JP2002091943A - Lifting method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a lifting method for suppressing the complicatedness of a memory management unit and the increase in the number of line memories by reducing the number of pieces of repeated data. SOLUTION: The value of data Y(2n-1) is set by using converted data Y(2n+1). Thus, data Y(2n) can be calculated on the basis of X(2n), X(2n+1) and X(2n+2) set in coordinates in a tile. Then, the data do not have to be set in coordinates whose value is <2n by repeating, and the number of registers where the data should be stored can be reduced.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

[0001] 1. Field of the Invention [0002] The present invention relates to a wavelet transform method, and particularly to a symmetric period extension method.

[0002]

2. Description of the Related Art JPEG (Joint
Photographic Coding Experts Group). Among them, International Organization for Standardization (ISO)
A method called JPEG2000, which is being studied by the JPEG method, is a DC method that has been adopted in the previous JPEG method.
T (Discrete Cosine Transform)
Instead, a wavelet transform is employed. The wavelet transform is a process of performing high-pass filtering and low-pass filtering on an input and outputting the result.

FIG. 17 is a schematic diagram showing a case where a one-stage wavelet transform is applied to a one-dimensional input. The low-side component obtained by the low-pass filter L and the high-side component obtained by the high-pass filter H are separately subjected to down-sampling in which the sampling frequency is halved, indicated by a downward arrow and a numeral 2, and output. Is done.

FIG. 18 is a schematic diagram illustrating a case where a four-stage wavelet transform is performed on a one-dimensional input.
The low-pass filter L, high-pass filter H, and down-sampling block in FIG. 17 are omitted. FIG.
8 is known as a Mallat-type wavelet transform. FIG. 19 is a schematic diagram illustrating another case of performing a four-stage wavelet transform on a one-dimensional input, which is known as a Spacle-type wavelet transform. FIG. 20 is a schematic diagram illustrating another case of performing three-stage wavelet transform on a one-dimensional input, which is known as a packet-type wavelet transform.

FIG. 21 is a schematic diagram showing a case in which a one-stage inverse wavelet transform is performed on a pair of one-dimensional inputs consisting of a low-side component and a high-side component. The low-side component and the high-side component are separately subjected to up-sampling, which is indicated by an upward arrow and a numeral 2, so that the sampling frequency is doubled. After being filtered by the low-pass filter L and the high-pass filter H, respectively,
The summed and reconstructed output is obtained.

FIG. 22 is a schematic diagram showing a case where one-stage wavelet transform is performed on a two-dimensional input. A two-dimensional input, for example, an image signal indicating an image spreading in the horizontal and vertical directions is subjected to one-dimensional one-stage wavelet transform in each of the horizontal and vertical directions.
First, low-pass filtering and down-sampling are performed in the horizontal direction to obtain a horizontal low component Lh. On the other hand, low-pass filtering and down-sampling in the vertical direction and high-pass filtering and down-sampling in the vertical direction are performed, and a component LhLv, which is a low component in the horizontal direction and a low component in the vertical direction, and a horizontal component, respectively. A component LhHv that is a low component in the direction and a high component in the vertical direction is obtained. Similarly, a component HhLv which is a high component in the horizontal direction and a low component in the vertical direction, and a component Hh which is a high component in the horizontal direction and a high component also in the vertical direction
hHv is obtained. FIG. 23 shows these components LhLv, L
It is a schematic diagram which shows the magnitude of the frequency of hHv, HhLv, HhHv. In FIG. 23, the frequency of the vertical component is higher in the downward direction in the figure, and the frequency of the horizontal component is higher in the right direction in the figure.

FIG. 24 is a schematic diagram illustrating a case in which four-stage wavelet transform is performed on a two-dimensional input, and the magnitude of the frequency is the same as that of FIG. The embodiment shown here is known as a Mallat-type wavelet transform. FIG. 25 is a schematic diagram illustrating another case of performing a four-stage wavelet transform on a two-dimensional input.
Also known as the acle-type wavelet transform. FIG. 26 is a schematic diagram illustrating another case of performing a three-stage wavelet transform on a two-dimensional input, which is known as a packet-type wavelet transform. In the two-dimensional inverse wavelet transform, the same processing as in the one-dimensional case is performed in the horizontal and vertical directions.

[0008] The above-described low-pass filtering and high-pass filtering are performed, for example, according to ISO / IEC / JTC1 SC29 / WG.
1 Calculated by lifting, as published in N1646. The filtering process includes types such as an integer type and a floating point type. Equation (1) is an example of an integer type
Lifting during wavelet transform of Reversible 5/3 type filter (hereinafter also referred to as "resolving side lifting")
Equation (2) is the lifting at the time of inverse wavelet transform of the same filter (hereinafter also referred to as “synthesis-side lifting”).
Are calculation formulas respectively shown below. Expression (3) is a calculation expression showing the decomposition-side lifting of a Daubechies 9/7 type filter, which is an example of a floating-point type, and Expression (4) is a calculation expression showing the synthesis-side lifting of the same filter. The symbol X is adopted as data before the wavelet transform, and the symbol Y is adopted as data after the wavelet transform, and the coordinate values are described in parentheses on the right side thereof. In the coordinate values, m is an integer.

[0009]

(Equation 1)

[0010]

(Equation 2)

[0011]

(Equation 3)

[0012]

(Equation 4)

In the formulas (1) and (2), the symbol ｛｝ indicates a function called a “floor” indicating a maximum integer not exceeding a value sandwiched between them. For example, $ 2.71
8 = 2 and {−2.718} = − 3. The same applies to the following mathematical expressions.

In equations (3) and (4), α, β, γ,
δ and κ are constants each having a predetermined value, and the arrow indicates that the left side is obtained from the right side while allowing an error due to floating point calculation.

The number of primes (') indicates that it is calculated for the first time in the step corresponding to the number. For example, in equation (3), Y ′ ″ (2m) is calculated for the first time in step 3. However, primes are required for data (X for decomposing lifting and Y for combined lifting) and data to be finally obtained (Y for separated lifting and X for combined lifting) when performing lifting. Omitted. For example, the left side of step 5 in equation (3) is calculated for the first time in step 5, but since this is the result of the wavelet transform to be obtained, five primes are not added.

By the way, in JPEG2000, a so-called tiling process is performed in which an image to be compressed is divided into a plurality of areas to be subjected to wavelet transform. The divided area (hereinafter referred to as “tile”) is calculated using the coordinates of the image before division. Therefore, depending on the way of tiling and the position of the tile, the coordinates of the end points of the coordinates in the horizontal and vertical directions of the tile may be odd or even.

However, when the equations (1) to (4) are calculated at the end points of the tile, some of the necessary data does not exist. Therefore, a symmetric extension method is known in which decomposition side lifting is performed using virtual data obtained by symmetrically folding data at an end point. Above all, the symmetric period extension method is known as a method of obtaining virtual data by folding data in a tile so as not to impair the period.

