JP7339903B2 - Image processing device and hologram recording/reproducing device - Google Patents

Description

The present invention relates to an image processing apparatus and a hologram recording/reproducing apparatus, and more particularly, to an image processing apparatus for estimating the amplitude or phase deviation (noise) generated in the in-plane direction of a hologram, and a hologram recording using the image processing apparatus. It relates to a playback device.

The hologram memory uses image data called page data obtained by two-dimensionally modulating (encoding) a bit string for recording and reproduction. A signal light modulated by an SLM (Spatial Light Modulator) that displays page data and an unmodulated reference light are simultaneously irradiated onto a hologram recording medium, and interference fringes (holograms) generated at that time are recorded. Data is recorded by writing to a recording medium. During reproduction, by irradiating the recorded interference fringes with reference light, the data carried by the original signal light can be reproduced as diffracted light, which is imaged by a camera and read out.

A hologram memory is characterized by a high transfer rate because two-dimensional information can be collectively recorded or reproduced by a single light irradiation. In addition, the hologram recording apparatus can record multiple holograms at the same location by using various multiplexing methods such as angle multiplexing, phase code multiplexing, and spherical reference beam shift multiplexing, thereby recording information at high density. be able to. In recent years, in order to further increase the storage capacity, the page data has been changed from the conventional binary code to a multi-level code to increase the amount of information. A recording/reproducing method combining amplitude modulation and phase modulation has been proposed (Non-Patent Document 1).

FIG. 19 shows an example of a hologram recording/reproducing apparatus that performs amplitude modulation and phase modulation.

First, data recording in the hologram recording/reproducing apparatus 100 will be described. A laser beam generated by a laser light source 101 advances through a lens 102, a beam splitter (BS) 103, and a beam splitter (BS) 104 in that order, and is split into two by the beam splitter (BS) 104. FIG. A laser beam reflected by a beam splitter (BS) 104 passes through an amplitude modulating SLM 105, a lens 106, a phase modulating SLM 107, and a lens 108, and reaches a recording medium 109 as modulated signal light. Here, the amplitude modulation SLM 105 modulates the amplitude of the laser light to add information (data), and the phase modulation SLM 107 modulates the phase of the laser light to add information. On the other hand, the light transmitted through the beam splitter (BS) 104 is reflected by the mirrors 110 and 111 and reaches the recording medium 109 as unmodulated reference light. Data is recorded on the recording medium 109 as interference fringes (holograms) generated by interference between the signal light and the reference light.

Next, reading of data in the hologram recording/reproducing apparatus 100, that is, reproduction of a hologram will be described. When reproducing the hologram, the laser light generated by the laser light source 101 travels along the path of the lens 102, the beam splitter (BS) 103, the beam splitter (BS) 104, the mirrors 110 and 111, and reaches the recording medium 109 as reference light. is irradiated to Data recorded in the recording medium 109 is reproduced as a hologram (diffracted light) by the irradiated reference light. The reproduced hologram is transmitted through a lens 112 and a beam splitter (BS) 113 and acquired as image data by a camera (imaging device) 114 . The image data is analyzed and decoded by the arithmetic unit 120, and the recorded data (bit string) is restored and read out. These optical systems are examples of hologram reproducing means.

Amplitude information obtained by amplitude modulation can be obtained directly by the camera 114 as intensity information (brightness information) of the reproduced light. remove it. That is, during reproduction, the probe light adjusted by the correction phase modulation SLM 115 so that there is no phase unevenness in the beam plane of the laser light source 101 is applied to the reproduction light diffracted by the recording medium 109 due to the irradiation of the reference light. When the waves are combined, the light beams are constructive in the region of the same phase, and the light beams are canceled in the region of the opposite phase. The piezo modulator 116 changes the phase of the probe light to 0, π/2, π, and 3/2π, and the camera captures the combined light four times, and the 4-step phase shift method (for example, Patent Document 1) is performed. Phase information can be acquired from the intensity information by using it.

Since the page data has an area equivalent to 1 square inch, low-frequency noise and unevenness occur in the plane due to expansion/contraction and misalignment of the recording medium 109, distortion and aberration of the optical system, and the like. Therefore, as a modulation code, a method has been proposed in which bright spots and dark spots are determined within a certain range (modulation block consisting of a plurality of symbols) obtained by dividing page data, such as a differential code (Patent Document 2). ). Even if there are various conditions during playback and uneven brightness in the in-plane direction of the laser beam, the relative magnitude of the brightness value can be determined within the modulation block, which is a local range, resulting in unevenness that occurs throughout the page data. can be ignored to some extent. This is equally applicable as a phase modulation code. On the other hand, as the number of values increases, the amplitude value and phase value must be determined more accurately. Therefore, in addition to the use of differential codes, noise compensation technology is required.

