CN109194959B - Compressed sensing imaging method, device, equipment, system and storage medium - Google Patents

Compressed sensing imaging method, device, equipment, system and storage medium Download PDF

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CN109194959B
CN109194959B CN201811139070.XA CN201811139070A CN109194959B CN 109194959 B CN109194959 B CN 109194959B CN 201811139070 A CN201811139070 A CN 201811139070A CN 109194959 B CN109194959 B CN 109194959B
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CN109194959A (en
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李云辉
王晓东
王稚
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Changchun Institute of Optics Fine Mechanics and Physics of CAS
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    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/10—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding
    • H04N19/102—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals using adaptive coding characterised by the element, parameter or selection affected or controlled by the adaptive coding
    • H04N19/132—Sampling, masking or truncation of coding units, e.g. adaptive resampling, frame skipping, frame interpolation or high-frequency transform coefficient masking
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
    • H04N19/42—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals characterised by implementation details or hardware specially adapted for video compression or decompression, e.g. dedicated software implementation
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04N19/00—Methods or arrangements for coding, decoding, compressing or decompressing digital video signals
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
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Abstract

The embodiment of the invention discloses a compressed sensing imaging method, a device, equipment and a system and a computer readable storage medium. The method comprises an image compression coding device for performing compression coding sampling on a target image, a sampling controller and an image reconstruction calculator. The image compression coding device comprises a one-dimensional coding aperture template and a linear array image detector, wherein the one-dimensional coding aperture template corresponds to the linear array image detector; the sampling controller controls and drives the one-dimensional coding aperture template and the linear array image detector to carry out coding sampling, and the obtained sampling data is sent to the image reconstruction calculator; and the image reconstruction calculator is used for obtaining a recovered target image by utilizing the integrated sparse coefficient matrix after independent iterative reconstruction of each dimension data based on the sampling data. The method and the device simplify the encoding process, reduce the cost, eliminate the blocking effect of the block compression sensing system, obviously improve the image quality and realize higher imaging quality with lower hardware cost.

Description

Compressed sensing imaging method, device, equipment, system and storage medium
Technical Field
The embodiment of the invention relates to the technical field of computational imaging, in particular to a compressive sensing imaging method, a device, equipment, a system and a computer readable storage medium.
Background
With the rapid development of signal processing technology, the application of compressed sensing theory is generated in order to break through the limitation of the traditional Nyquist sampling theorem. The theory states that if a signal is sparse in a certain transform domain, the original signal can be recovered with high probability by accurately recovering a small number of low-dimensional projection values of the signal in other uncorrelated transform domains. The requirements on signal acquisition equipment and the data volume are greatly reduced, the traditional one-to-one corresponding imaging mode is overturned, and the method is widely applied to the technical fields of space remote sensing, medical imaging, radar imaging, data compression and the like.
The compressed sensing method comprises compressed coding sensing and image restoration, and currently, researches of scholars in the field mainly include two directions: one is to search a more optimized measurement matrix, improve the sampling efficiency and further enhance the image quality; the other is to find an iterative algorithm capable of reducing the image recovery time and further improving the image quality, including a matching pursuit algorithm, a gradient projection algorithm, a total variation minimization algorithm and the like and improvements thereof, but no improvement is made on the compressed sensing theoretical model per se for a specific field.
The basic model of the compressed sensing theory is mainly directed at one-dimensional signals, the one-dimensional signals are directly applied to a two-dimensional imaging system, and the two-dimensional images need to be subjected to one-dimensional integration processing first and then the compressed sensing theoretical model and the corresponding recovery algorithm are applied. Obviously, the processing mode destroys the sparsity in a specific transform domain of the signal, which is the original basis of the compressed sensing theory, and obviously, the existing mode limits the improvement of the imaging quality of the compressed sensing system.
The Marco F.Duarte et al establishes a single-pixel compressive sensing imaging system based on a digital micromirror array, and uses a single-pixel detector to replace a traditional area array detector as the first application of a compressive sensing theory in the imaging system, thereby reducing the system cost. In order to improve the practicability of the system, scholars propose a block compression sensing imaging system based on a detector array, and the real-time performance of the system is remarkably improved by carrying out block processing and parallel coding on a target scene. In order to further improve the imaging quality of a compressed sensing imaging system, students take adaptive coding observation and reconstruction recovery modes in a dispute, and the basic idea is to predict the characteristics of an imaging target, further take adaptive processing on different regions of the target, increase the coding times of the regions with rich image textures, reduce the coding times of the regions with smooth gray scales, and further improve the image quality under limited resources. However, all the modes are based on an algorithm optimization strategy based on the block compressed sensing imaging system, and the theoretical model and the short board problem of the block compressed sensing system, such as the blocking effect, are not touched.
Disclosure of Invention
Embodiments of the present invention provide a compressed sensing imaging method, apparatus, device, system, and computer readable storage medium, which not only simplify the encoding process and reduce the cost, but also eliminate the blocking effect of the block compressed sensing system, significantly improve the image quality, and achieve higher imaging quality with lower hardware cost.
In order to solve the above technical problems, embodiments of the present invention provide the following technical solutions:
the embodiment of the invention provides a compressed sensing imaging system on one hand, which comprises an image compression coding device, a sampling controller and an image reconstruction calculator, wherein the sampling controller is respectively connected with the image compression coding device and the image reconstruction calculator;
the image compression coding device comprises a one-dimensional coding aperture template and a linear array image detector and is used for carrying out compression coding sampling on a target image;
the sampling controller is used for driving the one-dimensional coding aperture template and the linear array image detector to carry out coding sampling according to a compressed sensing coding method, and sending obtained sampling data to the image reconstruction calculator;
the image reconstruction calculator is used for obtaining a recovered target image by utilizing a sparse coefficient matrix which is integrated after independent iterative reconstruction of each dimension data based on the sampling data;
the one-dimensional coded aperture template corresponds to the linear array image detector, the target image scale is N x N, the array scale of the linear array image detector is 1 x N, and one pixel detector corresponds to the one-dimensional coded aperture template with the N x 1 scale.