FIG. 27 shows Reversible 5 near the starting point when the coordinate value of the starting point of the tile (which can be defined as the smaller of the horizontal (or vertical) coordinate values among the end points) is an odd number. FIG. 4 is a tree diagram schematically showing the lifting on the disassembly side of the / 3 type filter. In the tree diagram attached to this specification, a black circle located at the left end in the figure indicates data X of coordinates existing in the tile, and a white circle indicates data X adopted as described below for coordinates not present. I have.

The values attached to the circles (whether white or black) located below the column labeled step1, step2,... Are attached to the branches extending from the left side to the circles. A value obtained by multiplying a value given to a circle (regardless of a white circle or a black circle) on the opposite side of the branch and further performing an operation using a constant (not shown) (not shown). ing.

For example, data Y marked with a black circle in FIG.
(2n + 2) includes a branch extending from a black circle having data Y (2n + 1) and having a value (1/4), and a branch having data (1/4).
The branch extending from the black circle with (2n + 2) and having a value (1) and the branch extending from the black circle with data Y (2n + 3) and having a value (1/4) are from the left. Has reached. This is because m = n + 1 is adopted in step 2 of the equation (1), and a value obtained by multiplying the data Y (2n + 1) by (1/4) and a value obtained by multiplying the data Y (2n + 3) by (1/4) are obtained. , And a value obtained by taking the “floor” and data X (2
n + 2) and a value obtained by multiplying by 1 to add data Y (2n +
1) is obtained. The constant to be added in this case is 2/4 = 1/2.

If the coordinate value of the starting point is an odd number (2n + 1), where n is an integer equal to or greater than 0, the tile is at the coordinates (2n)
, The value X of the data required in step 1
(2n) also does not exist. Therefore, by the symmetric period extension method,
With respect to the coordinates (2n + 1) of the starting point, the coordinates (2
Data X (2n + 2) at the coordinates (2n + 2) in the tile symmetrical to (n) is adopted as the value of X (2n).
Such virtual data is displayed as white circles.

FIG. 28 is a tree diagram schematically showing decomposition-side lifting of the Reversible 5/3 type filter near the start point when the coordinate value of the start point of the tile is an even number. As can be seen from equation (1), in step 1, m = n, n-1
Is adopted, first, Y (2n-1), Y (2n + 1)
Is obtained, and Y (2n) is obtained in step 2. Data Y (2n
-1), the data X (2n-1), X
It is necessary to virtually provide two of (2n-2) by the symmetric period extension method. Therefore, data X (2n + 1) and X (2n + 2) at coordinates (2n + 1) and (2n + 2) in the tile, which are respectively symmetric with respect to coordinates (2n-1) and (2n-2) outside the tile with respect to the coordinates (2n) of the start point, , Respectively, as data X (2n-1) and X (2n-2). Since the data Y (2n-1) is not necessary as the data after the wavelet transform of the tile, it is indicated by a white circle.

FIG. 29 shows the reversible 5 near the end point when the coordinate value of the end point of the tile (which can be defined as the larger one of the horizontal (or vertical) coordinates among the end points) is an odd number. FIG. 4 is a tree diagram schematically showing the lifting on the disassembly side of the / 3 type filter. By the symmetric period extension method,
The coordinates (2n) outside the tile with respect to the coordinates (2n + 1) of the end point
The data X (2n) at the coordinates (2n) in the tile symmetric to (+2) is adopted as the value of X (2n + 2).

FIG. 30 is a tree diagram schematically showing decomposition-side lifting of the Reversible 5/3 type filter near the end point when the coordinate value of the end point of the tile is an even number. By the symmetric period extension method, data X (2n-1) at coordinates (2n-1) and (2n-1) outside the tile and coordinates (2n-1) and (2n-2) inside the tile, respectively, are symmetric with respect to the coordinates (2n) of the end point. ) And X (2n-2) are adopted as data X (2n + 1) and X (2n + 2), respectively.

The symmetric period extension method is similarly performed in lifting on the combining side. As can be seen from Equations (1) and (3), data obtained by performing wavelet transform on a tile also constitutes a tile (hereinafter, referred to as “transformed tile”).

FIG. 31 is a tree diagram schematically showing the composite-side lifting of the Reversible 5/3 type filter near the start point when the coordinate value of the start point of the conversion tile is an even number.
By the symmetric period extension method, the data Y (2n + 1) at the coordinates (2n + 1) in the conversion tile symmetrical to the coordinates (2n-1) outside the conversion tile with respect to the coordinates (2n) of the starting point are defined as data Y (2n-1). Adopted.

FIG. 32 is a tree diagram schematically showing the composite-side lifting of the Reversible 5/3 type filter near the start point when the coordinate value of the start point of the conversion tile is an odd number.
The coordinates (2n + 2) and (2n +) in the conversion tile symmetric with the coordinates (2n) and (2n-1) outside the conversion tile with respect to the coordinates (2n + 1) of the starting point by the symmetric period extension method, respectively.
Data Y (2n + 2), Y (2n + 3) in 3)
Are adopted as data Y (2n) and Y (2n-1), respectively.

FIG. 33 is a tree diagram schematically showing the composite-side lifting of the Reversible 5/3 type filter near the end point when the coordinate value of the end point of the conversion tile is an even number.
By the symmetric period extension method, data Y (2n-1) at coordinates (2n-1) inside the conversion tile symmetric with coordinates (2n + 1) outside the conversion tile with respect to the coordinates (2n) at the end point are defined as data Y (2n + 1). adopt.

FIG. 34 is a tree diagram schematically showing the composite-side lifting of the Reversible 5/3 type filter near the end point when the coordinate value of the end point of the conversion tile is an odd number.
The data Y (2n), Y in the coordinates (2n), (2n-1) in the transformation tile symmetrical to the coordinates (2n + 2), (2n + 3) outside the transformation tile with respect to the coordinates (2n + 1) of the end point by the symmetric period extension method (2n-1) is adopted as data Y (2n + 2) and Y (2n + 3), respectively.

The symmetric period extension method is adopted also in the floating point type Daubechies 9/7 type filter. FIG. 35 shows Da near the start point when the coordinate value of the start point of the tile is an even number.
FIG. 4 is a tree diagram schematically showing decomposition side lifting of a ubechies 9/7 type filter. Data Y whose coordinate value is even
In order to obtain (2n), in equation (3), m = n−
By adopting 2, n-1, n, n + 1, the data X
(2n-4), X (2n-3), X (2n-2), X
(2n-1), X (2n), X (2n + 1), X (2n
+2), X (2n + 3) and X (2n + 4) are required, but the former does not exist in the tile. Therefore, the coordinates (2n-4), (2n-3), (2n-2), (2n-2),
(2n-1) and coordinates (2n +
4), (2n + 3), (2n + 2), data X (2n + 4), X (2n + 3), X (2n) in (2n + 1)
+2) and X (2n + 1) are converted to data X (2n−
4), X (2n-3), X (2n-2), X (2n-
Adopted as 1).