For example, reference page data in which all pixel values are 255 (white pixels of 8-bit data) is recorded and reproduced in advance, and noise information superimposed on the page data surface is specified from the image acquired by the camera. A compensation method for amplitude noise has been proposed (Patent Document 3). Pixel values on which noise is superimposed fluctuate, so compensation can be achieved by dividing or subtracting the acquired noise information from the reproduced page data. Phase noise can be similarly compensated. In addition, it is also possible to obtain information on unevenness and noise generated in the plane by propagating through the optical system by directly imaging the page data displayed on the SLM multiple times with a camera without going through a recording medium. .

A method of not embedding specific known page data or symbols has also been proposed (Non-Patent Document 2). In the method of Non-Patent Document 2, a line thinner than the symbol size is used, and the phase noise is compensated for the reproduced data only by computation of spatial linear interpolation.

JP 2019-33467 A Japanese Patent No. 3209493 Japanese Patent No. 4863913

Teruyoshi Nobukawa and Takanori Nomura, "Multilevel recording of complex amplitude data pages in a holographic data storage system using digital holography," Opt. Express, Vol. 24, No. 18, (2016), pp. 21001-21011 Masatoshi Bunsen and Shosei Tateyama, "Detection method for the complex amplitude of a signal beam with intensity and phase modulation using the transport of intensity equation for holographic data storage," Optics Express, Vol. 27, No. 17, (2019), pp 24029-24042

However, in the method using reference page data (Patent Document 3), the reference page data must be recorded in advance, so the amount of information that can be recorded on the hologram recording medium is reduced by one page data. . In addition, calibration work for compensation is required before reproduction. In addition, since the recording medium and optical system expand and contract with temperature changes, accurate compensation cannot be performed if time has passed since calibration, or compensation is performed by frequently reproducing reference page data. I have to update the quantity. In particular, in phase modulation, the wavefront of the reproduction light is easily changed by the expansion and contraction of the recording medium, so the phase information cannot be accurately demodulated.

In addition, in the case of a method of performing compensation only by calculation from reproduced page data, it is necessary to configure one symbol with a relatively large size of about 10×10 pixels, and a fine and multi-pixel camera is required. Therefore, it is difficult to realize a system capable of large-capacity recording.

SUMMARY OF THE INVENTION Accordingly, an object of the present invention, which has been made in view of the above-described problems, is to reduce unevenness in amplitude or phase modulation in the plane of page data from a small number of samples (number of symbols) for page data reproduced by a hologram reproducing means. An object of the present invention is to provide an image processing device and a hologram recording/reproducing device capable of accurately obtaining an image.

In order to solve the above problems, an image processing apparatus according to the present invention is an image processing apparatus for processing page data reproduced by a hologram reproducing means, wherein a known amplitude value or phase value is obtained from the reproduced page data. and a known symbol extraction unit that outputs a reproduced amplitude value or phase value of the extracted symbol; and a frequency component of the page data or a page data noise estimating unit that obtains an aberration component of a wavefront by an optimization problem using compression sensing, and estimates amplitude or phase noise superimposed on the entire page data.

In the image processing apparatus, it is preferable that the page data noise estimator estimates noise by an optimization problem using a linear equation based on a two-dimensional basis function of inverse discrete cosine transform.

In the image processing apparatus, the page data noise estimator preferably estimates noise by an optimization problem using a linear equation based on a two-dimensional basis function of inverse discrete wavelet transform.

In the image processing apparatus, the page data noise estimator preferably estimates noise by an optimization problem using linear equations based on two-dimensional basis functions of Zernike polynomials.

Also, the image processing apparatus preferably processes page data in which symbols having known amplitude or phase values are arranged at regular intervals.

Also, the image processing apparatus preferably processes page data in which symbols having known amplitude or phase values are irregularly arranged according to an optimization problem using compressed sensing.

In addition, it is preferable that the image processing apparatus further includes a noise compensator for compensating the reproduced page data for amplitude or phase noise superimposed on the entire estimated page data.

Furthermore, in order to solve the above problems, a hologram recording/reproducing apparatus according to the present invention includes an optical system for recording and reproducing a hologram, the image processing apparatus described above, and a decoding section for decoding page data compensated for noise. It is characterized by

According to the image processing apparatus and the hologram recording/reproducing apparatus of the present invention, the amplitude or phase modulation unevenness in the page data surface of the page data reproduced by the hologram reproducing means can be accurately obtained from a small number of samples (the number of symbols). be able to.