Optionally, the obtaining a recovered target image by using a sparse coefficient matrix integrated after independent iterative reconstruction of each dimension data based on the sampling data includes:
the compressed sensing coding sampling process of the target image is described by the following compressed sensing coding formula:
Y′＝YΨT＝ΦΨTΘ＝ΩΘ；
respectively representing a two-dimensional observation result matrix and a sparse coefficient matrix by using the following formulas to obtain a disassembled compressed sensing coding formula:
Y′＝[Y′c1 Y′c2 … Y′cN]；
Θ＝[Θc1 Θc2 … ΘcN]；
Y′cj＝ΩΘcj(j＝1…N)；
performing individual iterative recovery for each column of the sparse coefficient matrix by solving the following optimization problem:
Figure BDA0001815343100000031
subject to Y′cj＝ΩΘcj(j＝1…N)；
integrating a plurality of one-dimensional sparse coefficient sub-matrixes obtained by recovery into a two-dimensional sparse coefficient matrix
Figure BDA0001815343100000032
Calculating to obtain a recovered target image according to the following formula
Figure BDA0001815343100000033
Figure BDA0001815343100000034
Wherein Y ═ Φ X ═ Φ ΨTΘΨ，
Figure BDA0001815343100000035
Is a two-dimensional signal matrix to be measured of the target image,
Figure BDA0001815343100000036
in the form of a matrix of results,
Figure BDA0001815343100000037
for the sparse coefficient matrix, Ψ is an orthogonal matrix,
Figure BDA0001815343100000038
in order to sample the measurement matrix, the measurement matrix is,
Figure BDA0001815343100000039
for the two-dimensional matrix of observations,
Figure BDA00018153431000000310
is a two-dimensional sensing matrix.
Optionally, the performing, for each column of the sparse coefficient matrix, separate iterative recovery by solving the following optimization problem includes:
performing iterative recovery on the first column of the sparse coefficient matrix according to the maximum iteration times based on the following formula:
Figure BDA00018153431000000311
subject to Y′c1＝ΩΘc1；
calculating the vector mode value (theta) of each column of the sparse coefficient matrix except the first column according to the following formulaj||(j＝2…N)：
Figure BDA0001815343100000041
θi，jThe element of the ith row and the jth column of the sparse coefficient matrix;
calculating the weight coefficients of other columns of the sparse coefficient matrix except the first column according to the following formula:
Wj＝20log(||Θj||+1)(j＝2…N)；
calculating the iteration times of other columns except the first column according to a preset iteration time distribution method based on the weight coefficients;
and performing iterative recovery on other columns of the sparse coefficient matrix except the first column according to the iteration times.
Optionally, the iteration number distribution method includes:
s31: calculating the iteration times of other columns of the sparse coefficient matrix except the first column according to the following formula:
Figure BDA0001815343100000042
Smaxis the maximum iteration number;
s32: and sequentially carrying out constraint limitation on the iteration times of other columns except the first column according to the maximum iteration time and the minimum iteration time:
Figure BDA0001815343100000043
Sminis the minimum number of iterations;
s33: judging whether the following formula is established or not, if not, executing S34, and returning to S32 for re-iteration; if yes, outputting the iteration times I of other columns except the first columnj(j＝2…N)；
Figure BDA0001815343100000044
I′rAs total number of iterations, IrDelta is a constant for a preset target total iteration number;
s34: the number of iterations to update the columns other than the first column is calculated according to:
Figure BDA0001815343100000051
optionally, the one-dimensional coded aperture template is
Figure BDA0001815343100000052
pFor the coding times, the observation result obtained by the linear array image detector through the compressed sensing coding method is
Figure BDA0001815343100000053
The observation process is then:
Figure BDA0001815343100000054
correspondingly, the sampling measurement matrix Φ in the compressed sensing coding formula is:
Φ＝[C(1) C(2) … C(m)]T，
the result matrix Y is Y ═ E (1) E (2) … E (m)]T。
Optionally, the sparse coefficient matrix is obtained by changing the two-dimensional signal matrix to be measured based on two-dimensional discrete cosine transform.
Another aspect of the embodiments of the present invention provides a compressed sensing imaging method, including:
acquiring sampling data obtained after a target image is coded and sampled by a one-dimensional compressed sensing coding method;
based on the sampling data, obtaining a recovered target image by utilizing a sparse coefficient matrix integrated after independent iterative reconstruction of each dimension data;
wherein, the obtaining of the recovered target image by using the integrated sparse coefficient matrix after the independent iterative reconstruction of each dimension data based on the sampling data comprises:
the compressed sensing coding sampling process of the target image is described by the following compressed sensing coding formula:
Y′＝YΨT＝ΦΨTΘ＝ΩΘ；
respectively representing a two-dimensional observation result matrix and a sparse coefficient matrix by using the following formulas to obtain a disassembled compressed sensing coding formula:
Y′＝[Y′c1 Y′c2 … Y′cN]；
Θ＝[Θc1 Θc2 … ΘcN]；
Y′cj＝ΩΘcj(j＝1…N)；
performing individual iterative recovery for each column of the sparse coefficient matrix by solving the following optimization problem:
Figure BDA0001815343100000061
subject to Y′cj＝ΩΘcj(j＝1…N)；
integrating a plurality of one-dimensional sparse coefficient sub-matrixes obtained by recovery into a two-dimensional sparse coefficient matrix
Figure BDA0001815343100000062
Calculating to obtain a recovered target image according to the following formula
Figure BDA0001815343100000063
Figure BDA0001815343100000064
Wherein Y ═ Φ X ═ Φ ΨTΘΨ，
Figure BDA0001815343100000065
Is a two-dimensional signal matrix to be measured of the target image,
Figure BDA0001815343100000066
in the form of a matrix of results,
Figure BDA0001815343100000067
for the sparse coefficient matrix, Ψ is an orthogonal matrix,
Figure BDA0001815343100000068
in order to sample the measurement matrix, the measurement matrix is,
Figure BDA0001815343100000069
for the two-dimensional matrix of observations,
Figure BDA00018153431000000610
is a two-dimensional sensing matrix.
