CN111862256B - Wavelet sparse basis optimization method in compressed sensing image reconstruction - Google Patents
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Abstract
The invention discloses a wavelet sparse basis optimization method in compressed sensing image reconstruction. In compressed perceptual image reconstruction, discrete wavelet transforms are typically used as a signal sparsity decomposition basis to make the original signal more sparse. However, to reconstruct higher quality images at lower sampling rates, the sparse representation performance of discrete wavelet transforms is often not good enough. Based on the characteristic that the coefficient distribution of the image column signals in the wavelet domain is approximately exponentially attenuated, the invention designs a corresponding suppression matrix with the exponential attenuation distribution of the diagonal elements as multiplication factors to be added into the wavelet decomposition base. By selecting proper inhibition parameters through experiments to achieve relatively optimal experimental results, compared with the traditional mode before wavelet base optimization, the method not only effectively improves the sparseness of wavelet coefficients, but also improves the peak signal-to-noise ratio of a reconstructed image by 1.5-2.5 dB, and the performance and the effectiveness of the method have been tested and proved through experiments.
Description
Technical Field
The invention relates to a wavelet sparse basis optimization method based on an exponential decay function in compressed sensing image reconstruction, which is characterized in that a suppression matrix with diagonal elements in exponential decay distribution is used as a multiplication factor to be added into discrete wavelet transformation, so that coefficients of an original non-sparse signal in a wavelet domain become coefficients which are more close to exponential distribution and are more sparse, and the quality and the precision of an original image reconstructed by a compressed sensing signal reconstruction algorithm are effectively improved by the optimized discrete wavelet transformation. The novel method provided by the invention can be applied to the directions of signal acquisition and recovery, image processing, computer vision and the like, and belongs to the field of signal recovery and reconstruction in signal and information processing.
Background
Compressed sensing (Compressed Sensing, CS) theory was proposed by Donoho, candys et al in 2006, the core idea of compressed sensing is to combine compression and sampling of signals on the premise that the original signals are sparse or can be sparsely represented, and the linear projection values of the signals are directly obtained with fewer sampling times through a measurement matrix. The compressed sensing sampling does not pass through the intermediate stage of Nyquist sampling (Nyquist) to realize the dimension compression of the signal, and then the original signal is directly restored and reconstructed by the measured value according to the corresponding reconstruction algorithm, so that the transmission and storage cost is saved, and the calculation complexity is reduced. The compressed sensing theory samples the signal at a frequency lower than Nyquist sampling (Nyquist), and has high compressibility and recoverability, so that the compressed sensing is widely applied in the field of signal processing.
In the process of compressed sensing sampling, an original signal x, x epsilon C is defined first n Multiplying x by m×n measurement matrix Φ to obtain measurement signal y, y∈C m M < n. The following signal measurement model is then present:
y＝Φx+e， (1)
e is gaussian white noise and y is an incomplete (unrercomplete) linear measurement of the original signal x obtained by the measurement matrix.
The recovery process of the original signal corresponds to the inverse of the signal measurement. The original signal x is recovered from the signal measurement y, and since the dimension of y is much smaller than that of signal x, an under-determined equation must be solved. Since solving the under-determined equation is often very difficult, the original signal x must be sparse or capable of sparse representation. The sparsity of discrete signals is typically represented by the L0 norm of the signal, |x| 0 The number of non-zero elements in x is indicated. However, sparse signals do not necessarily require that the original signal have few non-zero values, and some documents suggest that such an original signal may be considered approximately as a sparse signal when the elements in the original signal are arranged in a large to small order that can approximately exhibit an exponentially decaying distribution. The zero norm of the original signal x can be used as a regularization term for equation (1), so we can obtain the following expression:
wherein epsilon is a non-negative normal number, which is the upper error bound.Representing the approximation error of the reconstructed signal and the real signal.