1 is a conceptual diagram of an image processing apparatus of the present invention; FIG. It is an example of a pattern of unevenness/noise superimposed on page data. FIG. 4 is a diagram showing an example of page data composed of modulation blocks having known symbols at specific positions (same positions); FIG. 10 illustrates an example of a process of extracting known symbols from recovered page data of a 3×3 modulation block; This is noise estimated by resampling using known symbols embedded in every 3×3 symbols. FIG. 10 illustrates an example of a process for extracting known symbols from recovered page data of a 25×25 modulation block; This is noise estimated by resampling using known symbols embedded in every 25×25 symbols. FIG. 10 is a diagram showing a basis (8×8) of a two-dimensional discrete cosine transform; FIG. 4 is a diagram showing an image obtained by decomposing an image using two-dimensional discrete cosine transform; It is a figure which shows the inner product representation of inverse discrete cosine transform. FIG. 10 is a diagram showing an example of thinning of the basis B of the inverse discrete cosine transform; FIG. 10 illustrates the inner product representation of an optimization problem with compressed sensing; It is the noise estimated from the optimization problem with known symbols embedded every 3x3 symbols. Noise estimated from an optimization problem with known symbols embedded every 25×25 symbols. FIG. 10 is a diagram showing an example of page data in which known symbols are not arranged at regular intervals; FIG. 10 is a diagram showing an example of page data in which known symbols are arranged outside modulation blocks; This is noise estimated from an optimization problem in page data with different known symbol positions for every 3×3 symbols. It is a figure which shows the image which represented the image (wavefront aberration of light) with the Zernike polynomial. 1 is a diagram showing an example of a hologram recording/reproducing apparatus that performs amplitude modulation and phase modulation; FIG.

FIG. 1 shows a conceptual diagram of an image processing apparatus of the present invention. The image processing device 1 is a device for processing hologram page data, and includes a known symbol extraction unit 2, a page data noise estimation unit 3, and, if necessary, a noise compensation unit 4. The page data reproduced by the hologram reproducing means (for example, the optical system in FIG. 19) is input to the image processing apparatus 1 as image data. Note that the reproduced page data in the present invention means not only the page data recorded and reproduced on the hologram recording medium, but also the page data displayed on the SLM in the hologram recording/reproducing apparatus and transmitted through the camera (imaging device) through the hologram reproducing optical system. It may be the page data acquired in . The input page data partly contains a symbol having a known amplitude value or phase value as a reference. In order to simplify the explanation, in the case of the phase value, the page data that has undergone the process of obtaining the phase value by the 4-step phase shift method or the like and converting it into the amplitude value is input.

The known symbol extraction unit 2 extracts a symbol having a known amplitude value or phase value from input image data (page data), and extracts a reproduced amplitude value or phase value (reproduced information or phase value) of the extracted symbol. It may be called observation information.) is acquired and output to the page data noise estimation unit 3 .

As will be described later, the page data noise estimator 3 estimates amplitude or phase noise superimposed on the entire page data by resampling or compressed sensing, and outputs the estimated noise to the noise compensator 4 .

The noise compensator 4 removes (subtracts or divides) the noise estimated by the page data noise estimator 3 from the input image data (reproduced page data), thereby compensating for noise-compensated image data. (page data) is output as output data of the image processing apparatus 1 .

FIG. 2 shows an example of patterns of unevenness/noise (for example, phase noise) superimposed on page data specified in the present invention. In this specification and drawings, phase noise is also shown as being visually recognizable by converting it into image intensity. FIG. 2 shows phase noise obtained using a conventional method of recording and reproducing page data in which the phases of all symbols are set to 0 in advance. Low frequency (image frequency) noise is superimposed over the entire page data.

Amplitude noise can also be obtained by recording and reproducing page data in which all symbols are white pixels (for example, the pixel value is 255). Amplitude noise superimposed on the page data surface is also low-frequency noise, similar to phase noise. In the following description, phase noise will be mainly described, but amplitude noise can be treated in exactly the same way.

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described below.

(First embodiment)
In the present invention, a symbol having a known amplitude value or phase value (hereinafter sometimes referred to as "known symbol") is embedded in page data. In the first embodiment, for example, a modulation block is composed of a predetermined number of symbols, and a code is used in which a specific symbol position in the block is a known symbol. FIG. 3 is an example of page data composed of modulation blocks having known symbols at specific positions (same positions). The page data 10 is composed of a modulation block 11 (indicated by a thick frame) consisting of 3×3 symbols, and the center of the modulation block 11 is a known symbol 12 (indicated by a black symbol). The phase is assumed to be 0. Note that the known symbol 12 may be a symbol whose amplitude value is known.

FIG. 4 is an example of a process for extracting known symbols from recovered page data of a 3×3 modulation block. Page data (phase data) 10 of N×N (the number of symbols on one side is N) obtained by recording and reproducing with a modulation code composed of a 3×3 modulation block 11 having a known symbol (phase 0) 12 at the center. It is shown on the left side of FIG. This corresponds to the input image data of the image processing apparatus 1 in FIG. Known symbols are included at regular intervals (every three symbols) in both the vertical and horizontal directions. For noise estimation, only reproduced information (here, phase information) of known symbols within the page data surface is used.