The embodiment of the invention also provides a compressed sensing imaging device, which comprises:
the sampling data acquisition module is used for acquiring sampling data obtained after the target image is coded and sampled by a one-dimensional compressed sensing coding method;
the target image reconstruction module is used for obtaining a recovered target image by utilizing a sparse coefficient matrix which is integrated after independent iterative reconstruction of each dimension data based on the sampling data;
the target image reconstruction module includes:
a sampling description submodule, configured to describe a compressed perceptual coding sampling process of the target image by using the following compressed perceptual coding formula:
Y′＝YΨT＝ΦΨTΘ＝ΩΘ；
the sampling data disassembling submodule is used for respectively representing a two-dimensional observation result matrix and a sparse coefficient matrix by using the following formulas to obtain a disassembled compressive sensing coding formula:
Y′＝[Y′c1 Y′c2 … Y′cN]；
Θ＝[Θc1 Θc2 … ΘcN]；
Y′cj＝ΩΘcj(j＝1…N)；
an iterative recovery submodule for performing individual iterative recovery for each column of the sparse coefficient matrix by solving the following optimization problem:
Figure BDA0001815343100000071
subject to Y′cj＝ΩΘcj(j＝1…N)；
a sparse coefficient matrix reconstruction submodule for integrating the recovered multiple one-dimensional sparse coefficient sub-matrixes into a two-dimensional sparse coefficient matrix
Figure BDA0001815343100000072
An image reconstruction submodule for calculating to obtain the restored target image according to the following formula
Figure BDA0001815343100000073
Figure BDA0001815343100000074
Wherein Y ═ Φ X ═ Φ ΨTΘΨ，
Figure BDA0001815343100000075
Is a two-dimensional signal matrix to be measured of the target image,
Figure BDA0001815343100000076
in the form of a matrix of results,
Figure BDA0001815343100000077
for the sparse coefficient matrix, Ψ is an orthogonal matrix,
Figure BDA0001815343100000078
in order to sample the measurement matrix, the measurement matrix is,
Figure BDA0001815343100000079
for the two-dimensional matrix of observations,
Figure BDA00018153431000000710
is a two-dimensional sensing matrix.
The embodiment of the present invention further provides a compressive sensing imaging device, which includes a processor, and the processor is configured to implement the steps of the compressive sensing imaging method when executing the computer program stored in the memory.
Finally, an embodiment of the present invention provides a computer-readable storage medium, where a compressive sensing imaging program is stored on the computer-readable storage medium, and when the compressive sensing imaging program is executed by a processor, the steps of the compressive sensing imaging method are implemented.
The embodiment of the invention provides a compressed sensing imaging system, which comprises an image compression coding device for performing compression coding sampling on a target image, a sampling controller and an image reconstruction calculator. The image compression coding device comprises a one-dimensional coding aperture template and a linear array image detector, wherein the one-dimensional coding aperture template corresponds to the linear array image detector, the scale of a target image is N x N, the scale of an array of the linear array image detector is 1 x N, and one pixel detector corresponds to the one-dimensional coding aperture template with the scale of N x 1; the sampling controller drives the one-dimensional coding aperture template and the linear array image detector to perform coding sampling according to a compressed sensing coding method, and sends the obtained sampling data to the image reconstruction calculator; and the image reconstruction calculator is used for obtaining a recovered target image by utilizing the integrated sparse coefficient matrix after independent iterative reconstruction of each dimension data based on the sampling data.
The technical scheme provided by the application has the advantages that a one-dimensional coding mode is adopted, the conventional area array detector is replaced by the linear array detector, the coding process is simplified, the system cost is reduced, a compression sensing theoretical model based on a two-dimensional image signal framework is built, the two-dimensional image does not need to be subjected to one-dimensional integration processing, and then the compression sensing theoretical model and a corresponding recovery algorithm are applied, so that the system imaging quality is theoretically and effectively improved; in addition, compared with the traditional block compressed sensing imaging system, the hardware implementation is simpler, the blocking effect existing in the block compressed sensing system is eliminated, the image quality is obviously improved, and the higher imaging quality is realized at lower hardware cost.
In addition, the embodiment of the invention also provides a corresponding implementation device, equipment, a system and a computer readable storage medium for the compressive sensing imaging method, so that the method has higher practicability, and the device, the equipment and the computer readable storage medium have corresponding advantages.
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In order to more clearly illustrate the embodiments or technical solutions of the present invention, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained based on these drawings without creative efforts.
Fig. 1 is a block diagram of a specific implementation of a compressed sensing imaging system according to an embodiment of the present invention;
fig. 2 is a schematic diagram of an equivalent relationship of elements of a sparse coefficient matrix according to an embodiment of the present invention;
fig. 3 is a schematic flow chart of an iteration number distribution method according to an embodiment of the present invention;
FIG. 4 is a flowchart illustrating a compressed sensing imaging method according to an embodiment of the present invention;
fig. 5 is a block diagram of a specific embodiment of a compressive sensing imaging device according to an embodiment of the present invention.
Detailed Description
In order that those skilled in the art will better understand the disclosure, the invention will be described in further detail with reference to the accompanying drawings and specific embodiments. It is to be understood that the described embodiments are merely exemplary of the invention, and not restrictive of the full scope of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The terms "first," "second," "third," "fourth," and the like in the description and claims of this application and in the above-described drawings are used for distinguishing between different objects and not for describing a particular order. Furthermore, the terms "comprising" and "having," as well as any variations thereof, are intended to cover non-exclusive inclusions. For example, a process, method, system, article, or apparatus that comprises a list of steps or elements is not limited to only those steps or elements but may include other steps or elements not expressly listed.
Having described the technical solutions of the embodiments of the present invention, various non-limiting embodiments of the present application are described in detail below.
Referring to fig. 1, the compressive sensing imaging system may include an image compression encoding device 1, a sampling controller 2, and an image reconstruction calculator 3, where the sampling controller 2 is connected to the image compression encoding device 1 and the image reconstruction calculator 2, respectively.
The image compression encoding device 1 is used for performing compression encoding sampling on a target image, and can be composed of a front-end optical lens group 11, an encoding aperture template 12, a rear-end optical lens group 13 and an image detector 14. An imaging target (target image) is incident on the coded aperture template 12 through the front-end optical lens group 11, is incident on a focal plane of the image detector 14 through the rear-end optical lens group 13 after being coded, and both the spatial position relationship (or light path building) of each device and the function of each device of the image compression coding device 1 respond to the block compression sensing imaging system, which can refer to the block compression sensing imaging system, and is not described herein again.