FIG. 36 is a tree diagram schematically showing the decomposition side lifting of the Daubechies 9/7 type filter near the start point when the coordinate value of the start point of the tile is an odd number. By the symmetric period extension method, coordinates (2n + 4), (2n + 3), (2n + 3), and (2n + 4) in a tile symmetric to coordinates (2n-2), (2n-1), and (2n) outside the tile with respect to the coordinates (2n + 1) of the starting point.
Data X (2n + 4) and X (2n + 2) in (2n + 2)
+3) and X (2n + 2) are converted into data X (2n−
2), X (2n-1) and X (2n).

FIG. 37 is a tree diagram schematically showing the decomposition side lifting of the Daubechies 9/7 type filter near the end point when the coordinate value of the end point of the tile is an even number. By the symmetric period extension method, coordinates (2n + 4), (2n + 3), (2n + 2), (2n + 2),
Coordinates (2n-4) in a tile symmetrical to (2n + 1),
Data X (2n-4), X (2n-3), X (2n-) in (2n-3), (2n-2) and (2n-1)
2) and X (2n-1) are converted to data X (2n +
4), X (2n + 3), X (2n + 2), X (2n +
Adopted as 1).

FIG. 38 is a tree diagram schematically showing the decomposition side lifting of the Daubechies 9/7 type filter near the end point when the coordinate value of the end point of the tile is an odd number. The coordinates (2n + 4), (2n + 3), (2n + 3) outside the tile with respect to the coordinates (2n + 1) of the end point are obtained by the symmetric period extension method.
The coordinates (2n-2) and (2n-
1), data X (2n-2), X (2n) in (2n)
n-1) and X (2n) are converted to data X (2n +
4), X (2n + 3) and X (2n + 2).

FIG. 39 is a tree diagram schematically showing the lifting on the synthesis side of the Daubechies 9/7 type filter near the start point when the coordinate value of the start point of the transform tile is an even number.
In order to obtain data X (2n + 1) whose coordinate values are odd, m = n−2, n−1, n, n +
By adopting 1, n + 2, the data Y (2n−3),
Y (2n-2), Y (2n-1), Y (2n), Y (2n)
n + 1), Y (2n + 2), Y (2n + 3), Y (2n
+4), Y (2n + 5), but the former three do not exist in the transform tile. Therefore, the coordinates (2n-3), (2n + 3), (2n-3), (2n-3), (2n-2), and (2n-1) in the conversion tile that are symmetric with respect to the coordinates (2n) of the starting point outside the conversion tile by the symmetric period extension method. 2n + 2), (2n
+1), Y (2n + 3) and Y (2n +
2) and Y (2n + 1) are converted to data Y (2n−
3), Y (2n-2) and Y (2n-1).

FIG. 40 is a tree diagram schematically showing lifting on the synthesis side of the Daubechies 9/7 type filter near the start point when the coordinate value of the start point of the transformed tile is an odd number.
By the symmetric period extension method, coordinates (2n-3), (2n-2),
Coordinates (2n + 5), (2n + 4), (2n + 3), (2n + 5) in the transformed tile symmetrical to (2n-1) and (2n)
2) data Y (2n + 5), Y (2n + 4),
Y (2n + 3) and Y (2n + 2) are converted to data Y
(2n-3), Y (2n-2), Y (2n-1), Y
(2n).

FIG. 41 is a tree diagram schematically showing lifting on the synthesis side of the Daubechies 9/7 type filter near the end point when the coordinate value of the end point of the transformed tile is an even number.
The coordinates (2n + 3), (2n + 2), (2n + 2) outside the transform tile with respect to the coordinates (2n) of the end point are obtained by the symmetric period extension method.
+1) and coordinates (2n-3), (2
n-2) and data Y (2n-) in (2n-1).
3), Y (2n-2) and Y (2n-1) are converted into data Y (2n + 3), Y (2n + 2) and Y (2n + 1), respectively.
To be adopted.

FIG. 42 is a tree diagram schematically showing lifting on the synthesis side of the Daubechies 9/7 type filter near the end point when the coordinate value of the end point of the transformed tile is an odd number.
By the symmetric period extension method, the coordinates (2n + 5), (2n + 4),
Coordinates (2n-3), (2n-2), (2n-1), (2) in the transformation tile symmetrical to (2n + 3) and (2n + 2)
n), Y (2n-3), Y (2n-2),
Y (2n-1) and Y (2n) are respectively converted into data Y (2n).
n + 5), Y (2n + 4), Y (2n + 3), Y (2n
+2).

[0038]

In the conventional symmetric period extension method, the data is folded at the end point as described above. Therefore, as the number of taps of the filter increases, the number of data to be folded increases. As the number of data to be turned back increases, there is a problem that a memory management unit required to execute the symmetric period extension method becomes complicated.

Such a problem also causes a problem of an increase in the number of line memories when a technique called a line base wavelet or an inverse line wavelet is used for two-dimensional data.

FIG. 43 is a conceptual diagram showing a line-based wavelet, and FIG. 44 is a conceptual diagram showing an inverse line-based wavelet. In FIG. 43, data input in raster scan order is filtered in the vertical direction (column direction in the figure) while scanning in the horizontal direction (row direction in the figure) of the arrow. For example, filtering is performed on the leftmost column C11 of the tile to obtain a wavelet coefficient for each of the low-pass in the vertical direction and the high-pass in the vertical direction for each column. After that, the same filtering is performed on the right column C12. When the column is scanned in the row direction up to the right end of the tile, the column is shifted by one row in the vertical direction of the arrow to the column C21.
And filter it. Similarly, in the inverted line-based wavelet, filtering is performed in the vertical direction (the column direction in the figure) while scanning the transformed tile in the horizontal direction of the arrow, and one composite image (decompressed image) is obtained from a pair of transformed tiles. (FIG. 44).

In order to perform the above operation, FIG.
As shown in the block diagram, a line memory for storing one row of data is required in a number corresponding to the number of taps. Then, as the number of data to be turned back by the symmetric period extension method increases, the number of required line memories also increases.

The present invention has been made in view of the above circumstances, and has as its object to reduce the number of data to be looped back, thereby obtaining an effect of suppressing the complexity of the memory management unit and the increase in the number of line memories.

[0043]

Means for Solving the Problems Claim 1 of the present invention
Is a lifting method of converting first data given for each coordinate and obtaining second data for each coordinate in an area given discrete coordinates including a pair of end points, The second data corresponding to the first coordinates in the area adjacent to the coordinates of the one end point as the second data in the second coordinates symmetrical to the first coordinates with respect to the coordinates of the one end point It is characterized by adoption.

According to a second aspect of the present invention, there is provided the lifting method according to the first aspect, wherein the conversion is performed based on an odd number of the data to obtain one data after the conversion.

According to a third aspect of the present invention, there is provided the lifting method according to the second aspect, wherein the conversion is performed by using
Wavelet transform using a versible 5/3 type filter.

According to a fourth aspect of the present invention, there is provided the lifting method according to the third aspect, wherein the coordinate value of the one end point is an even number.

According to a fifth aspect of the present invention, there is provided the lifting method according to the second aspect, wherein the conversion is performed by using
This is an inverse wavelet transform using a versible 5/3 type filter.