Therefore, for noise estimation, only 1/9 of the symbols in the page data are extracted as having valid information. By thinning out regions where information is not known (symbols not used for noise estimation) and arranging them closely, an observed image G20 (on the right side of FIG. 4) with the number of elements (the number of symbols) of M×M can be created. This extraction work is performed by the known symbol extraction unit 2 of the image processing apparatus 1 shown in FIG.

Next, the noise of the entire page data is estimated from the reproduced information of the extracted known symbols. In this embodiment, for example, the image G (M×M) 20 is subjected to image enlargement processing using interpolation or extrapolation so that the number of symbols is nine times as large as possible, thereby estimating the noise superimposed on the entire page data. can. As the processing, for example, a method of interpolating by resampling (sampling corresponding to the number of enlarged symbols) such as bilinear interpolation (bilinear) or bicubic interpolation (bicubic) can be used when enlarging an image. The page data noise estimating section 3 of the image processing apparatus 1 in FIG.

FIG. 5 shows noise estimated by resampling using known symbols embedded in every 3×3 symbols. FIG. 5 actually shows the page data with N=75 using the 3×3 modulation block (FIG. 3). This is the result of obtaining the phase (phase noise) of . A pattern equivalent to the noise pattern in FIG. 2 is obtained. MSE (Mean Squared Error) was used as an index for quantitative evaluation of noise estimation. The MSE is represented by the following equation (1) based on the actual signal x and the estimated signal x _est (in the equation, x is indicated by adding ^).

A smaller MSE value indicates more accurate estimation. For noise estimated using a modulation code with one known symbol in a modulation block of 3×3 symbols (FIG. 5), the MSE was 4.02.

As another example of noise estimation, an evaluation experiment was performed with a modulation block size of 25×25. FIG. 6 is an example of a process for extracting known symbols from recovered page data of 25×25 modulated blocks. N×N (75×75) page data 10 obtained by recording with a modulation code in which one known symbol is provided at the center of a modulation block of 25×25 symbols and reproduced is shown on the left side of FIG. At this time, only 1/625 of all the symbols in the page data 10 are known symbols having valid information. The right side of FIG. 6 shows an observation image G21 having the number of elements M×M (3×3) in which the known symbols are extracted and the symbols not used for noise estimation are thinned out and arranged.

The noise of the entire page data was estimated from the reproduction information of the extracted known symbols in FIG. 6 by image enlargement processing using interpolation or extrapolation. FIG. 7 shows noise estimated by resampling using known symbols embedded every 25×25 symbols. Due to the feature that the superimposed noise (phase noise) has low frequency components, the noise distribution of the entire page data can be estimated even if the number of samples is small. As a result of evaluating this noise estimation, the MSE was 36.8.

After the noise estimation process, noise compensation can be performed if necessary. For example, the noise compensation unit 4 of the image processing device 1 in FIG. processing) and perform noise compensation.

According to this embodiment, amplitude or phase noise (unevenness) superimposed on each symbol forming the page data can be almost accurately specified from a small amount of known amplitude or phase information embedded in the page data. Therefore, the amplitude value or phase value of the symbol can be estimated without significantly reducing the amount of information that can be recorded on the hologram recording medium, compared to using the entire page data as a reference. Furthermore, by subtracting or dividing the page data image acquired by the camera by the estimated amplitude or phase unevenness, the amplitude or phase unevenness can be compensated.

(Second embodiment)
In a second embodiment, compressed sensing is used to estimate the noise (eg, phase noise) across the page data. Compressed sensing is a technology that can restore target data from observed (reproduced) data with fewer unknowns than the required number of unknowns, if the target data to be estimated is sparse. When applied to this embodiment, the observed data are phase values corresponding to the number of known symbols, and the data to be estimated are the phase values (phase noise) of all the symbols in the page data. For example, when the modulation block of 3×3 symbols in FIG. 3 is used, the number of observed data is only 1/9 of the estimation target data. However, since the data to be estimated has sparseness, accurate estimation is possible.

The amplitude information or phase information of the entire page data to be estimated is two-dimensional image information. A two-dimensional image acquired by a camera is sparse in terms of frequency. For example, JPEG (Joint Photographic Expert Group) used for image compression uses discrete cosine transform, and JPEG2000 uses discrete wavelet transform to transform signals into the frequency domain and remove unnecessary frequency information that takes values close to 0. The image data is compressed by making it a sparse signal. In particular, in the case of in-plane noise (for example, phase noise) that is the object of compensation in the present invention, the noise consists of extremely low-frequency components, so even if the number of observation data to be obtained is extremely small, Also, the phase value of the entire page data can be estimated with high accuracy by compressed sensing.