Different from the block compressed sensing imaging system, the coded aperture template 12 of the present application is a one-dimensional coded aperture template, the image detector 14 is a linear array image detector, and the one-dimensional coded aperture template and the linear array image detector have a strict correspondence relationship, if the target image scale is N × N and the array scale of the linear array image detector is 1 × N, then one pixel detector corresponds to the one-dimensional coded aperture template of N × 1 scale, or in other words, if the target image scale is N × N, one pixel detector corresponds to the one-dimensional coded aperture template of N × 1 scale, the array scale of the linear array image detector is 1 × N, or for example, if the target image scale is M × N, one pixel detector corresponds to the one-dimensional coded aperture template of M × 1 scale, the array scale of the linear array image detector is 1 × N.
The sampling controller 2 is used for driving the one-dimensional coding aperture template and the linear array image detector to carry out coding sampling according to a compressed sensing coding method, and sending obtained sampling data to the image reconstruction calculator 3.
The image reconstruction calculator 3 is used for obtaining a recovered target image by utilizing a sparse coefficient matrix which is integrated after independent iterative reconstruction of each dimension data based on the sampling data.
Because the matrix obtained by corresponding the coded sampling data is a two-dimensional matrix, the two-dimensional matrix cannot be directly restored by the compressive sensing imaging theory, and the two-dimensional sparse coefficient matrix corresponding to the original target image data and the two-dimensional sampling data can be disassembled, the disassembling does not mean that the two-dimensional original data is integrated into one-dimensional data in the prior art, then the compressive sensing theory model is forcibly applied, but each column or each row in the two-dimensional matrix is taken as a whole, each whole (each column or each row) of the sparse coefficient matrix is sequentially and independently subjected to iterative restoration to obtain the integrated sparse coefficient matrix, and then image reconstruction is performed on the basis of the reconstructed sparse coefficient matrix and the sampling data to obtain the restored target image.
The sparse coefficient matrix is a transformation matrix of the target image when transforming to the sparse domain, and the specific concept can refer to the compressive sensing theory, which is not described herein again.
Based on the compressed sensing imaging system, the built compressed sensing theory model can be described by adopting the following processes:
viewing the target image as a two-dimensional signal matrix to be measured
Figure BDA0001815343100000101
Transforming it into a sparse coefficient matrix by a predetermined transformation relation, e.g. by a two-dimensional Discrete Cosine Transform (2D-DCT)
Figure BDA0001815343100000102
Namely, the method comprises the following steps:
Y＝ΨTΘΨ，
Figure BDA0001815343100000103
as a result matrix, Ψ is an orthogonal matrix,
Figure BDA0001815343100000104
to sample the measurement matrix, the entire sampling process can be described as:
Y＝ΦX＝ΦΨTΘΨ，
since Ψ is an orthogonal matrix, there is ΨT＝Ψ-1The formula is further finished to obtain:
Y′＝YΨT＝ΦΨTΘ＝ΩΘ，
Figure BDA0001815343100000105
for the two-dimensional matrix of observations,
Figure BDA0001815343100000106
is a two-dimensional sensing matrix.
The compressed sensing imaging system is corresponding to the set up of the compressed sensing theoretical model, and the corresponding relationship can be as follows:
the target image is a two-dimensional signal matrix to be measured
Figure BDA0001815343100000107
Target image
Figure BDA0001815343100000108
After being incident to the one-dimensional coded aperture template through the front-stage optical lens assembly 11, the one-dimensional coded aperture template performs one-dimensional compressed sensing coding on the one-dimensional coded aperture template, which may be
Figure BDA0001815343100000111
pFor the number of encoding times, the observation result obtained after encoding is
Figure BDA0001815343100000112
That is, the sampling data on the linear array detector is
Figure BDA0001815343100000113
Then, the observation process can be expressed as:
Figure BDA0001815343100000114
based on this, the sampling measurement matrix Φ in the compressed sensing theory model can be expressed as:
Φ＝[C(1) C(2) … C(m)]T；
the result matrix Y can be expressed as:
Y＝[E(1) E(2) … E(m)]T。
after the matrix corresponding transformation is completed, the target image can be reconstructed according to the theoretical model.
In the technical scheme provided by the embodiment of the invention, a one-dimensional coding mode is adopted, and a linear array detector is used for replacing a traditional area array detector, so that the coding process is simplified, the system cost is reduced, a compression sensing theoretical model based on a two-dimensional image signal framework is established, the two-dimensional image is not required to be subjected to one-dimensional integration processing, and then the compression sensing theoretical model and a corresponding recovery algorithm are applied, so that the system imaging quality is theoretically and effectively improved; in addition, compared with the traditional block compressed sensing imaging system, the hardware implementation is simpler, the blocking effect existing in the block compressed sensing system is eliminated, the image quality is obviously improved, and the higher imaging quality is realized at lower hardware cost.
Optionally, when the image reconstruction calculator 3 performs the step of obtaining the restored target image based on the sampled data and by using the integrated sparse coefficient matrix after the independent iterative reconstruction of each dimensional data, the method may specifically be performed according to the following manner for the size of the target image being N × N:
the compressed sensing coding sampling process of the target image is described by using the following compressed sensing coding formula:
Y′＝YΨT＝ΦΨTΘ＝ΩΘ；
respectively representing a two-dimensional observation result matrix and a sparse coefficient matrix by using the following formulas to obtain a disassembled compressed sensing coding formula:
Y′＝[Y′c1 Y′c2 … Y′cN]；
Θ＝[Θc1 Θc2 … ΘcN]；
Y′cj＝ΩΘcj(j ═ 1 … N), j being the number of columns;
performing individual iterative recovery for each column of the sparse coefficient matrix by solving the following optimization problem:
Figure BDA0001815343100000121
subject to Y′cj＝ΩΘcj(j＝1…N)；
after N groups of iterative reconstruction, N reconstructed one-dimensional sparse coefficient sub-matrixes obtained by recovery are obtained and integrated into a two-dimensional sparse coefficient matrix
Figure BDA0001815343100000122
Calculating to obtain a recovered target image according to the following formula
Figure BDA0001815343100000123
Figure BDA0001815343100000124
Wherein Y ═ Φ X ═ Φ ΨTΘΨ，
Figure BDA0001815343100000125
Is a two-dimensional signal matrix to be measured of the target image,
Figure BDA0001815343100000126
in the form of a matrix of results,
Figure BDA0001815343100000127
for the sparse coefficient matrix, Ψ is an orthogonal matrix,
Figure BDA0001815343100000128
in order to sample the measurement matrix, the measurement matrix is,
Figure BDA0001815343100000129
in the form of a two-dimensional observation matrix,
Figure BDA00018153431000001210
is a two-dimensional sensing matrix.