If the original signal x is non-sparse, the signal x must be sparsely represented. We use sparse variationalSparse representation of x by replacing an orthogonal basis or redundant dictionary ψ, ψ= [ ψ ] 1 ,ψ 2 ,ψ 3 ,…,ψ n ]. Thus, there are:
wherein s= [ s ] 1 ,s 2 ,s 3 ,…,s n ] T S is the sparse representation coefficient of signal x on sparse basis ψ [] T Is the transpose operator. If most of the coefficients in s are zero or close to zero, it is stated that the signal x can be sparsely represented and that such a signal can be well compressed. In the present invention, the sparse basis ψ we use is a discrete wavelet sparse basis. Therefore, to solve the sparse representation s, we can get a completely new expression of the formula (3):
wherein ,for the solution approximation of the sparse coefficient vector s, we therefore find the approximation solution of the original signal as
Therefore, from the above analysis, the sparsity of the signals, the construction of the measurement matrix, and the reconstruction algorithm of the signals are three main parts of the compressed sensing theory. For the signal reconstruction algorithm, the prior common algorithms include a greedy algorithm, a minimum norm optimization algorithm and a threshold algorithm, in the invention, the measurement matrix used by the algorithm is a 0-1 binary sparse measurement matrix, and the signal reconstruction algorithm is an orthogonal matching pursuit algorithm (OMP algorithm).
Disclosure of Invention
The invention aims to solve the technical problems that: in image signal reconstruction based on compressed sensing, discrete wavelet transformation is generally used for performing sparse transformation on non-sparse original signals, but the sparsity of sparse coefficients in a wavelet domain obtained by traditional discrete wavelet transformation is still not high enough, and the requirement of reconstructing a higher-precision image under the condition of lower sampling rate cannot be generally met. Therefore, to improve the accuracy of compressed perceived image reconstruction, we have optimized the traditional discrete wavelet transform.
The technical scheme adopted for solving the technical problems is as follows: based on the characteristic that non-sparse discrete signals are exponentially attenuated in wavelet domain, an inhibition matrix with exponentially attenuated diagonal elements is designed to enable original wavelet coefficients to be sparser, so that the reconstruction of the original signals by using a compressed sensing algorithm is facilitated. The method comprises the following steps:
step 1, carrying out sparsification on a discrete random non-sparse original image column signal by using discrete wavelet transformation, observing the distribution condition of sparse coefficients in a wavelet domain, and finding out that the wavelet coefficients show gradually attenuated approximate exponential distribution, wherein the sparse coefficients in the exponential distribution state can be regarded as approximate sparse signals;
step 2, according to the characteristic of the approximate exponential decay distribution of the non-sparse signal in the wavelet domain, the limiting condition based on the exponential decay function is applied to the wavelet coefficient of the approximate exponential distribution, and the distribution of the wavelet coefficient is more similar to the real and sparse exponential distribution in an exponential superposition mode;
step 3, based on the limitation condition of the exponential decay distribution, using a suppression matrix to shape the sparser wavelet coefficient, wherein the diagonal elements of the suppression matrix are exponential discrete sequences with the leader decreasing gradually, and the diagonal elements are values larger than 0 and smaller than 1 except the leader, so that the smaller the value of the original wavelet coefficient is, the higher the suppression degree is, and the sparser the wavelet coefficient is;
and 4, selecting relatively optimal inhibition parameters through experiments, so that the best image reconstruction effect is achieved, adding an inhibition matrix with the exponential decay distribution of the diagonal elements as multiplication factors into discrete wavelet transformation, so that the optimization of the traditional discrete wavelet transformation is realized, reconstructing column signals of an image column by using a compressed sensing algorithm through the optimized wavelet basis, and effectively improving the quality and the precision of the reconstructed image.
It is noted that, because the image is a two-dimensional plane array signal, the image is measured and reconstructed by adopting a compressed sensing method, the column signals of the original image are sampled and reconstructed column by column respectively, and finally the reconstructed column signals are combined and spliced to form the two-dimensional original image.
Compared with the prior art, the invention has the advantages that:
(1) Based on the characteristic that the coefficients of the original non-sparse column signals in a discrete wavelet domain are distributed in an exponential decay trend, the invention provides a suppression condition for suppressing the small coefficients in the original wavelet coefficients, and the smaller the wavelet coefficients are, the higher the suppression degree is, so that the sparsity of the wavelet coefficients is effectively improved.
(2) The suppression matrix with exponential decay of the diagonal elements designed based on the limiting condition of the suppression small coefficient is simple and easy to realize, and the relatively optimal suppression parameters are determined by selecting the proper suppression factors, so that a better experimental effect is achieved, and the sparsification level of the original signals is increased without excessively increasing the calculation amount of signal sparsification and compressed sensing signal reconstruction.
