CN112946636B - Multi-frequency near-field millimeter wave sparse image reconstruction method - Google Patents

Multi-frequency near-field millimeter wave sparse image reconstruction method Download PDF

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CN112946636B
CN112946636B CN202110141094.4A CN202110141094A CN112946636B CN 112946636 B CN112946636 B CN 112946636B CN 202110141094 A CN202110141094 A CN 202110141094A CN 112946636 B CN112946636 B CN 112946636B
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唐宇
毕东杰
吕珏
谢永乐
李西峰
谢暄
帅萍
李洪
彭礼彪
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Abstract

The invention discloses a multi-frequency near-field millimeter wave sparse image reconstruction method, which comprises the following steps of: s1, scanning a region to be detected through a multi-frequency near-field millimeter wave device to obtain a multi-frequency sparse observation sequence; s2, obtaining a reconstructed scanning image of the region to be measured through a mixed imaging algorithm based on a matrix weighted norm structure tensor total variation fusion operator according to the multi-frequency sparse observation sequence; the invention solves the problem of how to effectively reconstruct images from multi-frequency sparse observation data.

Description

Multi-frequency near-field millimeter wave sparse image reconstruction method
Technical Field
The invention relates to an image reconstruction method, in particular to a multi-frequency near-field millimeter wave sparse image reconstruction method.
Background
For a near-field millimeter wave imaging system working at a single frequency, the imaging quality of the near-field millimeter wave imaging system is often influenced by various factors such as noise, reconstruction artifacts, system hardware limitation and the like, and in order to ensure relatively stable image reconstruction quality, the near-field millimeter wave imaging system working at multiple frequencies can be selected to perform average processing on reconstructed images at all frequencies so as to generate images with more stable quality. For a single-frequency near-field millimeter wave sparse imaging system, the sparsity of the image can be represented by a mixed sparse function formed by an l1 norm and a TV operator, so that the algorithm can reconstruct the image from sparse observation data acquired at a low undersampling rate. For a multi-frequency near-field millimeter wave sparse imaging system, because the measured object has different degrees of millimeter wave back scattering of different frequencies, the sparsity represented by the reconstructed images also has differences, and at the moment, a mixed sparsity function which is more suitable for measuring the sparsity of the images needs to be considered.
Disclosure of Invention
Aiming at the defects in the prior art, the multi-frequency near-field millimeter wave sparse image reconstruction method provided by the invention solves the problem of how to reconstruct images from multi-frequency sparse observation data effectively.
In order to achieve the aim of the invention, the invention adopts the following technical scheme: a multi-frequency near-field millimeter wave sparse image reconstruction method comprises the following steps:
s1, scanning a region to be detected through a multi-frequency near-field millimeter wave device to obtain a multi-frequency sparse observation sequence;
s2, obtaining a reconstructed scanning image of the region to be measured through a mixed imaging algorithm based on a matrix weighted norm structure tensor total variation fusion operator according to the multi-frequency sparse observation sequence.
Further, the step S2 includes the steps of:
s21, setting an iteration mark i, an image reconstruction sequence, a first primary cache sequence, an intermediate factor, a first secondary cache sequence and an initial value of a second secondary cache sequence in a computer system;
s22, iterating an image reconstruction sequence according to an iteration equation set of a hybrid imaging algorithm of a full-variation fusion operator of a basis weight norm structure tensor according to a current first-level buffer sequence, an intermediate factor, a first-level buffer sequence and a second-level buffer sequence, and adding an iteration mark i by 1;
s23, judging a matrix weighted norm structure tensor total variation fusion operator
Figure BDA0002926503550000021
Whether or not it is greater than the interrupt tolerance->
Figure BDA0002926503550000022
If yes, jumping to the step S24, if not, jumping to the step S25;
s24, judging whether the iteration mark i is larger than the iteration upper limit, if so, jumping to the step S25, and if not, jumping to the step S22;