In this embodiment, the discrete cosine transform is used for transforming the image. FIG. 8 shows the basis (8×8) of the two-dimensional discrete cosine transform. A discrete cosine transform is possible by decomposing the image into each frequency component that the basis contains. FIG. 9 shows an image obtained by decomposing an image using two-dimensional discrete cosine transform.

The original information can be restored by inverse transforming the elements (coefficients) of each frequency component obtained by the discrete cosine transform. Using this, the image data can be represented by the product of the basis B of the inverse discrete cosine transform and the sparse elements obtained by the discrete cosine transform. In particular, by making a one-dimensional vector (N ² , 1) obtained by rearranging the elements of the image data of the number of pixels N×N in raster scan order, the image is converted into a one-dimensional vector of the basis B of the inverse discrete cosine transform and the elements. can be expressed by the inner product of

FIG. 10 shows the inner product representation of the inverse discrete cosine transform. The left side of the equation shown in FIG. 10 is an image with N×N pixels, the left side of the right side is the basis B (N ² ×N ² ) of the inverse discrete cosine transform, and the right side of the right side is the frequency components of the image. A one-dimensional vector (N ² ×1) of elements is shown. The one-dimensional vector of the elements on the right side is actually a vector in which each element (coefficient) is arranged in a line. It has numerical values and expresses that the elements of high frequency components (lower side) are almost 0 (sparse). Therefore, the inverse discrete cosine transform formula in FIG. 10 is represented by a linear function of the form y=ax (where y, a, and x are vectors; the same applies hereinafter). Note that ^the image with ^the number of pixels N×N on the left side ^of FIG ^. are rearranged into (N×N).

Compressive sensing utilizes the fact that x is sparse when solving linear simultaneous one-dimensional equations such as y=ax. i.e.

is solved (Basis Pursuit method), an estimated solution x _est (in the formula, x is indicated by adding ^) can be obtained. On the other hand, considering that there are other noise components w (camera thermal noise, etc.) in addition to the noise to be estimated, this model can be expressed as y=ax+w. This solution is obtained from the optimization problem of Equation (3), called LASSO (Least absolute shrinkage and selection operator) regression.

When applied to this embodiment, the relationship G=Bx is obtained. First, since the observation image G has only the number M ² of known symbols in the page data as elements, the number of rows of the base B of the inverse discrete cosine transform is Thinning is performed so as to match M ² , and a new base B′ is created. At that time, the line at the same position as the observed image G is left and thinned out so that the linear relationship is satisfied. FIG. 11 shows an example of the relationship between the known symbol position (a) in the page data and the decimation (b) of the base B of the inverse discrete cosine transform.

Furthermore, by using an image G′ obtained by rearranging the observed image G (the number of pixels M×M) in raster scan order, it can be expressed by the inner product of matrices G′=B′×x. FIG. 12 shows the inner product representation of the optimization problem with compressed sensing. The left side of the equation shown in FIG. 12 is the image G′ (M ² ×1) rearranged in raster scan order, and the left side of the right side is the base B′ (M ² ×N ² ) of the decimated inverse discrete cosine transform. , and the right side of the right side indicates the one-dimensional vector x(N ² ×1) of the elements of each frequency component of the image. Note that the one-dimensional vector x is actually a vector in which each element (coefficient) is arranged in a line. sparse).

The equation G'=B'·x shown in FIG. 12 can similarly estimate the solution x _est (that is, the frequency component of the page data) by the LASSO regression described above. Then, the noise (phase noise) superimposed on the entire page data can be estimated by the inner product of the base B of the inverse discrete cosine transform and the obtained solution x _est . That is, noise can be estimated by an optimization problem using a linear equation based on a two-dimensional basis function.

The page data (N×N) in which the center symbol of the modulation block composed of 3×3 symbols in FIG. 3 is known was evaluated with N=75 as in the first embodiment. Since a known symbol exists every three symbols in both the vertical and horizontal directions, the known symbol image G (M×M) is M=25. Phase noise was estimated by solving the LASSO regression optimization problem for the equation G'=B'.x shown in FIG. FIG. 13 shows the noise estimated from the optimization problem with known symbols embedded every 3×3 symbols. A pattern equivalent to the noise pattern in FIG. 2 is obtained. The MSE, which is a quantitative evaluation index, was 2.48, and although the calculation was more complicated than in the first embodiment, the phase noise of the entire page data could be estimated with higher accuracy.

A similar evaluation was also made when the size of the modulation block was set to 25×25. Figure 14 shows the noise estimated from the optimization problem with known symbols embedded every 25x25 symbols. A pattern equivalent to the noise pattern in FIG. 2 was obtained, and the MSE, which is a quantitative evaluation index, was 26.8. As a result, even when the number of known symbols is small, it is possible to estimate noise (phase distribution) with high accuracy by compressed sensing.

A case of performing noise estimation according to the second embodiment in the image processing apparatus 1 of FIG. 1 will be described.