(3) In the invention, the diagonal suppression matrix and the traditional discrete wavelet transformation matrix have the same dimension, and the suppression matrix is added into the discrete wavelet transformation as a multiplication factor, compared with the traditional wavelet sparse matrix, the sparse level of the discrete wavelet matrix is effectively improved, the method is simple and effective, and the accuracy and quality of signal reconstruction are finally and effectively improved in a mode of improving the signal representation sparsity.
Drawings
FIG. 1 is a flow chart of a wavelet sparse basis optimization method based on an exponential decay function in compressed sensing image reconstruction of the present invention;
fig. 2 is a graph of coefficient distribution before and after wavelet transformation of discrete random non-sparse column signals, where fig. 2 (a) is an original non-sparse column signal and fig. 2 (b) is a coefficient distribution of the original signal in the wavelet domain;
FIG. 3 is a discrete histogram of an exponential decay function and corresponding sequences;
FIG. 4 is a wavelet coefficient suppression matrix;
FIG. 5 is a graph of peak signal to noise ratio (PSNR) and wavelet coefficient suppression factor p for reconstructed Building and House images with a 0-1 binary measurement matrix;
fig. 6 is a result of reconstructing a build and House image before and after optimizing a discrete wavelet transform, in which fig. 6 (a) is a result of Building image reconstruction before optimization, fig. 6 (b) is a result of Building image reconstruction after optimization, fig. 6 (c) is a result of House image reconstruction before optimization, and fig. 6 (d) is a result of House image reconstruction after optimization.
Detailed Description
The invention is further described in the following description of the preferred embodiments with reference to the figures.
The principle and innovation improvement of the invention are as follows: a wavelet sparse basis optimization method based on an exponential decay function in compressed sensing image reconstruction. Based on the basic principle of compressed sensing signal reconstruction, in compressed sensing signal reconstruction, based on the characteristic that the coefficients of original non-sparse column signals in a discrete wavelet domain are distributed in an exponential decay trend, a suppression condition is provided for suppressing the wavelet coefficients of the original wavelet coefficients, the smaller the wavelet coefficients are, the higher the suppression degree is, so that the sparsity of the wavelet coefficients is effectively improved; meanwhile, an inhibition matrix which is designed based on the limiting condition of small inhibition coefficients and has exponential decay of diagonal elements is simple and easy to realize, and the relatively optimal inhibition parameters are determined by selecting proper inhibition factors, so that a better experimental effect is achieved, and the sparsification level of an original signal is increased without excessively increasing the calculation amount of signal sparsification and compressed sensing signal reconstruction; the diagonal suppression matrix designed by the invention has the same dimension as the traditional discrete wavelet transformation matrix, and the suppression matrix is added into the discrete wavelet transformation as a multiplication factor, compared with the traditional wavelet sparse matrix, the sparse level of the discrete wavelet matrix is effectively improved, the method is simple and effective, and the accuracy and quality of signal reconstruction are finally and effectively improved in a mode of improving the signal sparsity.
The invention provides a wavelet sparse basis optimization method based on an exponential decay function in compressed sensing image reconstruction, and a specific implementation mode of the wavelet sparse basis optimization method is described below.
In compressed sensing, a sparse original signal is a necessary condition for a successful reconstruction of the original signal, but this does not mean that there must be k non-zero elements in the original sparse signal and all other elements are 0. Some theories and studies have demonstrated that if all coefficients in a signal are arranged in a large-to-small manner, and then the rearranged coefficients exhibit a distribution that approximates exponential decay, such a signal may be considered as an approximately sparse signal or a compressible signal. Through a great deal of experiments, we find that after discrete wavelet transformation of non-sparse signals, coefficients in the wavelet domain are very close to a distribution approximating exponential decay. Fig. 2 is a graph of coefficients before and after wavelet transform of discrete random non-sparse column signals, and we can see that discrete wavelet transform can make non-sparse signals more sparse, as shown by the dashed line in fig. 2 (b), wavelet coefficients show a tendency to gradually decay and very close to exponential decay distribution.
Based on the characteristics of discrete wavelet transformation and coefficient exponential decay distribution in wavelet domain, the invention provides an exponential decay limiting condition for optimizing wavelet decomposition base, which can make wavelet coefficient become more sparse and more approximate to real exponential decay distribution. This new constraint is that the positive real exponential decay sequence with the first order of 1, in other words the wavelet coefficients are multiplied by the positive real exponential decay sequence with the first order of 1. This exponential decay curve and the corresponding discrete histogram are shown in fig. 3.
