, F _f, G _fCoefficient in expression 8 * 8 direct transform matrixes, and be integer;

Especially, also comprise following four groups of direct transform matrix coefficients:

(1)A _f＝2841，B _f＝2408，C _f＝1609，D _f＝565，E _f＝2676，F _f＝1108，G _f＝2408，SCALE _f＝11；

(2)A _f＝5681，B _f＝4816，C _f＝3218，D _f＝1130，E _f＝5352，F _f＝2217，G _f＝4096，SCALE _f＝12；

(3)A _f＝11363，B _f＝9633，C _f＝6436，D _f＝2260，E _f＝10703，F _f＝4433，G _f＝8192，SCALE _f＝13；

(4)A _f＝22725，B _f＝19266，C _f＝12873，D _f＝4520，E _f＝21407，F _f＝8867，G _f＝16384，SCALE _f＝14。

4, a kind of method that applies to the discrete cosine transform of image encoding and video coding is characterized in that:

For inverse transformation, choose N * N inverse transformation matrix IDCT according to following two formulas _FpN:

{IDCT}_{fpN} = round (\sqrt{N} {g 2}^{{SCALE}_{i}} gIDCT) / 2^{S {CALE}_{i}};

Wherein IDCT is theoretical N * N inverse discrete cosine transform matrix; SCALE _iBe preassigned nonnegative integer, be used to obtain N * N inverse transformation matrix; Round (g) is the common operation that rounds up; Adopt or adjust SCALE for inverse transformation _iReach different precision and different implementation complexity;

According to selected N * N inverse transformation matrix, carry out corresponding inverse transformation process:

The IS0 position that before conversion, moves to left earlier, the IS1 position that behind one-dimensional transform, moves to right, the IS2 position moves to right behind two-dimensional transform; IS0 wherein, IS1, IS2 are integer, represent not carry out shifting function when value is zero, represent to carry out the shifting function of the above direction when being worth for positive integer, are worth for negative integer and represent to carry out the shifting function opposite with above-mentioned direction; For inverse transformation, adopt or adjust IS0, IS1, among the IS2 one, two or three reach different precision and different implementation complexity.

5, according to the method for the discrete cosine transform that applies to image encoding and video coding described in the claim 4, it is characterized in that, adopt or adjust N * N inverse transformation matrix IDCT _FpNIn coefficient reach different precision and different implementation complexity, promptly use IDCT _FpNrReplace IDCT _FpN, satisfy:

| (IDCT _FpNr(i, j)-IDCT _FpN(i, j))/IDCT _FpN(i, j) |≤1% 0≤i≤N-1,0≤j≤N-1; IDCT wherein _FpNr(i, j) and IDCT _FpN(i j) represents FDCT respectively _FpNAnd FDCT _FpNMeta is changed to (i, coefficient j).

6, according to the method for the discrete cosine transform that applies to image encoding and video coding described in claim 4 or 5, it is as follows that the method that it is characterized in that the said N of choosing * N inverse transformation matrix specifically is applied to 8 * 8 inverse transformation matrixes:

Adopt following 8 * 8 inverse transformation matrix IDCT _Fp8:

{IDCT}_{fp 8} - round (\sqrt{8} {g 2}^{{SCALE}_{i}} gIDCT) / 2^{{SCALE}_{i}} = [\begin{matrix} G_{i} & A_{i} & E_{i} & B_{i} & G_{i} & C_{i} & F_{i} & D_{i} \\ G_{i} & B_{i} & F_{i} & {- D}_{i} & {- G}_{i} & {- A}_{i} & {- E}_{i} & {- C}_{i} \\ G_{i} & C_{i} & {- F}_{i} & {- A}_{i} & {- G}_{i} & D_{i} & E_{i} & B_{i} \\ G_{i} & D_{i} & - E_{i} & {- C}_{i} & G_{i} & B_{i} & {- F}_{i} & {- A}_{i} \\ G_{i} & - D_{i} & - E_{i} & C_{i} & G_{i} & {- B}_{i} & {- F}_{i} & A_{i} \\ G_{i} & {- C}_{i} & {- F}_{i} & A_{i} & {- G}_{i} & {- D}_{i} & E_{i} & - B_{i} \\ G_{i} & {- B}_{i} & F_{i} & D_{i} & {- G}_{i} & A_{i} & {- E}_{i} & C_{i} \\ G_{i} & {- A}_{i} & E_{i} & {- B}_{i} & G_{i} & {- C}_{i} & F_{i} & {- D}_{i} \end{matrix}] / 2^{{SCALE}_{i}}