Image data (N×N) including known symbols is input to the image processing apparatus 1 . The known symbol extractor 2 extracts known symbols from the image data and outputs them to the page data noise estimator 3 as an observed image G (M×M).

The page data noise estimation unit 3 generates an image G′ by rearranging the observed image G, and generates a thinned base B′ corresponding to known symbols based on the base B of the inverse discrete cosine transform, The solution x _est (that is, the frequency component of the page data) is estimated and obtained from the above equation G′=B′·x by an optimization problem using compressed sensing. Furthermore, the noise superimposed on the entire page data is estimated by the inner product of the base B of the inverse discrete cosine transform and the solution x _est , and is output to the noise compensator 4 .

If necessary, the noise compensator 4 removes noise estimated by the page data noise estimator 3 from the page data input to the image processing device 1 (for example, subtraction or division). Perform noise compensation.

According to the second embodiment, it is possible to accurately identify amplitude or phase unevenness superimposed on each symbol forming page data from a small amount of known amplitude or phase information embedded in page data. In addition, the estimation method using compressed sensing can estimate the phase noise of the entire page data with higher accuracy than the noise image resampling (image enlargement by interpolation) method. Therefore, the amplitude value or phase value of the symbol can be compensated without greatly reducing the amount of information that can be recorded on the hologram recording medium.

(Third embodiment)
The third embodiment uses compressed sensing to estimate the noise of the entire page data as in the second embodiment. is performed.

FIG. 15 shows an example of page data 10 in which known symbols 12 are not arranged at regular intervals. This is the case when a modulation code is used in which the symbol at the same position in the modulation block is not necessarily the known symbol 12 . Also, FIG. 16 is an example of page data 10 in which known symbols 12 are arranged outside the modulation block 11 . By using a known symbol 12 as a sync pattern for detecting the position of the entire page data, a known signal is generated outside the modulation block 11 (consisting of 3×3 symbols and arranged with adjacent symbols shifted from each other). symbol 12 is embedded. In such a case, the known symbol positions are not arranged at regular intervals within the page data, and it is difficult to estimate the phase of the entire page data by interpolation/extrapolation as in the first embodiment.

On the other hand, in the compressed sensing method, an estimated solution can be obtained if only the positions of known symbols are known. In the example of FIG. 15, the known symbol position is different for each modulation block composed of 3×3 symbols, but the position of each known symbol 12 is known, and each It is possible to extract the known symbol 12 and obtain its reproduction information. Therefore, the observed pixel values of the known symbol 12 are arranged in a predetermined order (for example, raster scan order) to create an image G' (M ² ×1). Further, since the position of the known symbol 12 is grasped, as in FIG. 11(b), the row corresponding to the position of the known symbol is left from the base B of the inverse discrete cosine transform, and the other rows are thinned out. , to form the basis B'(M ² ×N ² ) of the decimated inverse discrete cosine transform. From these G' and B', the equation G'=B'x shown in FIG. 12 can be derived, and is solved by an optimization problem using compressed sensing as in the second embodiment, for example, by LASSO regression. x _est can be estimated. Then, the phase noise superimposed on the entire page data can be estimated by the inner product of the base B of the inverse discrete cosine transform and the obtained solution x _est .

FIG. 17 shows the noise estimated from the optimization problem in the page data 10 with different known symbol positions for every 3×3 symbols. A pattern equivalent to the noise pattern in FIG. 2 was obtained, and the MSE, which is a quantitative evaluation index for the phase information of the entire page data, was calculated to be 1.34. Therefore, even when the known symbols are arranged irregularly, it can be estimated with the same accuracy as when the known symbols are embedded at regular intervals.

In this way, when compressed sensing is used, even if the symbols in which known amplitude or phase information is embedded are not arranged at regular intervals, the amplitude or phase unevenness of the entire page data can be accurately calculated.

A case of performing noise estimation according to the third embodiment in the image processing apparatus 1 of FIG. 1 will be described.

Image data (page data) including irregularly arranged known symbols is input to the image processing apparatus 1 . The known symbol extraction unit 2 extracts known symbols arranged irregularly from the image data and outputs the reproduction information to the page data noise estimation unit 3 .

The page data noise estimating unit 3 generates an image G' from the reproduced information of the irregularly arranged known symbols, and based on the base B of the inverse discrete cosine transform, the base B is thinned out corresponding to the known symbols. ', and the solution x _est (that is, the frequency component of the page data) is estimated and obtained from the above equation G'=B'·x by the optimization problem using compressed sensing. Furthermore, the phase noise superimposed on the entire page data is estimated by the inner product of the base B of the inverse discrete cosine transform and the solution x _est , and is output to the noise compensator 4 .

If necessary, the noise compensator 4 removes noise estimated by the page data noise estimator 3 from the page data input to the image processing device 1 (for example, subtraction or division). Perform noise compensation.