Based on the constraint of the exponential decay function, we designed a diagonal decay of the diagonal elementMatrix formation is performed as shown in fig. 4. We represent this suppression matrix as W, where the diagonal element is (p) i-1 P is an inhibition factor capable of regulating inhibition degree, p is more than 0 and less than 1, i is the ith diagonal element, and n is the length of the original signal. This suppression matrix can be expressed by the following formula:
W＝diag(p 0 ,p 1 ,...,p i-1 ,...,p n ),0＜p＜1,i＝1,2,...,n. (5)
according to equation (5), the wavelet coefficients multiplied by W will become a more exponentially decaying sparse form, the suppression matrix is added to the Discrete Wavelet Transform (DWT), so equation (4) can be expressed as:
equation (6) obtains an estimated value of the wavelet coefficient by solving with a quadratic constraint linear programmingThe estimated value of the reconstructed original signal is obtained by:
since the columns of the original signal are non-sparse column signals, the above approach to suppressing the matrix theoretically enables the original image to be represented more sparsely. The invention can effectively improve the image reconstruction quality, and the effectiveness of the method is proved by the following experiment.
As is clear from the analysis of the above suppression matrix, when the p value is too large, the degree of suppression of the wavelet coefficients is reduced, the purpose of making the wavelet coefficients more sparse is not achieved, and when the p value is too small, the calculation amount of discrete wavelet transform and the difficulty of image reconstruction are increased. Therefore, the p value is not good for reconstructing the image, and the selection of a proper p value is very important. To empirically select the parameter p that performs relatively well, in the case of using a 0-1 binary measurement matrix, when m=64 and n=256, we reconstruct the image Building and House using different p values. According to the wavelet decomposition of the column signals, the image columns with the size of 256×256 are measured and reconstructed column by column, so that the size of the reconstructed image column signals is 256×1, and finally the reconstructed column signals are spliced column by column to form a complete two-dimensional planar image. The relationship between the peak signal-to-noise ratio and the p-value of the reconstructed image before and after wavelet sparse basis optimization is shown in fig. 5. Since the 0-1 binary measurement matrix is randomly generated, we take the average of five experimental results as the final experimental result.
As shown in FIG. 5, the peak signal to noise ratio of the reconstructed images Building and House shows a trend of increasing and then decreasing with increasing p value, and the range of the p value relative to the optimized value interval is [0.995,0.997]. From the results of fig. 5, we set the p value to 0.996 after fully considering the results of balancing both image build and House reconstruction. Thus, the experimental results of our reconstructed images Building and House before and after optimization are shown in FIG. 6.
As shown in fig. 6, after adding the constraint of exponential decay to the conventional discrete wavelet decomposition basis, both the peak signal-to-noise ratio (PSNR) and the Structural Similarity (SSIM) of the reconstructed image are effectively improved. The peak signal-to-noise ratio of the reconstructed Building image is improved by about 1.5dB, the peak signal-to-noise ratio of the reconstructed House image is improved by about 2dB, and the structural similarity is improved by about 0.05. Compared with the mode before optimization, the method for reconstructing the image by using the method has better visual effect and clearer texture details, lower noise and higher contrast, such as clearer and more obvious window outline in the image. In addition, the method of the invention ensures that the structure of the reconstructed image becomes more balanced and stable, has less image distortion, and can effectively inhibit column effect noise generated by reconstructing the image column by column. The above experiments demonstrate the effectiveness of our proposed method in optimizing wavelet sparse basis in compressed perceptual image reconstruction.
In summary, the present invention proposes a wavelet sparse basis optimization method based on an exponential decay function in compressed sensing image reconstruction, and based on a traditional discrete wavelet transform, we propose an exponential decay constraint condition for optimizing signal sparse decomposition, and a diagonal suppression matrix with corresponding diagonal elements decaying exponentially is added as a multiplication factor to a traditional wavelet decomposition basis to optimize the wavelet transform. After proper inhibition parameters are selected, the method provided by the invention not only makes wavelet coefficients more sparse, but also effectively improves the quality and effect of image reconstruction. The effectiveness of the method is proved by an image reconstruction experiment, so that the novel method provided by the invention expands a compressed sensing image processing method and has a certain meaning for more extensive application and research in the field.