According to a sixth aspect of the present invention, there is provided the lifting method according to the fifth aspect, wherein the coordinate value of the one end point is an odd number.

According to the seventh aspect of the present invention,
A lifting method of converting first data given for each of the coordinates to obtain second data for each of the coordinates in an area where discrete coordinates including a pair of endpoints are given,
Third data is calculated for each of the coordinates during the conversion from the first data to the second data, and the third data corresponding to the first coordinates in the area adjacent to the coordinates of the one end point is calculated. And the third data at the second coordinates symmetrical to the first coordinates with respect to the coordinates of the one end point.

According to an eighth aspect of the present invention, there is provided the lifting method according to the seventh aspect, wherein the conversion is performed by using the Da method.
ubechies Wavelet transform using a 9/7 type filter.

According to a ninth aspect of the present invention, there is provided the lifting method according to the eighth aspect, wherein the coordinate value of the one end point is an even number.

According to a tenth aspect of the present invention, there is provided the lifting method according to the eighth aspect, wherein the coordinate value of the one end point is an odd number.

According to an eleventh aspect of the present invention, there is provided the lifting method according to the tenth aspect, wherein the first method comprises:
The first data corresponding to the coordinates is adopted as the first data at the second coordinates.

According to a twelfth aspect of the present invention, there is provided the lifting method according to the seventh aspect, wherein the conversion is
This is an inverse wavelet transform using a Daubechies 9/7 type filter.

According to a thirteenth aspect of the present invention, there is provided the lifting method according to the twelfth aspect, wherein the coordinate value of the one end point is an even number.

According to a fourteenth aspect of the present invention, there is provided the lifting method according to the twelfth aspect, wherein the coordinate value of the one end point is an odd number.

According to a fifteenth aspect of the present invention, there is provided the lifting method according to the fourteenth aspect, wherein:
The second data corresponding to the coordinates is adopted as the second data at the second coordinates.

[0058]

DESCRIPTION OF THE PREFERRED EMBODIMENTS First Embodiment In the present embodiment, an invention relating to the lifting on the decomposition side of the Reversible 5/3 type filter will be described. Equation (1) is also employed in the present embodiment as a calculation equation. FIGS. 1 to 4 are tree diagrams conceptually showing the first embodiment of the present invention, in which the meanings of white circles, black circles, and branches are the same as in the prior art.

FIG. 1 schematically shows the calculation of the lifting on the decomposition side when the coordinate value of the starting point of the tile is an odd number. When the coordinate value of the starting point is an odd number (2n + 1), the tile does not exist at the coordinate (2n) as in the conventional technique (FIG. 27), and thus the data value X (2
n) also does not exist. Therefore, the data X at the coordinates (2n + 2) in the tile symmetric with the coordinates (2n) outside the tile with respect to the coordinates (2n + 1) of the starting point by the symmetric period extension method.
(2n + 2) is adopted as the value of X (2n).

FIG. 2 schematically shows the calculation of the lifting on the decomposition side when the coordinate value of the starting point of the tile is an even number. In the related art (FIG. 28), data Y (2n-1) necessary for calculating data Y (2n) is obtained by combining data X (2n) for coordinates (2n) existing in a tile and symmetric period extension. X (2n-1), X obtained by the
It was calculated using (2n-2).

However, data X (2n-1) and X (2n
-2) are data X (2n + 1) and X (2n +
The value of 2) was adopted. Therefore, data Y (2n−2) calculated in step 1 of equation (1) with m = n−1
1) is the data Y (2n +
It is equal to 1). Focusing on this point in the present invention, the folding in the symmetric period extension method is performed not on the data provided in step 1 of equation (1) but on the data obtained in step 1 of equation (1). That is, in equation (1), m
= N−1 without executing step 1, the data Y (2n−1) = Y (2
n + 1) is obtained, and step 2 is executed for m = n to obtain data Y (2n) corresponding to the coordinates 2n of the starting point. In other words, when the coordinate value of the starting point is 2n, step2 of the equation (1) is performed only when m = n.

[0062]

(Equation 5)

Will be replaced with

As described above, in comparison with the prior art,
The number of data to be virtually set is reduced by two.

FIG. 3 schematically shows the calculation of the decomposition side lifting when the coordinate value of the end point of the tile is an odd number. If the coordinate value of the end point is an odd number (2n + 1), the tile is set to the coordinates (2n +
Since it does not exist in 2), the value X of the data required in step 1
(2n + 2) also does not exist. Therefore, the data X (2n) at the coordinates (2n) in the tile symmetrical to the coordinates (2n + 2) outside the tile with respect to the coordinates (2n + 1) of the end point is adopted as the value of X (2n + 2) by the symmetric period extension method.

FIG. 4 schematically shows the calculation of the decomposition-side lifting when the coordinate value of the end point of the tile is an even number. In the related art (FIG. 30), data Y (2n + 1) necessary for calculating data Y (2n) is obtained by using data X (2n) for coordinates (2n) existing in a tile and symmetric period extension method. Obtained data X (2n + 1), X
It was calculated using (2n + 2).

However, data X (2n + 1) and X (2n
+2) are data X (2n-1) and X (2n-
The value of 2) was adopted. Therefore, data Y (2n + 1) calculated by setting m = n in step 1 of equation (1)
Is the data Y (2n−2) calculated on the assumption that m = n−1.
It is equal to 1). Focusing on this point in the present invention, the folding in the symmetric period extension method is performed not on the data provided in step 1 of equation (1) but on the data obtained in step 1 of equation (1). That is, in equation (1), m
= N−1 without executing step 1 for m = n−1, the data Y (2n + 1) = Y (2
n-1) is obtained, and step 2 is executed for m = n to obtain data Y (2n) corresponding to the coordinates 2n of the starting point. In other words, when the coordinate value of the end point is 2n, step2 of the equation (1) is performed only when m = n.

[0068]

(Equation 6)

Will be replaced with

As described above, in comparison with the prior art,
The number of data to be virtually set is reduced by two.

In the present embodiment, when the coordinate value of the end point of the tile is an even number in the lifting on the decomposition side of the Reversible 5/3 type filter, the wavelet transform corresponding to the coordinate in the tile adjacent to the coordinate of the end point is performed. The subsequent data will be adopted by looping back. Thus, the number of data to be referred to in order to loop the data, the number of calculation steps, and the number of registers for storing the data can be reduced, and the complexity of the memory management unit can be reduced. Such an effect also brings about an effect of suppressing an increase in the number of line memories. The complexity of the memory management unit and the increase in the number of line memories can be suppressed.

Second Embodiment In the present embodiment, Rev.
The invention on the composite side lifting of the rsible 5/3 type filter is shown. Equation (2) is also used as a calculation equation in the present embodiment. FIGS. 5 to 8 are tree diagrams conceptually showing the second embodiment of the present invention, in which the meanings of white circles, black circles, and branches are the same as those in the prior art.