According to the third embodiment, amplitude or phase unevenness superimposed on each symbol forming the page data can be accurately identified from a small amount of known amplitude or phase information irregularly embedded in the page data. Therefore, any known symbol arrangement can be used without being limited to a specific modulation block, increasing the degree of freedom in encoding page data. Also, as in the second embodiment, the phase noise of the entire page data can be estimated with higher accuracy than the noise image resampling method. Therefore, the amplitude value or phase value of the symbol can be compensated without greatly reducing the amount of information that can be recorded on the hologram recording medium.

(Fourth embodiment)
In the fourth embodiment, discrete wavelet transform is used for image transform. That is, an image is decomposed into high-frequency components and low-frequency components in multiple stages by two-dimensional discrete wavelet transform, and amplitude or phase noise in the in-plane direction is estimated. By using the discrete wavelet transform instead of the discrete cosine transform, noise can be estimated by a process equivalent to that of the second or third embodiment.

That is, image data (page data) including known symbols arranged regularly or irregularly is input to the image processing apparatus 1 . The known symbol extractor 2 extracts known symbols from image data and outputs the reproduced information to the page data noise estimator 3 .

The page data noise estimator 3 uses the image obtained from the reproduced information of the known symbol, the basis of the inverse discrete wavelet transform thinned corresponding to the known symbol, and each element (coefficient) corresponding to the discrete wavelet basis. , a linear equation is created, and the solution x _est (that is, each element (coefficient) corresponding to the discrete wavelet basis corresponding to the frequency component of the page data) is estimated and obtained by an optimization problem using compressed sensing. Further, the noise superimposed on the entire page data is estimated by the inner product of the base of the inverse discrete wavelet transform and the solution x _est , and output to the noise compensator 4 .

If necessary, the noise compensator 4 removes noise estimated by the page data noise estimator 3 from the page data input to the image processing device 1 (for example, subtraction or division). Perform noise compensation.

According to the fourth embodiment, the amplitude or phase unevenness superimposed on each symbol forming the page data can be accurately detected from a small amount of known amplitude or phase information regularly or irregularly embedded in the page data. can be identified.

(Fifth embodiment)
The fifth embodiment uses compressed sensing to estimate noise (for example, phase information) of the entire page data as in the second to fourth embodiments, but uses Zernike polynomials for image transformation. noise estimation.

In the second and third embodiments, the sparsification is performed by using the basis of the inverse discrete cosine transform, and in the fourth embodiment, by using the basis of the inverse discrete wavelet transform. On the other hand, the noise (particularly, phase noise) that is the object of estimation in the present invention is due to expansion/contraction of the recording medium and aberrations of lenses and the like included in the optical system. The wavefront aberration of such light can be expanded and represented by Zernike polynomials. The basis of each term represents tilt aberration, coma aberration, spherical aberration, and the like. The in-plane noise (for example, phase noise) to be estimated by the present invention contains almost no complex high-order term components, and is dominated by low-order term components and has sparsity. Therefore, wavefront expansion by Zernike polynomials can be used to estimate unevenness/noise in the page data plane from a small number of known symbols.

FIG. 18 shows an image (wavefront aberration of light) represented by Zernike polynomials. If each coefficient of the Zernike polynomial is known in this way, it is possible to express the in-plane noise, which is the estimation target of the present invention. That is, each basis of the Zernike polynomials is made one-dimensional, and the matrix combined in the row direction is used as the basis, and the optimization problem using compressed sensing is solved by the same method as in the second to fourth embodiments. , the amplitude information or phase information in the page data plane can be estimated with high accuracy.

That is, image data (reproduced page data) including known symbols arranged regularly or irregularly is input to the image processing apparatus 1 . The known symbol extractor 2 extracts known symbols from image data and outputs the reproduced information to the page data noise estimator 3 .

The page data noise estimator 3 creates a linear equation from the image obtained from the reproduced information of the known symbol, the basis of the Zernike polynomial corresponding to the known symbol, and each element (coefficient) of the Zernike polynomial, and performs compressed sensing. A solution x _est (that is, each element (coefficient) of the Zernike polynomial obtained when the unevenness/noise in the page data surface is expanded by the Zernike polynomial) is estimated and obtained by the optimization problem used. Furthermore, by performing wave field synthesis from the Zernike polynomials based on the solution x _est , the noise superimposed on the entire page data is estimated and output to the noise compensator 4 .

If necessary, the noise compensator 4 removes noise estimated by the page data noise estimator 3 from the page data input to the image processing device 1 (for example, subtraction or division). Perform noise compensation.

According to the fifth embodiment, the unevenness of amplitude or phase superimposed on each symbol forming the page data can be accurately detected from a small amount of known amplitude or phase information regularly or irregularly embedded in the page data. can be identified. In addition, by representing the wavefront aberration of light with a Zernike polynomial, it is possible to perform conversion with a high degree of approximation with a small number of terms, and to accurately calculate the unevenness of the amplitude or phase of the entire page data.