When each column of the sparse coefficient matrix is subjected to independent iterative recovery, in order to further improve the quality of the whole image, the application also provides a weight coefficient generation method based on frequency distribution estimation.
Taking the example of 2D-DCT transformation, the sparse coefficient moments after 2D-DCT transformationIn the matrix theta, different elements thetai,jThe representative image contains amplitudes of signals with different frequencies, and on the premise that the target image is regarded as the information amplitude magnitude of the frequency points corresponding to the horizontal and vertical directions and is basically consistent, the representative image comprises the following components:
θi,j≈θp,q(i+j＝p+q)，θi，jis the element of the ith row and the jth column of the sparse coefficient matrix.
As shown in fig. 2, the other columns of the sparse coefficient matrix are approximately equivalent to the known first column according to the above formula, i.e. the elements in the same color box in fig. 2 are equivalent. Although each column has several more elements at the bottom of the column vector compared to the partial equivalent elements of the first column, the partial elements can be ignored in comparison to the consideration that the element values decrease sharply with the increasing frequency points. The specific calculation steps are as follows:
according to Y ═ Y ΨTThe calculation of Y' is carried out,
Figure BDA0001815343100000131
in the form of a matrix of results,
Figure BDA0001815343100000132
a two-dimensional observation result matrix;
and performing iterative recovery on the first column of the sparse coefficient matrix according to the maximum iteration times based on the following formula:
Figure BDA0001815343100000133
subject to Y′c1＝ΩΘc1；
calculating the vector modulus theta of each column of the sparse coefficient matrix except the first column according to the following formulaj||(j＝2…N)：
Figure BDA0001815343100000134
θi，jThe element of the ith row and the jth column of the sparse coefficient matrix;
calculating the weight coefficients of other columns of the sparse coefficient matrix except the first column according to the following formula:
Wj＝20log(||Θj||+1)(j＝2…N)；
calculating the iteration times of other columns except the first column according to a preset iteration time distribution method based on the weight coefficients;
and performing iterative recovery on other columns of the sparse coefficient matrix except the first column according to the iteration times.
It should be noted that, the method and the device adopt the steps that a first column of a sparse coefficient matrix is recovered firstly, and the weight coefficients of the rest columns are calculated according to data of the first column; of course, any column in the sparse coefficient matrix may also be recovered at random, and then the weight coefficients of the remaining columns are calculated according to the recovered data, which does not affect the implementation of the present application.
In a specific embodiment, the iteration number assignment method can be implemented according to the following manner:
s31: and calculating the iteration times of other columns of the sparse coefficient matrix except the first column according to the following formula:
Figure BDA0001815343100000141
Smaxis the maximum iteration number;
s32: and sequentially carrying out constraint limitation on the iteration times of other columns except the first column according to the maximum iteration time and the minimum iteration time:
Figure BDA0001815343100000142
Sminis the minimum number of iterations;
s33: judging whether the following formula is established or not, if not, executing S34, and returning to S32 for re-iteration; if yes, outputting the iteration times I of other columns except the first columnj(j＝2…N)；
Figure BDA0001815343100000143
I′rAs total number of iterations, IrDelta is a constant for a preset target total iteration number;
s34: the number of iterations to update the columns other than the first column is calculated according to:
Figure BDA0001815343100000144
when the image reconstruction calculator 3 reconstructs the target image, the first column of the sparse coefficient matrix can be completed according to the received sampling data sent by the sampling controller 2
Figure BDA0001815343100000145
According to the weight coefficient generation algorithm, generating the weight coefficient W of each column of the sparse coefficient matrixjAnd then calculating the iteration times I of each column according to an iteration time distribution methodjAnd recovering each row of the sparse coefficient matrix according to the iteration times
Figure BDA0001815343100000146
After it is connected with the first column
Figure BDA0001815343100000147
After integration into a complete sparse coefficient matrix, based on
Figure BDA0001815343100000148
The final restored two-dimensional image can be obtained.
The method for restoring the weighted image optimizes the reconstruction process in limited reconstruction time, improves image quality, further improves image quality at a small time cost, has the advantage of high cost performance compared with the traditional block compressed sensing system, and provides a better solution for realizing a compressed sensing imaging system.
The embodiment of the invention also provides a corresponding implementation algorithm for the compressed sensing imaging system, so that the system is more feasible. The following describes a compressive sensing imaging method provided by an embodiment of the present invention, and the compressive sensing imaging method described below and the compressive sensing imaging system described above may be referred to correspondingly.
Referring to fig. 4, fig. 4 is a schematic flowchart of a compressed sensing imaging method according to an embodiment of the present invention, where the embodiment of the present invention includes the following:
s401: and acquiring sampling data obtained after the target image is coded and sampled by a one-dimensional compressed sensing coding method.
S402: and based on the sampled data, obtaining a recovered target image by utilizing the integrated sparse coefficient matrix after independent iterative reconstruction of each dimension data.
Wherein, the specific process of S402 may include:
the compressed sensing coding sampling process of the target image is described by using the following compressed sensing coding formula:
Y′＝YΨT＝ΦΨTΘ＝ΩΘ；
respectively representing a two-dimensional observation result matrix and a sparse coefficient matrix by using the following formulas to obtain a disassembled compressed sensing coding formula:
Y′＝[Y′c1 Y′c2 … Y′cN]；
Θ＝[Θc1 Θc2 … ΘcN]；
Y′cj＝ΩΘcj(j＝1…N)；
performing individual iterative recovery for each column of the sparse coefficient matrix by solving the following optimization problem:
Figure BDA0001815343100000151
subject to Y′cj＝ΩΘcj(j＝1…N)；
integrating a plurality of one-dimensional sparse coefficient sub-matrixes obtained by recovery into a two-dimensional sparse coefficient matrix
Figure BDA0001815343100000152
Calculating to obtain a recovered target image according to the following formula
Figure BDA0001815343100000153
Figure BDA0001815343100000154
Wherein Y ═ Φ X ═ Φ ΨTΘΨ，
Figure BDA0001815343100000155
Is a two-dimensional signal matrix to be measured of the target image,
Figure BDA0001815343100000156
in the form of a matrix of results,
Figure BDA0001815343100000157
for the sparse coefficient matrix, Ψ is an orthogonal matrix,
Figure BDA0001815343100000158
in order to sample the measurement matrix, the measurement matrix is,
Figure BDA0001815343100000161
in the form of a two-dimensional observation matrix,
Figure BDA0001815343100000162
is a two-dimensional sensing matrix.