FIG. 5 schematically shows the calculation of the composite-side lifting when the coordinate value of the starting point of the conversion tile is an even number. When the coordinate value of the start point is an even number (2n), the converted tile is set to the coordinates (2n) in the same manner as in the related art (FIG. 31).
n-1), there is no data value Y (2n-1) required in step1. Therefore, the coordinates (2n + 1) outside the conversion tile and the coordinates (2n + 1) inside the conversion tile that are symmetric with respect to the coordinates (2n) of the starting point by the symmetric period extension method
Is adopted as the value of Y (2n-1).

FIG. 6 schematically shows the calculation of the composite-side lifting when the coordinate value of the starting point of the conversion tile is an odd number. In the related art (FIG. 32), data X (2n) necessary for calculating data X (2n + 1) is data Y (2n +) for coordinates (2n + 1) existing in the tile.
1) and data Y (2) obtained by the symmetric period extension method.
n) and Y (2n-1).

However, data Y (2n) and Y (2n-
1) respectively represent data Y (2n + 2) and Y (2n +
The value of 3) was adopted. Therefore, data X (2n) calculated in step 1 of equation (2) with m = n is:
It is equal to data X (2n + 2) calculated with m = n + 1. Focusing on this point in the present invention, the folding in the symmetric period extension method is performed not on the data provided in step 1 of the equation (2) but on the data obtained in step 1 of the equation (2). That is, in the equation (2), the step for m = n + 1 is performed without executing the step 1 for m = n.
The data X (2n) = X (2n + 2) is obtained by executing ep1, and the step 2 is executed for m = n to execute the coordinates (2
Data X (2n + 1) corresponding to (n + 1) is obtained. In other words, when the coordinate value of the end point is (2n + 1), m
= N only when step2 of equation (2)

[0076]

(Equation 7)

Will be replaced with

As described above, the number of data to be virtually set is reduced by two as compared with the prior art.

FIG. 7 schematically shows the calculation of the composite-side lifting when the coordinate value of the end point of the conversion tile is an even number. When the coordinate value of the end point is an even number (2n), the conversion tile is set to the coordinates (2n) in the same manner as in the related art (FIG. 33).
Since it does not exist in (n + 1), the value Y (2n + 1) of the data required in step 1 also does not exist. Then, the coordinates (2n + 1) outside the conversion tile and the coordinates (2n-1) inside the conversion tile that are symmetric with respect to the coordinates (2n) of the end point by the symmetric period extension method.
Is adopted as the value of Y (2n + 1).

FIG. 8 schematically shows the calculation of the composite-side lifting when the coordinate value of the end point of the conversion tile is an odd number. In the related art (FIG. 34), data X (2n + 2) necessary for calculating data X (2n + 1) is obtained by using data Y (2n + 1) for coordinates (2n + 1) existing in the tile.
n + 1) and the data Y obtained by the symmetric period extension method
The calculation was performed using (2n + 2) and Y (2n + 3).

However, data Y (2n + 2) and Y (2n
+3) are data Y (2n) and Y (2n-1), respectively.
Was adopted. Therefore, data X (2n + 2) calculated in step 1 of equation (2) with m = n + 1
Is equal to the data X (2n) calculated with m = n. Focusing on this point in the present invention, the folding in the symmetric period extension method is performed not on the data provided in step 1 of the equation (2) but on the data obtained in step 1 of the equation (2). That is, in equation (2), step 1 for m = n is performed without executing step 1 for m = n + 1.
To obtain data X (2n + 2) = X (2n), execute step 2 for m = n, and execute the coordinates of the end point (2n
+1) is obtained as data X (2n + 1). In other words, when the coordinate value of the end point is (2n + 1), m =
step2 of equation (2) only for n

[0082]

(Equation 8)

Will be replaced with

As described above, the number of data to be virtually set is reduced by two as compared with the prior art.

In this embodiment, when the coordinate value of the end point of the conversion tile is an odd number in the synthesis-side lifting of the Reversible 5/3 type filter, the coordinates corresponding to the coordinates in the conversion tile adjacent to the coordinates of the end point are used. The same effect as in the first embodiment can be obtained by folding the data after the inverse wavelet transform and adopting it.

Third Embodiment In the present embodiment, Daub
Fig. 2 shows an invention on the lifting side of the echies 9/7 type filter. Equation (3) is also used as a calculation equation in the present embodiment. FIGS. 9 to 12 are tree diagrams conceptually showing the third embodiment of the present invention. The meanings of white circles, black circles, and branches are the same as those in the conventional art.

FIG. 9 schematically shows the calculation of the lifting on the decomposition side when the coordinate value of the starting point of the tile is an even number. In the related art (FIG. 35), data Y ″ ″ (2n) necessary for calculating data Y (2n) is data X (2n) for coordinates (2n) to (2n + 4) existing in the tile.
n) to X (2n + 4) and the data X (2n-1) to X (2n-4) obtained by the symmetric period extension method.

However, data X (2n-1) and X (2n
-2), X (2n-3) and X (2n-4) are data X (2n + 1), X (2n + 2) and X (2n +
3), the value of X (2n + 4) was adopted. Therefore, the data Y ′ ″ (2n−1) calculated by adopting m = n−1 in step 3 of the equation (3) becomes m = n in step 3
Is equal to the data Y ′ ″ (2n + 1) calculated by adopting The data Y ′ (2n−1) used in calculating the data Y ″ (2n) in the step 2 of the equation (3) by using m = n is obtained by adopting the m = n in the step 1. It is equal to the calculated data Y '(2n + 1).

Focusing on this point in the present invention, the return in the symmetric period extension method is not the data provided to step 1 of equation (3), but the data obtained by step 1 and step 3 of equation (3), ie, the wavelet transform. Is performed on data that is temporarily calculated on the way. That is, equation (3)
, By executing step1 and step3 on m = n without executing step1 and step3 on m = n−1, data Y ′ (2n−1) = Y ′ (2n + 1),
Y ′ ″ (2n−1) = Y ″ ′ (2n + 1), and m =
This is used for the calculation of step 4 in n. In other words,
When the coordinate value of the starting point is 2n, the equation (3) is not executed when m <n−1, and step1 and st are performed only when m = n−1.
ep3 each

[0090]

(Equation 9)

Will be replaced with

As described above, the number of data to be virtually set is reduced by six as compared with the conventional technique.

FIG. 10 schematically shows the calculation of the decomposition side lifting when the coordinate value of the starting point of the tile is an odd number.
In the prior art (FIG. 36), data Y ′ ″ (2n + 1) necessary to calculate data Y (2n + 1) is data X (2n + 1) for coordinates (2n + 1) to (2n + 4) existing in the tile. To X (2n + 4) and data X (2n) to X (2n−
It was calculated using 2).

However, data X (2n) and X (2n-
1) and X (2n-2) are data X (2n +
2), X (2n + 3), and X (2n + 4). Therefore, the data Y ″ (2n) calculated by using m = n in step 2 of equation (3) is the data Y ″ (2n +) calculated by using m = n + 1 in step 2.
It is equal to 2).