The present invention is not described in detail in part as being well known to those skilled in the art.
It will be appreciated by persons skilled in the art that the above embodiments are provided for illustration only and not for limitation of the invention, and that variations and modifications of the above described embodiments will fall within the scope of the claims of the invention as long as they fall within the true spirit of the invention.
Claims (5)
1. A wavelet sparse basis optimization method in compressed sensing image reconstruction is characterized by comprising the following steps: the method comprises the following steps:
step 1, carrying out sparsification on a discrete random non-sparse original image column signal by using discrete wavelet transformation, observing the distribution condition of sparse coefficients in a wavelet domain, and finding out that the wavelet coefficients show gradually attenuated approximate exponential distribution, wherein the sparse coefficients in the exponential distribution state can be regarded as approximate sparse signals;
step 2, according to the characteristic of the approximate exponential decay distribution of the non-sparse signal in the wavelet domain, the limiting condition based on the exponential decay function is applied to the wavelet coefficient of the approximate exponential distribution, and the distribution of the wavelet coefficient is more similar to the real and sparse exponential distribution in an exponential superposition mode;
step 3, based on the limitation condition of the exponential decay distribution, using a suppression matrix to shape the sparser wavelet coefficient, wherein the diagonal elements of the suppression matrix are exponential discrete sequences with the leader decreasing gradually, and the diagonal elements are values larger than 0 and smaller than 1 except the leader, so that the smaller the value of the original wavelet coefficient is, the higher the suppression degree is, and the sparser the wavelet coefficient is;
in the process of compressed sensing sampling, an original signal x, x epsilon C is defined first n Multiplying x by m×n measurement matrix Φ to obtain measurement signal y, y∈C m ，m<n; the following signal measurement model is then present:
y＝Φx+e， (1)
e is white gaussian noise, y is an incomplete (unrercomplete) linear measurement of the original signal x obtained by the measurement matrix;
the recovery process of the original signal corresponds to the inverse process of signal measurement, the original signal x is recovered according to the signal measurement value y, an underdetermined equation must be solved because the dimension of y is far smaller than that of the signal x, the original signal x must be sparse or can be sparsely represented because the underdetermined equation is usually difficult to solve, the sparsity of the discrete signal is usually represented by the L0 norm of the signal, and the I < x > I 0 The zero norm of the original signal x can be used as a regularization term of the formula (1) to represent the number of non-zero elements in x, thus obtaining the following expression:
wherein epsilon is a non-negative normal number, which is the upper error bound,representing an approximation error of the reconstructed signal and the real signal;
if the original signal x is non-sparse, the signal x must be sparsely represented, using a sparse transform orthogonal basis or redundant dictionary ψ to sparsely represent x, ψ= [ ψ ] 1 ,ψ 2 ,ψ 3 ,...,ψ n ]Thus there are:
wherein s= [ s ] 1 ,s 2 ,s 3 ,...,s n ] T S is the sparse representation coefficient of signal x on sparse basis ψ [] T For the transpose operator, if most of coefficients in s are zero or close to zero, it is explained that the signal x can perform sparse representation, such signal can perform very good compression, the sparse basis ψ adopted is a discrete wavelet sparse basis, and in order to solve the sparse representation s, a brand new expression form of the formula (3) is obtained:
wherein ,solving the approximation value of the sparse coefficient vector s to obtain the approximation solution of the original signal as +.>
Wherein the suppression matrix is represented as W, wherein the diagonal element is (p) i-1 P is a suppression factor capable of adjusting the suppression degree, 0 < p < 1, i is the ith diagonal element, n is the length of the original signal, and the suppression matrix can be expressed by the following formula:
W＝diag(p 0 ,p 1 ,...,p i-1 ,...,p n ),0＜p＜1,i＝1,2,...,n. (5)
according to equation (5), the wavelet coefficients multiplied by W will become a more exponentially decaying sparse form, the suppression matrix is added to the Discrete Wavelet Transform (DWT), so equation (4) can be expressed as:
equation (6) obtains an estimated value of the wavelet coefficient by solving with a quadratic constraint linear programmingThe estimated value of the reconstructed original signal is obtained by:
and 4, selecting relatively optimal inhibition parameters through experiments, so that the best image reconstruction effect is achieved, adding an inhibition matrix with the exponential decay distribution of the diagonal elements as multiplication factors into discrete wavelet transformation, so that the optimization of the traditional discrete wavelet transformation is realized, reconstructing column signals of an image column by using a compressed sensing algorithm through the optimized wavelet basis, and effectively improving the quality and the precision of the reconstructed image.