Optionally, in a specific embodiment, the separately iteratively recovering each column of the sparse coefficient matrix by solving the following optimization problem may specifically include:
and performing iterative recovery on the first column of the sparse coefficient matrix according to the maximum iteration times based on the following formula:
Figure BDA0001815343100000163
subject to Y′c1＝ΩΘc1；
calculating the vector modulus theta of each column of the sparse coefficient matrix except the first column according to the following formulaj||(j＝2…N)：
Figure BDA0001815343100000164
θi，jThe element of the ith row and the jth column of the sparse coefficient matrix;
calculating the weight coefficients of other columns of the sparse coefficient matrix except the first column according to the following formula:
Wj＝20log(||Θj||+1)(j＝2…N)；
calculating the iteration times of other columns except the first column according to a preset iteration time distribution method based on the weight coefficients;
and performing iterative recovery on other columns of the sparse coefficient matrix except the first column according to the iteration times.
In addition, the specific implementation method of the iteration number distribution method may be as follows:
s31: and calculating the iteration times of other columns of the sparse coefficient matrix except the first column according to the following formula:
Figure BDA0001815343100000165
Smaxis the maximum iteration number;
s32: and sequentially carrying out constraint limitation on the iteration times of other columns except the first column according to the maximum iteration time and the minimum iteration time:
Figure BDA0001815343100000171
Sminis the minimum number of iterations;
s33: judging whether the following formula is established or not, if not, executing S34, and returning to S32 for re-iteration; if yes, outputting the iteration times I of other columns except the first columnj(j＝2…N)；
Figure BDA0001815343100000172
I′rAs total number of iterations, IrFor preset target total iterationThe number of times, δ, is a constant;
s34: the number of iterations to update the columns other than the first column is calculated according to:
Figure BDA0001815343100000173
therefore, the embodiment of the invention not only simplifies the encoding process and reduces the cost, but also eliminates the block effect existing in the block compression sensing system, obviously improves the image quality and realizes higher imaging quality with lower hardware cost.
The embodiment of the invention also provides a corresponding implementation device for the compressed sensing imaging method, so that the method has higher practicability. In the following, the compressive sensing imaging device provided by the embodiment of the present invention is introduced, and the compressive sensing imaging device described below and the compressive sensing imaging method described above may be referred to correspondingly.
Referring to fig. 5, fig. 5 is a block diagram of a compressed sensing imaging apparatus according to an embodiment of the present invention, where the apparatus may include:
and the sampling data acquisition module 501 is configured to acquire sampling data obtained by coding and sampling the target image by a one-dimensional compressive sensing coding method.
And a target image reconstruction module 502, configured to obtain a recovered target image by using a sparse coefficient matrix integrated after independent iterative reconstruction of each dimensional data based on the sampled data.
The target image reconstruction module 502 may specifically include:
a sampling description submodule, configured to describe a compressed perceptual coding sampling process of the target image by using the following compressed perceptual coding formula:
Y′＝YΨT＝ΦΨTΘ＝ΩΘ；
the sampling data disassembling submodule is used for respectively representing a two-dimensional observation result matrix and a sparse coefficient matrix by using the following formulas to obtain a disassembled compressive sensing coding formula:
Y′＝[Y′c1 Y′c2 … Y′cN]；
Θ＝[Θc1 Θc2 … ΘcN]；
Y′cj＝ΩΘcj(j＝1…N)；
and the iteration recovery submodule is used for carrying out independent iteration recovery on each column of the sparse coefficient matrix by solving the following optimization problems:
Figure BDA0001815343100000181
subject to Y′cj＝ΩΘcj(j＝1…N)；
a sparse coefficient matrix reconstruction submodule for integrating the recovered multiple one-dimensional sparse coefficient sub-matrixes into a two-dimensional sparse coefficient matrix
Figure BDA0001815343100000182
An image reconstruction submodule for calculating to obtain the restored target image according to the following formula
Figure BDA0001815343100000183
Figure BDA0001815343100000184
Wherein Y ═ Φ X ═ Φ ΨTΘΨ，
Figure BDA0001815343100000185
Is a two-dimensional signal matrix to be measured of the target image,
Figure BDA0001815343100000186
in the form of a matrix of results,
Figure BDA0001815343100000187
for the sparse coefficient matrix, Ψ is an orthogonal matrix,
Figure BDA0001815343100000188
in order to sample the measurement matrix, the measurement matrix is,
Figure BDA0001815343100000189
in the form of a two-dimensional observation matrix,
Figure BDA00018153431000001810
is a two-dimensional sensing matrix.
Optionally, in some embodiments of this embodiment, the iterative recovery sub-module may further include:
a first column recovery unit, configured to perform iterative recovery on a first column of the sparse coefficient matrix according to a maximum iteration number based on the following formula:
Figure BDA00018153431000001811
subject to Y′c1＝ΩΘc1；
a vector module value calculating unit, configured to calculate a vector module value | | | Θ of each column of the sparse coefficient matrix except the first column according to the following formulaj||(j＝2…N)：
Figure BDA0001815343100000191
θi，jThe element of the ith row and the jth column of the sparse coefficient matrix;
a weight coefficient calculation unit, configured to calculate a weight coefficient of each column of the sparse coefficient matrix except for the first column according to the following formula:
Wj＝20log(||Θj||+1)(j＝2…N)；
the iteration number calculating unit is used for calculating the iteration number of each other column except the first column according to a preset iteration number distribution method based on each weight coefficient;
and the recovery unit is used for performing iterative recovery on other columns of the sparse coefficient matrix except the first column according to the iteration times.