(Sixth embodiment)
In the hologram recording/reproducing apparatus 100 shown in FIG. 19, the image processing apparatus 1 shown in FIG. 1 is incorporated in the arithmetic unit 120 that reproduces the hologram. The image processing apparatus 1 may perform any processing of the first to fifth embodiments.

Page data containing known symbols is reproduced by, for example, the optical system shown in FIG. In the arithmetic device 120, the page data is first input to the image processing device 1 shown in FIG. 1, where the in-plane noise (amplitude noise or phase noise) is estimated and noise-compensated.

Thereafter, the decoding unit in the arithmetic unit 120 reads the modulated block from the noise-compensated page data, performs decoding processing to decode the modulated block, and restores the recorded data (bit string). be done.

According to this embodiment, since the image processing device 1 performs noise compensation, the hologram recording/reproducing device 100 can restore recorded data with high precision.

Although the configuration and operation of the image processing apparatus 1 have been described in the above-described first embodiment, the present invention is not limited to this. It may be configured as an estimation method for estimating phase modulation unevenness/noise. That is, according to the data flow of FIG. 1, a step of extracting known symbols from the image data, and amplitude or phase noise superimposed on the page data surface from the amplitude or phase values of the known symbols is extracted using resampling. estimating by an image interpolation/extrapolation method.

Further, in the above-described second to fifth embodiments, the configuration and operation of the image processing apparatus 1 have been described, but the present invention is not limited to this. It may be configured as an estimation method for estimating in-plane amplitude or phase modulation unevenness/noise. That is, according to the data flow of FIG. 1, a step of extracting known symbols from the image data, and from the amplitude value or phase value of the known symbols, the amplitude or phase noise superimposed on the page data surface is detected using compressed sensing. and estimating by an optimization problem.

A computer can be suitably used to function as the image processing apparatus 1 described above. , and the program is read and executed by the CPU of the computer. This program can be recorded on a computer-readable recording medium.

Although the above embodiments have been described as representative examples, it will be apparent to those skilled in the art that many modifications and substitutions may be made within the spirit and scope of the invention. Therefore, the present invention should not be construed as limited by the embodiments described above, and various modifications and changes are possible without departing from the scope of the appended claims. For example, it is possible to combine a plurality of configuration blocks described in the embodiments into one or divide one configuration block.

1 image processing device 2 known symbol extraction unit 3 page data noise estimation unit 4 noise compensation unit 100 hologram recording/reproducing device 101 laser light source 102 lens 103 beam splitter (BS)
104 beam splitter (BS)
105 amplitude modulation SLM
106 lens 107 phase modulation SLM
108 lens 109 recording medium 110 mirror 111 mirror 112 lens 113 beam splitter (BS)
114 camera (imaging device)
115 corrective phase-modulating SLM
116 piezo modulator 120 computing device

Claims (8)

An image processing device for processing page data reproduced by a hologram reproducing means,
a known symbol extraction unit that extracts a symbol having a known amplitude value or phase value from the reproduced page data and outputs the reproduced amplitude value or phase value of the extracted symbol;
From the extracted amplitude value or phase value of the symbol, the frequency component or wavefront aberration component of the page data is obtained by an optimization problem using compression sensing, and the amplitude or phase noise superimposed on the entire page data is estimated. a page data noise estimator that
An image processing device comprising: The image processing device according to claim 1 ,
The image processing apparatus according to claim 1, wherein the page data noise estimator estimates noise by an optimization problem using a linear equation based on a two-dimensional basis function of an inverse discrete cosine transform. The image processing device according to claim 1 ,
The image processing apparatus, wherein the page data noise estimator estimates noise by an optimization problem using a linear equation based on a two-dimensional basis function of an inverse discrete wavelet transform. The image processing device according to claim 1 ,
The image processing apparatus according to claim 1, wherein the page data noise estimator estimates noise by an optimization problem using a linear equation based on two-dimensional basis functions of Zernike polynomials. The image processing device according to any one of claims 1 to 4 ,
An image processing apparatus for processing page data in which symbols having known amplitude or phase values are arranged at regular intervals. The image processing device according to any one of claims 1 to 4 ,
An image processing apparatus for processing page data in which symbols having known amplitude or phase values are arranged irregularly. The image processing device according to any one of claims 1 to 6 ,
An image processing apparatus, further comprising: a noise compensator for compensating amplitude or phase noise superimposed on the entire estimated page data with respect to the reproduced page data. A hologram recording/reproducing apparatus comprising: an optical system for recording/reproducing a hologram; the image processing apparatus according to claim 7 ; and a decoding section for decoding noise-compensated page data.

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