2. The method for optimizing wavelet sparse basis in compressed sensing image reconstruction according to claim 1, wherein the method is characterized by comprising the following steps: based on the basic principle of compressed sensing signal measurement and reconstruction, the traditional discrete wavelet transformation is used for carrying out sparse transformation on non-sparse discrete random column signals, and the characteristic that original non-sparse signals are in exponential attenuation sparse distribution in a sparse domain is observed.
3. The method for optimizing wavelet sparse basis in compressed sensing image reconstruction according to claim 1, wherein the method is characterized by comprising the following steps: observing the coefficient distribution characteristics in the wavelet domain, wherein the discrete non-sparse signals show approximately exponentially decaying distribution in the wavelet coefficients in the wavelet domain, and in order to make the wavelet coefficients become more sparse, the constraint conditions of exponential decay are utilized to apply to the wavelet coefficients.
4. The method for optimizing wavelet sparse basis in compressed sensing image reconstruction according to claim 1, wherein the method is characterized by comprising the following steps: based on the distribution characteristics of the exponential decay function, a diagonal inhibition matrix with the diagonal elements in exponential decay distribution is obtained, wherein the first term of the diagonal element sequence is 1, the rest terms are in exponential distribution with gradual decay, and all the terms except the first term are positive numbers larger than 0 and smaller than 1.
5. A wavelet sparse basis optimization method in compressed sensing image reconstruction according to claim 2 or 3 or 4, wherein: adding the suppression matrix as a multiplication factor into wavelet sparse transformation, wherein the smaller the value of the wavelet coefficient is, the higher the suppression degree is, and therefore the more the wavelet coefficient value is, the more the wavelet coefficient is close to the actual exponential decay distribution and the more sparse the wavelet coefficient can be constrained; because the wavelet sparseness becomes more sparse, the sparse optimized wavelet coefficient can be calculated more easily and accurately column by column through a compressed sensing image column signal reconstruction algorithm, then the column signal of the image is reconstructed through the optimized wavelet inverse transformation, and finally the original image with higher quality is reconstructed.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104952046A (en) * | 2015-04-01 | 2015-09-30 | 哈尔滨工业大学深圳研究生院 | Statistics-based compressed-sensing low-complexity image restoring method |
| CN107016656A (en) * | 2017-04-01 | 2017-08-04 | 中国科学院光电技术研究所 | Wavelet Sparse Basis Optimization Method in Image Reconstruction Based on Compressed Sensing |
| CN107123097A (en) * | 2017-04-26 | 2017-09-01 | 东北大学 | A kind of imaging method of the calculation matrix based on optimization |
| CN107516301A (en) * | 2017-08-30 | 2017-12-26 | 中国科学院光电技术研究所 | Construction optimization method for measuring matrix in image reconstruction based on compressed sensing |
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104952046A (en) * | 2015-04-01 | 2015-09-30 | 哈尔滨工业大学深圳研究生院 | Statistics-based compressed-sensing low-complexity image restoring method |
| CN107016656A (en) * | 2017-04-01 | 2017-08-04 | 中国科学院光电技术研究所 | Wavelet Sparse Basis Optimization Method in Image Reconstruction Based on Compressed Sensing |
| CN107123097A (en) * | 2017-04-26 | 2017-09-01 | 东北大学 | A kind of imaging method of the calculation matrix based on optimization |
| CN107516301A (en) * | 2017-08-30 | 2017-12-26 | 中国科学院光电技术研究所 | Construction optimization method for measuring matrix in image reconstruction based on compressed sensing |
Non-Patent Citations (2)
| Title |
|---|
| 基于第二代Bandelet基的SAR图像压缩感知及其重建;徐虎;谢晓春;;赣南师范学院学报(第03期);全文 * |
| 徐虎 ; 谢晓春 ; .基于第二代Bandelet基的SAR图像压缩感知及其重建.赣南师范学院学报.2013,(第03期),全文. * |
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