Specifically, the iteration number calculating unit may further include:
a calculating subunit, configured to calculate, according to the following formula, the number of iterations of each column of the sparse coefficient matrix except for the first column:
Figure BDA0001815343100000192
Smaxis the maximum iteration number;
and the constraint subunit is used for sequentially constraining and limiting the iteration times of other columns except the first column according to the maximum iteration time and the minimum iteration time:
Figure BDA0001815343100000193
Sminis the minimum number of iterations;
the iteration subunit is used for calculating the iteration times of other columns except the first column according to the following formula if the following formula does not hold, and utilizing the constraint subunit to iterate again;
Figure BDA0001815343100000194
Figure BDA0001815343100000201
I′ras total number of iterations, IrDelta is a constant for a preset target total iteration number;
an iteration number output subunit for outputting when a condition is satisfied (i.e. the iteration number output subunit is used for outputting when the condition is satisfied
Figure BDA0001815343100000202
True), the number of iterations I of each column other than the first column is outputj(j＝2…N)。
The functions of the functional modules of the compressive sensing imaging apparatus according to the embodiment of the present invention may be implemented according to the specific implementation in the system embodiment, and the specific implementation process may refer to the related description of the system embodiment, which is not described herein again.
Therefore, the embodiment of the invention not only simplifies the encoding process and reduces the cost, but also eliminates the block effect existing in the block compression sensing system, obviously improves the image quality and realizes higher imaging quality with lower hardware cost.
The embodiment of the present invention further provides a compressed sensing imaging device, which specifically includes:
a memory for storing a computer program;
a processor for executing a computer program to implement the steps of the compressed sensing imaging method as described in any of the above embodiments.
The functions of the functional modules of the compressive sensing imaging device according to the embodiments of the present invention may be specifically implemented according to the method in the foregoing method embodiments, and the specific implementation process may refer to the related description of the foregoing method embodiments, which is not described herein again.
Therefore, the embodiment of the invention not only simplifies the encoding process and reduces the cost, but also eliminates the block effect existing in the block compression sensing system, obviously improves the image quality and realizes higher imaging quality with lower hardware cost.
The embodiment of the present invention further provides a computer-readable storage medium, in which a compressive sensing imaging program is stored, and the steps of the compressive sensing imaging method according to any one of the above embodiments are performed when the compressive sensing imaging program is executed by a processor.
The functions of the functional modules of the computer-readable storage medium according to the embodiment of the present invention may be specifically implemented according to the method in the foregoing method embodiment, and the specific implementation process may refer to the related description of the foregoing method embodiment, which is not described herein again.
Therefore, the embodiment of the invention not only simplifies the encoding process and reduces the cost, but also eliminates the block effect existing in the block compression sensing system, obviously improves the image quality and realizes higher imaging quality with lower hardware cost.
The embodiments are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same or similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.
Those of skill would further appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the various illustrative components and steps have been described above generally in terms of their functionality in order to clearly illustrate this interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may reside in Random Access Memory (RAM), memory, Read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.
The compressed sensing imaging method, device, equipment, system and computer readable storage medium provided by the invention are described in detail above. The principles and embodiments of the present invention are explained herein using specific examples, which are presented only to assist in understanding the method and its core concepts. It should be noted that, for those skilled in the art, it is possible to make various improvements and modifications to the present invention without departing from the principle of the present invention, and those improvements and modifications also fall within the scope of the claims of the present invention.

Claims (9)

1. A compressed sensing imaging system is characterized by comprising an image compression coding device, a sampling controller and an image reconstruction calculator, wherein the sampling controller is respectively connected with the image compression coding device and the image reconstruction calculator;
the image compression coding device comprises a one-dimensional coding aperture template and a linear array image detector and is used for carrying out compression coding sampling on a target image;
the sampling controller is used for driving the one-dimensional coding aperture template and the linear array image detector to carry out coding sampling according to a compressed sensing coding method, and sending obtained sampling data to the image reconstruction calculator;
the image reconstruction calculator is used for obtaining a recovered target image by utilizing a sparse coefficient matrix which is integrated after independent iterative reconstruction of each dimension data based on the sampling data;
the one-dimensional coded aperture template corresponds to the linear array image detector, the target image scale is N x N, the array scale of the linear array image detector is 1 x N, and one pixel detector corresponds to the one-dimensional coded aperture template with the N x 1 scale;
the obtaining of the recovered target image by using the integrated sparse coefficient matrix after the independent iterative reconstruction of each dimension data based on the sampling data comprises:
the compressed sensing coding sampling process of the target image is described by the following compressed sensing coding formula:
Y′＝YΨT＝ΦΨTΘ＝ΩΘ；
respectively representing a two-dimensional observation result matrix and a sparse coefficient matrix by using the following formulas to obtain a disassembled compressed sensing coding formula:
Y′＝[Y′c1 Y′c2…Y′cN]；
Θ＝[Θc1 Θc2…ΘcN]；
Y′cj＝ΩΘcj(j＝1...N)；
performing individual iterative recovery for each column of the sparse coefficient matrix by solving the following optimization problem:
Figure FDA0002772191730000011
subject to Y′cj＝ΩΘcj(j＝1...N)；
integrating a plurality of one-dimensional sparse coefficient sub-matrixes obtained by recovery into a two-dimensional sparse coefficient matrix
Figure FDA0002772191730000012
Calculating to obtain a recovered target image according to the following formula
Figure FDA0002772191730000013
Figure FDA0002772191730000014
Wherein Y ═ Φ X ═ Φ ΨTΘΨ，
Figure FDA0002772191730000021
Is a two-dimensional signal matrix to be measured of the target image,
Figure FDA0002772191730000022
in the form of a matrix of results,
Figure FDA0002772191730000023
for the sparse coefficient matrix, Ψ is an orthogonal matrix,
Figure FDA0002772191730000024
in order to sample the measurement matrix, the measurement matrix is,
Figure FDA0002772191730000025
for the two-dimensional matrix of observations,
Figure FDA0002772191730000026
is a two-dimensional sensing matrix.
2. The compressed sensing imaging system of claim 1, wherein the separately iterative recovery of each column of the sparse coefficient matrix by solving the following optimization problem comprises:
performing iterative recovery on the first column of the sparse coefficient matrix according to the maximum iteration times based on the following formula:
Figure FDA0002772191730000027
subject to Y′c1＝ΩΘc1；
calculating the vector mode value (theta) of each column of the sparse coefficient matrix except the first column according to the following formulaj||(j＝2...N)：
Figure FDA0002772191730000028
θi，jThe element of the ith row and the jth column of the sparse coefficient matrix;
calculating the weight coefficients of other columns of the sparse coefficient matrix except the first column according to the following formula:
Wj＝20log(||Θj||+1)(j＝2...N)；
calculating the iteration times of other columns except the first column according to a preset iteration time distribution method based on the weight coefficients;
and performing iterative recovery on other columns of the sparse coefficient matrix except the first column according to the iteration times.