Focusing on this point, the present invention adopts data X (2n + 2) as data X (2n) for the wrapping in the symmetric period extension method.
1), X (2n-2) as data X (2n + 3), X
(2n + 4) is not adopted. Instead, data X
(2n-1) and Y (2n + 2) as temporary data Y '' (2n) which indirectly required X (2n-2)
Do the wrapping to adopt. That is, in the formula (3), by executing step2 on m = n + 1 without executing step2 on m = n, Y ″ (2n) = Y ″
(2n + 2) is obtained and used for calculation of step3 and step5 when m = n. In other words, the coordinate value of the starting point is 2n
In the case of +1, when m <n, the equation (3) is not executed,
Step1 and step3 only when m = n

[0096]

(Equation 10)

Will be replaced with

As described above, the number of data to be virtually set is reduced by three as compared with the conventional technique.

FIG. 11 schematically shows calculation of decomposition lifting when the coordinate value of the end point of the tile is an even number.
In the related art (FIG. 37), data Y ″ ″ (2n) necessary for calculating data Y (2n) is data X ′ of coordinates (2n) to (2n−4) existing in the tile.
The calculation is performed using (2n) to X (2n-4) and data X (2n + 1) to X (2n + 4) obtained by the symmetric period extension method.

However, data X (2n + 1) and X (2n
+2), X (2n + 3) and X (2n + 4) are data X (2n-1), X (2n-2) and X (2n-
3) and X (2n-4). Therefore, data Y ′ ″ (2n + 1) calculated by adopting m = n in step 3 of equation (3) is m = n−1 in step 3
Is equal to the data Y ′ ″ (2n−1) calculated. The data Y ′ (2n + 1) used when calculating the data Y ″ (2n) in the step 2 of the equation (3) by adopting m = n is obtained by adopting m = n−1 in the step 1. It is equal to the calculated data Y '(2n-1).

Focusing on this point, the present invention focuses on the folding in the symmetric period extension method, not on the data provided in step 1 of equation (3), but on the temporary data obtained in step 1 and step 3 of equation (3). It is done for. That is, in equation (3), by executing step1 and step3 for m = n−1 without executing step1 and step3 for m = n, data Y ′ (2n + 1) = Y ′ (2n−
1), Y ′ ″ (2n + 1) = Y ′ ″ (2n−1) is obtained, and is subjected to the calculation of step 4 when m = n. In other words, when the coordinate value of the end point is 2n, the equation (3) is not executed when m> n, and step1 and st are performed only when m = n.
ep3 each

[0102]

[Equation 11]

Will be replaced with

As described above, the number of data to be virtually set is reduced by six as compared with the prior art.

FIG. 12 schematically shows the calculation of the lifting on the decomposition side when the coordinate value of the end point of the tile is an odd number.
In the related art (FIG. 38), data Y ′ ″ (2n + 1) necessary to calculate data Y (2n + 1) is data X () of coordinates (2n−2) to (2n + 1) existing in the tile. 2n-2) to X (2n + 1) and data X (2n + 2) to X (2
n + 4).

However, data X (2n + 2), X (2n
+3) and X (2n + 4) are the data X (2
n), X (2n-1), and X (2n-2). Therefore, data Y ″ (2n + 2) calculated by adopting m = n + 1 in step 2 of equation (3) is
, The data Y ″ (2) calculated using m = n
n).

Focusing on this point, the present invention adopts the data X (2n) as the data X (2n + 2) for the return in the symmetric period extension method.
3), X (2n + 4) as data X (2n-1), X
(2n-2) is not adopted. Instead, data X
(2n + 3) and X "(2n + 4) are used as temporary data Y" (2n + 2) which are indirectly required and Y "(2n).
Do the wrapping to adopt. That is, in the equation (3), by executing step2 on m = n without executing step2 on m = n + 1, Y ″ (2n + 2) =
Y ″ (2n) is obtained and used for calculation of step 3 and step 5 when m = n. In other words, the coordinate value of the starting point is 2n
In the case of +1, when m> n, the equation (3) is not executed, and
Step1 and step3 only when m = n

[0108]

(Equation 12)

Will be replaced with

As a result, the number of data to be virtually set is reduced by three as compared with the prior art.

In the present embodiment, when the coordinate value of the end point of the tile is an even number in the lifting on the decomposition side of the Daubechies 9/7 type filter, the wavelet transform corresponding to the coordinate in the tile adjacent to the coordinate of the end point is performed. The same effect as in the first embodiment can be obtained by folding back and using the temporary data therein.

In the lifting on the decomposition side of the Daubechies 9/7 type filter, when the coordinate value of the end point of the tile is an odd number, the temporary value during the wavelet transform corresponding to the coordinate in the tile adjacent to the coordinate of the end point is determined. The same effect as in the first embodiment can be obtained by adopting such data in a folded manner. However, data corresponding to the coordinates in the tile adjacent to the coordinates of the end point of the tile is adopted by folding the coordinates of the end point of the tile.

Fourth Embodiment In the present embodiment, Daub
3 shows an invention for lifting on the synthesis side of an echies 9/7 type filter. Equation (4) is also employed in the present embodiment as a calculation equation. 13 to 16 show a fourth embodiment of the present invention.
FIG. 3 is a tree diagram conceptually showing the embodiment of FIG.
The meanings of the black circles and the branches are the same as in the prior art.

FIG. 13 schematically shows the calculation of the composite-side lifting when the coordinate value of the starting point of the conversion tile is an even number. In the related art (FIG. 39), data X ″ ″ (2n−1) necessary for calculating data X (2n) is data on coordinates (2n) and (2n + 1) existing in the conversion tile. Y (2n), Y (2n + 1) and data Y (2n−1), Y (2n−) obtained by the symmetric period extension method.
2) and Y (2n-3).

However, data Y (2n-1) and Y (2n
-2) and Y (2n-3) are data Y (2n +
1), Y (2n + 2), and Y (2n + 3). Therefore, data X ″ ″ (2n−1) calculated by adopting m = n−1 in step 4 of equation (4) is
4. Data X ″ ″ calculated using m = n in 4.
It is equal to (2n + 1). Further, data X ″ (2n−1) used when calculating data X ′ ″ (2n) by adopting m = n in step 3 of equation (4) is obtained by adopting m = n in step 2. Data X ″ to be calculated (2n + 1)
Is equal to

Focusing on such a point in the present invention, the folding in the symmetric period extension method is not the data used for step 1 and step 2 in the equation (4), but the steps 2, 2 and 3 in the equation (4).
This is performed on the temporary data obtained in step 4. That is, in equation (4), step =
2. For m = n without executing step3 and step4
By executing step2 and step4, the data X ″ (2n
-1) = X ″ (2n + 1), X ″ ″ (2n−1) =
X ″ ″ (2n + 1) is obtained, and is subjected to the calculation of step 3 when m = n. In other words, the coordinate value of the starting point is 2n
When m <n, the equation (4) is not executed, and m = n
Step3 and step5 only for n

[0117]

(Equation 13)

Will be replaced with

As described above, the number of data to be virtually set is reduced by six as compared with the conventional technique.