Wherein IDCT is 8 * 8 theoretical inverse discrete cosine transform matrixes; SCALE _iBe preassigned nonnegative integer, be used to obtain 8 * 8 inverse transformation matrixes; Round (g) is the common operation that rounds up; A _i, B _i, C _i, D _i, E _i, F _i, G _iCoefficient in expression 8 * 8 inverse transformation matrixes, and be integer; Especially, also comprise following four groups of direct transform matrix coefficients and inverse transformation matrix coefficient:

(1)A _i＝2841，B _i＝2408，C _i＝1609，D _i＝565，E _i＝2676，F _i＝1108，G _i＝2408，SCALE _i＝11；

(2)A _i＝5681，B _i＝4816，C _i＝3218，D _i＝1130，E _i＝5352，F _i＝2217，G _i＝4096，SCALE _i＝12；

(3)A _i＝11363，B _i＝9633，C _i＝6436，D _i＝2260，E _i＝10703，F _i＝4433，G _i＝8192，SCALE _i＝13；

(4)A _i＝22725，B _i＝19266，C _i＝12873，D _i＝4520，E _i＝21407，F _i＝8867，G _i＝16384，SCALE _i＝14。

7, a kind of device that applies to the discrete cosine transform of image encoding and video coding is characterized in that:

The direct transform device comprises pre-shift unit, the first dimension direct transform device, the first dimension direct transform backward shift device, the second dimension direct transform device, the second dimension direct transform backward shift device; The input of pre-shift unit links to each other with the input data before the conversion, the output of pre-shift unit links to each other with the input of the first dimension direct transform device, the output of the first dimension direct transform device links to each other with the input of the first dimension direct transform backward shift device, the output of the first dimension direct transform backward shift device links to each other with the second dimension direct transform device input, the second dimension direct transform device output links to each other with the second dimension direct transform backward shift device input, and the second dimension direct transform backward shift device output links to each other with the conversion dateout.

8, a kind of device that applies to the discrete cosine transform of image encoding and video coding according to claim 7 is characterized in that: for the direct transform device, also comprise direct transform precision complexity control device; Direct transform precision complexity control device is by switch and pre-shift unit, and first ties up the direct transform device, the first dimension direct transform backward shift device, and the second dimension direct transform device, the second dimension direct transform backward shift device links to each other;

9, a kind of device that applies to the discrete cosine transform of image encoding and video coding is characterized in that:

Inverse transformation device comprises pre-shift unit, the first dimension inverse transformation device, the first dimension inverse transformation backward shift device, the second dimension inverse transformation device, the second dimension inverse transformation backward shift device; The input of pre-shift unit links to each other with the input data before the conversion, the output of pre-shift unit links to each other with the input of the first dimension inverse transformation device, the output of the first dimension inverse transformation device links to each other with the input of the first dimension inverse transformation backward shift device, the output of the first dimension inverse transformation backward shift device links to each other with the second dimension inverse transformation device input, the second dimension inverse transformation device output links to each other with the second dimension inverse transformation backward shift device input, and the second dimension inverse transformation backward shift device output links to each other with the conversion dateout.

10, a kind of device that applies to the discrete cosine transform of image encoding and video coding according to claim 9 is characterized in that: for inverse transformation device, also comprise inverse transformation precision complexity control device; Inverse transformation precision complexity control device is by switch and pre-shift unit, and first ties up inverse transformation device, the first dimension inverse transformation backward shift device, and the second dimension inverse transformation device, the second dimension inverse transformation backward shift device links to each other.