3. The compressed sensing imaging system of claim 2, wherein the iteration number assignment method comprises:
s31: calculating the iteration times of other columns of the sparse coefficient matrix except the first column according to the following formula:
Figure FDA0002772191730000029
Smaxis the maximum iteration number;
s32: and sequentially carrying out constraint limitation on the iteration times of other columns except the first column according to the maximum iteration time and the minimum iteration time:
Figure FDA00027721917300000210
Sminis the minimum number of iterations;
s33: judging whether the following formula is established or not, if not, executing S34, and returning to S32 for re-iteration; if yes, outputting the iteration times I of other columns except the first columnj(j＝2...N)；
Figure FDA0002772191730000031
I′rAs total number of iterations, IrDelta is a constant for a preset target total iteration number;
s34: the number of iterations to update the columns other than the first column is calculated according to:
Figure FDA0002772191730000032
4. the compressed sensing imaging system of claim 1, wherein the one-dimensional coded aperture template is
Figure FDA0002772191730000033
p is the number of coding times, and the observation result obtained by the linear array image detector through the compressed sensing coding method is
Figure FDA0002772191730000034
The observation process is then:
Figure FDA0002772191730000035
correspondingly, the sampling measurement matrix Φ in the compressed sensing coding formula is:
Φ＝[C(1) C(2)…C(m)]T，
the result matrix Y is Y ═ E (1) E (2) … E (m)]T。
5. The compressive sensing imaging system of claim 3, wherein the sparse coefficient matrix is a two-dimensional discrete cosine transform-based matrix of the two-dimensional signal under test.
6. A method of compressed sensing imaging, comprising:
acquiring sampling data obtained after a target image is coded and sampled by a one-dimensional compressed sensing coding method;
based on the sampling data, obtaining a recovered target image by utilizing a sparse coefficient matrix integrated after independent iterative reconstruction of each dimension data;
wherein, the obtaining of the recovered target image by using the integrated sparse coefficient matrix after the independent iterative reconstruction of each dimension data based on the sampling data comprises:
the compressed sensing coding sampling process of the target image is described by the following compressed sensing coding formula:
Y′＝YΨT＝ΦΨTΘ＝ΩΘ；
respectively representing a two-dimensional observation result matrix and a sparse coefficient matrix by using the following formulas to obtain a disassembled compressed sensing coding formula:
Y′＝[Y′c1 Y′c2…Y′cN]；
Θ＝[Θc1 Θc2…ΘcN]；
Y′cj＝ΩΘcj(j＝1...N)；
performing individual iterative recovery for each column of the sparse coefficient matrix by solving the following optimization problem:
Figure FDA0002772191730000041
subject to Y′cj＝ΩΘcj(j＝1...N)；
integrating a plurality of one-dimensional sparse coefficient sub-matrixes obtained by recovery into a two-dimensional sparse coefficient matrix
Figure FDA0002772191730000042
Calculating to obtain a recovered target image according to the following formula
Figure FDA0002772191730000043
Figure FDA0002772191730000044
Wherein Y ═ Φ X ═ Φ ΨTΘΨ，
Figure FDA0002772191730000045
Is a two-dimensional signal matrix to be measured of the target image,
Figure FDA0002772191730000046
in the form of a matrix of results,
Figure FDA0002772191730000047
for the sparse coefficient matrix, Ψ is an orthogonal matrix,
Figure FDA0002772191730000048
in order to sample the measurement matrix, the measurement matrix is,
Figure FDA0002772191730000049
for the two-dimensional matrix of observations,
Figure FDA00027721917300000410
is a two-dimensional sensing matrix.
7. A compressed sensing imaging apparatus, comprising:
the sampling data acquisition module is used for acquiring sampling data obtained after the target image is coded and sampled by a one-dimensional compressed sensing coding method;
the target image reconstruction module is used for obtaining a recovered target image by utilizing a sparse coefficient matrix which is integrated after independent iterative reconstruction of each dimension data based on the sampling data;
the target image reconstruction module includes:
a sampling description submodule, configured to describe a compressed perceptual coding sampling process of the target image by using the following compressed perceptual coding formula:
Y′＝YΨT＝ΦΨTΘ＝ΩΘ；
the sampling data disassembling submodule is used for respectively representing a two-dimensional observation result matrix and a sparse coefficient matrix by using the following formulas to obtain a disassembled compressive sensing coding formula:
Y′＝[Y′c1 Y′c2…Y′cN]；
Θ＝[Θc1 Θc2…ΘcN]；
Y′cj＝ΩΘcj(j＝1...N)；
an iterative recovery submodule for performing individual iterative recovery for each column of the sparse coefficient matrix by solving the following optimization problem:
Figure FDA00027721917300000411
subject to Y′cj＝ΩΘcj(j＝1...N)；
a sparse coefficient matrix reconstruction submodule for integrating the recovered multiple one-dimensional sparse coefficient sub-matrixes into a two-dimensional sparse coefficient matrix
Figure FDA0002772191730000051
Image duplicationA construction module for calculating to obtain the restored target image according to the following formula
Figure FDA0002772191730000052
Figure FDA0002772191730000053
Wherein Y ═ Φ X ═ Φ ΨTΘΨ，
Figure FDA0002772191730000054
Is a two-dimensional signal matrix to be measured of the target image,
Figure FDA0002772191730000055
in the form of a matrix of results,
Figure FDA0002772191730000056
for the sparse coefficient matrix, Ψ is an orthogonal matrix,
Figure FDA0002772191730000057
in order to sample the measurement matrix, the measurement matrix is,
Figure FDA0002772191730000058
for the two-dimensional matrix of observations,
Figure FDA0002772191730000059
is a two-dimensional sensing matrix.
8. A compressive sensing imaging device comprising a processor for implementing the steps of the compressive sensing imaging method as claimed in claim 6 when executing a computer program stored in a memory.
9. A computer readable storage medium, having a compressive sensing imaging program stored thereon, which when executed by a processor, performs the steps of the compressive sensing imaging method as claimed in claim 6.
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