FIG. 14 schematically shows the calculation of the composite-side lifting when the coordinate value of the starting point of the conversion tile is an odd number. In the conventional technique (FIG. 40), data necessary for calculating data X (2n + 1) is data Y for coordinates (2n + 1) to (2n + 5) existing in the conversion tile.
The calculation is performed using (2n + 1) to Y (2n + 5) and data Y (2n) to Y (2n−3) obtained by the symmetric period extension method.

However, data Y (2n) and Y (2n-
1), Y (2n-2) and Y (2n-3) are data Y (2n + 2), Y (2n + 3) and Y (2n +
4), the value of Y (2n + 5) was adopted. Therefore, the data X ′ ″ (2n) calculated by using m = n in step 3 of the equation (4) is the same as the data X ′ ″ (2n + 2) calculated by using m = n + 1 in step 3. equal.
The data X (2n) calculated by using m = n in step 5 of the equation (4) is equal to the data X (2n + 2) calculated by using m = n + 1 in step 5.

In the present invention, attention is paid to such a point, and the return in the symmetric period extension method is performed by data Y (2n) to Y (2n).
Data Y (2n + 2) to Y (2n + 5) are not adopted as -3). Instead, the temporary data X '''
(2n), data X (2n) after inverse wavelet transform
Is performed using X ′ ″ (2n + 2) and X (2n + 2), respectively. That is, in the formula (4), X ′ ″ (2n) = X ′ by executing step1, step3, and step5 on m = n + 1 without executing step1, step3, and step5 on m = n. '' (2n + 2), X
(2n) = X (2n + 2) is obtained, and step at m = n is obtained.
6 is provided. In other words, when the coordinate value of the starting point is 2n + 1, the equation (3) is not executed when m <n + 1, and the steps 4 and 6 are performed only when m = n + 1.

[0123]

[Equation 14]

Will be replaced with

As described above, the number of data to be virtually set is reduced by 10 as compared with the conventional technique.

FIG. 15 schematically shows the calculation of the composite-side lifting when the coordinate value of the end point of the conversion tile is an even number. In the related art (FIG. 41), data X ″ ″ (2n + 1) necessary for calculating data X (2n) is data on coordinates (2n) and (2n−1) existing in the conversion tile. Y (2n), Y (2n-1) and data Y (2n + 1), Y (2n +
2), Y (2n + 3).

However, data Y (2n + 1) and Y (2n
+2) and Y (2n + 3) are data Y (2n−
1), Y (2n-2), and Y (2n-3). Therefore, the data X ″ ″ (2n + 1) calculated by using m = n in step 4 of equation (4) is the data X ″ ″ calculated by using m = n−1 in step 4.
It is equal to (2n-1). Further, data X ″ (2n + 1) used when calculating data X ′ ″ (2n) by adopting m = n in step 3 of equation (4) is obtained by adopting m = n−1 in step 2. The calculated data X ″ (2n−
It is equal to 1).

In the present invention, attention is paid to this point, and the return in the symmetric period extension method is not the data used for step 1 and step 2 in equation (4), but the data for step 2, step 3 and equation 3 in equation (4).
This is performed on the temporary data obtained in step 4. That is, in equation (4), for m = n, step2
For m = n-1 without executing step3 and step4
By executing step2 and step4, the data X ″ (2n
+1) = X ″ (2n−1), X ″ ″ (2n + 1) =
X ″ ″ (2n−1) is obtained, and is used for calculation of step 3 when m = n. In other words, the coordinate value of the end point is 2n
When m> n, the equation (4) is not executed and m = n
Step3 and step5 only for n

[0129]

(Equation 15)

Will be replaced with

As described above, the number of data to be virtually set is reduced by six as compared with the prior art.

FIG. 16 schematically shows the calculation of the composite-side lifting when the coordinate value of the end point of the conversion tile is an odd number. In the conventional technique (FIG. 42), data necessary for calculating data X (2n + 1) is data Y for coordinates (2n-3) to (2n + 1) existing in the conversion tile.
The calculation is performed using (2n−3) to Y (2n + 1) and data Y (2n + 2) to Y (2n + 5) obtained by the symmetric period extension method.

However, data Y (2n + 2) and Y (2n
+3), Y (2n + 4), and Y (2n + 5) are data Y (2n), Y (2n-1), Y (2n-2),
The value of Y (2n-3) was adopted. Therefore, equation (4)
In step 3, the data X ′ ″ (2n + 2) calculated using m = n + 1 is equal to the data X ′ ″ (2n) calculated in step 3 using m = n. The data X (2n + 2) calculated by using m = n + 1 in step 5 of equation (4) is equal to the data X (2n) calculated by using m = n in step 5.

Focusing on this point in the present invention, the return in the symmetric period extension method is based on data X (2n + 2) to X
Data X (2n) to X (2n-3) as (2n + 5)
Is not adopted. Instead, the temporary data X '''
(2n + 2), data X (2
As (n + 2), folding is performed using X ″ ′ (2n) and X (2n), respectively. That is, in the formula (4), X ′ ″ (2n + 2) = X ′ by executing step1, step3, and step5 for m = n without executing step1, step3, and step5 for m = n + 1. '' (2n), X
(2n + 2) = X (2n), and at m = n + 1
This is used for the calculation in step 6. In other words, when the coordinate value of the starting point is 2n + 1, the equation (3) is not executed when m> n, and step4 and step6 are performed only when m = n.

[0135]

(Equation 16)

Will be replaced with

As described above, the number of data to be virtually set is reduced by 10 as compared with the conventional technique.

In the present embodiment, in the lifting of the synthesis side of the Daubechies 9/7 type filter, the temporary data during the inverse wavelet transform corresponding to the coordinates in the tile adjacent to the coordinates of the end point of the tile is used by being folded back. By doing so, the same effect as in the first embodiment can be obtained. However, when the coordinate value of the end point is an odd number, the data after conversion corresponding to the coordinates in the conversion tile adjacent to the coordinates of the end point of the conversion tile is adopted by folding the coordinates of the end point of the conversion tile.

[0139]

According to the lifting method of the present invention, it is possible to reduce the number of data to be referred to in order to wrap data, the number of calculation steps, and the number of registers for storing data. The complexity can be reduced. As a result, the effect of suppressing an increase in the number of line memories is also brought. Therefore, the complexity of the memory management unit and the increase in the number of line memories can be suppressed.

[Brief description of the drawings]

FIG. 1 is a tree diagram schematically showing a lifting method according to a first embodiment of the present invention.

FIG. 2 is a tree diagram schematically showing a lifting method according to the first embodiment of the present invention.

FIG. 3 is a tree diagram schematically showing a lifting method according to the first embodiment of the present invention.

FIG. 4 is a tree diagram schematically showing a lifting method according to the first embodiment of the present invention.

FIG. 5 is a tree diagram schematically showing a lifting method according to a second embodiment of the present invention.

FIG. 6 is a tree diagram schematically showing a lifting method according to a second embodiment of the present invention.

FIG. 7 is a tree diagram schematically showing a lifting method according to a second embodiment of the present invention.

FIG. 8 is a tree diagram schematically illustrating a lifting method according to a second embodiment of the present invention.

FIG. 9 is a tree diagram schematically showing a lifting method according to a third embodiment of the present invention.

FIG. 10 is a tree diagram schematically showing a lifting method according to a third embodiment of the present invention.

FIG. 11 is a tree diagram schematically showing a lifting method according to a third embodiment of the present invention.

FIG. 12 is a tree diagram schematically showing a lifting method according to a third embodiment of the present invention.

FIG. 13 is a tree diagram schematically illustrating a lifting method according to a fourth embodiment of the present invention.

FIG. 14 is a tree diagram schematically showing a lifting method according to a fourth embodiment of the present invention.

FIG. 15 is a tree diagram schematically showing a lifting method according to a fourth embodiment of the present invention.

FIG. 16 is a tree diagram schematically showing a lifting method according to a third embodiment of the present invention.

FIG. 17 is a schematic diagram showing a case where one-stage wavelet transform is performed on a one-dimensional input;

FIG. 18 is a schematic diagram showing a Mallat-type wavelet transform.

FIG. 19 is a schematic diagram showing a Spacle-type wavelet transform.

FIG. 20 is a schematic diagram illustrating a packet-type wavelet transform.

FIG. 21 is a schematic diagram showing a case where one-stage inverse wavelet transform is performed on a pair of one-dimensional inputs.

FIG. 22 is a schematic diagram showing a case where one-stage wavelet transform is performed on a two-dimensional input.

FIG. 23 is a schematic diagram showing the magnitude of the frequency of each component of the wavelet transform.

FIG. 24 is a schematic diagram showing a Mallat-type wavelet transform.

FIG. 25 is a schematic diagram showing a Spacle-type wavelet transform.

FIG. 26 is a schematic diagram showing a packet-type wavelet transform.

FIG. 27 shows a case where the coordinate value of the starting point of a tile is an odd number.
FIG. 4 is a tree diagram schematically showing a decomposition-side lifting of a Reversible 5/3 type filter.

FIG. 28 shows a case where the coordinate value of the starting point of a tile is an even number.
FIG. 4 is a tree diagram schematically showing a decomposition-side lifting of a Reversible 5/3 type filter.

FIG. 29 shows a case where the coordinate value of the end point of a tile is an odd number.
FIG. 4 is a tree diagram schematically showing a decomposition-side lifting of a Reversible 5/3 type filter.

FIG. 30 shows a case where the coordinate value of the end point of a tile is an even number.
FIG. 4 is a tree diagram schematically showing a decomposition-side lifting of a Reversible 5/3 type filter.

FIG. 31 is a tree diagram schematically showing the composite-side lifting of the Reversible 5 / 3-type filter when the coordinate value of the starting point of the conversion tile is an even number.

FIG. 32 is a tree diagram schematically showing the composite-side lifting of the Reversible 5 / 3-type filter when the coordinate value of the start point of the conversion tile is an odd number.

FIG. 33 is a tree diagram schematically illustrating lifting on the synthesis side of the Reversible 5/3 type filter when the coordinate value of the end point of the conversion tile is an even number.

FIG. 34 is a tree diagram schematically showing the composite-side lifting of the Reversible 5/3 type filter when the coordinate value of the end point of the conversion tile is an odd number.

FIG. 35: When the coordinate value of the starting point of the tile is an even number
FIG. 4 is a tree diagram schematically showing the decomposition side lifting of the Daubechies 9/7 type filter.

FIG. 36 shows a case where the coordinate value of the starting point of a tile is an odd number.
FIG. 4 is a tree diagram schematically showing the decomposition side lifting of the Daubechies 9/7 type filter.

FIG. 37 shows a case where the coordinate value of the end point of a tile is an even number.
FIG. 4 is a tree diagram schematically showing the decomposition side lifting of the Daubechies 9/7 type filter.

FIG. 38: When the coordinate value of the end point of a tile is an odd number,
FIG. 4 is a tree diagram schematically showing the decomposition side lifting of the Daubechies 9/7 type filter.

FIG. 39 is a tree diagram schematically illustrating lifting on the synthesis side of the Daubechies 9 / 7-type filter when the coordinate value of the start point of the conversion tile is an even number.

FIG. 40 is a tree diagram schematically illustrating lifting on the synthesis side of the Daubechies 9 / 7-type filter when the coordinate value of the start point of the conversion tile is an odd number.

FIG. 41 is a tree diagram schematically illustrating lifting on the synthesis side of the Daubechies 9 / 7-type filter when the coordinate value of the end point of the conversion tile is an even number.

FIG. 42 is a tree diagram schematically showing lifting on the synthesis side of the Daubechies 9 / 7-type filter when the coordinate value of the end point of the conversion tile is an odd number.

FIG. 43 is a conceptual diagram showing a line-based wavelet.

FIG. 44 is a conceptual diagram showing an inverse line-based wavelet.

FIG. 45 is a block diagram showing a line memory.

[Explanation of symbols]

X (s) Data before wavelet transform using s as coordinate values (s is an integer) Y (t) Data after wavelet transform using t as coordinate values (t is an integer)

Claims (15)

[Claims] 1. A method of converting first data given for each coordinate in a region given discrete coordinates including a pair of end points to obtain second data for each coordinate, The second data corresponding to the first coordinates in the area adjacent to the coordinates of the end point is adopted as the second data in the second coordinates symmetrical to the first coordinates with respect to the coordinates of the one end point. Lifting method characterized by doing. 2. The lifting method according to claim 1, wherein said conversion is performed based on an odd number of said data to obtain one said converted data. 3. The lifting method according to claim 2, wherein the transform is a wavelet transform using a Reversible 5/3 type filter. 4. The lifting method according to claim 3, wherein the coordinate value of the one end point is an even number. 5. The lifting method according to claim 2, wherein the transform is an inverse wavelet transform using a Reversible 5/3 type filter. 6. The lifting method according to claim 5, wherein the coordinate value of the one end point is an odd number. 7. A method of converting first data given for each coordinate in a region given discrete coordinates including a pair of end points to obtain second data for each coordinate, Third data is calculated for each of the coordinates during the conversion from the first data to the second data. A lifting method, wherein the third data is adopted as second data at a second coordinate symmetric to the first coordinate with respect to the coordinates of the one end point. 8. The lifting method according to claim 7, wherein the transform is a wavelet transform using a Daubechies 9/7 type filter. 9. The lifting method according to claim 8, wherein the coordinate value of the one end point is an even number. 10. The coordinate value of the one end point is an odd number.
The lifting method according to claim 8. 11. The lifting method according to claim 10, wherein the first data corresponding to the first coordinates is adopted as the first data at the second coordinates. 12. The lifting method according to claim 7, wherein the transform is an inverse wavelet transform using a Daubechies 9/7 type filter. 13. The coordinate value of the one end point is an even number.
The lifting method according to claim 12. 14. The coordinate value of the one end point is an odd number.
The lifting method according to claim 12. 15. The lifting method according to claim 14, wherein the second data corresponding to the first coordinates is adopted as the second data at the second coordinates.