s25, storing the current image reconstruction sequence to obtain a reconstructed scanning image of the region to be detected.
Further, in the step S21, the initial value of the iteration flag i is set to 1, and the initial values of the image reconstruction sequence, the first level one buffer sequence, the intermediate factor, the first level two buffer sequence and the second level two buffer sequence are set according to the following formulas:
g (i) ＝M # s
y (i) ＝g (i)
γ (i) ＝1
Figure BDA0002926503550000025
Figure BDA0002926503550000026
wherein ,g(i) Image reconstruction sequence for the ith iteration, M # The matrix M is the inverse matrix of the matrix M, the matrix M is the transmission matrix of the multi-frequency near-field millimeter wave device, s is a multi-frequency sparse observation sequence, y (i) For the first level one cache sequence of the ith iteration, gamma (i) As an intermediate factor for the i-th iteration,
Figure BDA0002926503550000023
for the first level two cache sequence of the ith iteration,/i>
Figure BDA0002926503550000024
Second level buffer sequence for ith iteration, J K For the weighting block jacobian, W is the weighting matrix.
Further, the iterative equation set of the hybrid imaging algorithm based on the tany weighted norm structure tensor total variation fusion operator in the step S22 includes the following equations:
Figure BDA0002926503550000031
Figure BDA0002926503550000032
Figure BDA0002926503550000033
Figure BDA0002926503550000034
Figure BDA0002926503550000035
wherein ,g(i) Reconstructing a sequence for an image for an ith iteration, pi C (. Cndot.) is the projection of real space C, b (i) For the first iteration temporary storage sequence lambda 1 Lambda is the first sparseness tradeoff parameter 2 For the second sparse trade-off parameter, τ is the minimized Lipschitz constant, x is convolution, W is the weighting matrix, J K For the weighting block jacobian operator,
Figure BDA0002926503550000036
is->
Figure BDA0002926503550000037
Is->
Figure BDA0002926503550000038
Is l ∞ -S q Norm unit sphere space, ++>
Figure BDA0002926503550000039
Is->
Figure BDA00029265035500000310
Is->
Figure BDA00029265035500000311
Ball space in gini index GIN units, y (i+1) First level cache sequence for the i+1st iteration, gamma (i) Intermediate factor for the ith iteration, +.>
Figure BDA00029265035500000312
For the first secondary cache sequence of the ith iteration,
Figure BDA00029265035500000313
the second level buffer sequence for the ith iteration.
Further, the first iterative temporary storage sequence b (i) The calculation formula of (2) is as follows:
Figure BDA00029265035500000314
wherein ,y(i) For the first level cache sequence of the ith iteration, τ is the minimized Lipschitz constant, M # The matrix M is an inverse matrix of the matrix M, the matrix M is a transmission matrix of the multi-frequency near-field millimeter wave device, and s is a multi-frequency sparse observation sequence.
Further, the said
Figure BDA00029265035500000315
Projection of +.>
Figure BDA00029265035500000316
The calculation formula of (2) is as follows:
Figure BDA00029265035500000317
wherein ,
Figure BDA0002926503550000041
is->
Figure BDA0002926503550000042
Is->
Figure BDA0002926503550000043
Lambda for the first secondary cache sequence of the ith iteration 1 Lambda is the first sparseness tradeoff parameter 2 For the second sparsity trade-off parameter, τ is the minimized Lipschitz constant, ρ 1 Approximating the performance balance parameter, L, for the first Moreau envelope 1 Gradient Lipschitz constant for first dual objective subfunction, J K Is a weighted block Jacobian operator, pi C (. Cndot.) is the projection of real space C, (. Cndot.)>
Figure BDA0002926503550000044
The sequence is buffered for a second iteration.
Further, the second iterative temporal sequence
Figure BDA0002926503550000045
The calculation formula of (2) is as follows:
Figure BDA0002926503550000046
wherein τ is the minimized Lipschitz constant, b (i) For the first iteration temporary storage sequence lambda 1 Lambda is the first sparseness tradeoff parameter 2 For the second sparseness tradeoff parameter ρ 1 Approximating the performance balance parameter, g, for the first Moreau envelope (i) Image reconstruction sequence for the ith iteration, J K For the weighting block jacobian operator,
Figure BDA0002926503550000047
a first secondary cache sequence for the ith iteration.
Further, the said
Figure BDA0002926503550000048
Projection of +.>
Figure BDA0002926503550000049
The calculation formula of (2) is as follows:
Figure BDA00029265035500000410
wherein ,
Figure BDA00029265035500000411
is->
Figure BDA00029265035500000412
Is->
Figure BDA00029265035500000413
Lambda for the second level buffer sequence of the ith iteration 1 Lambda is the first sparseness tradeoff parameter 2 For the second sparsity trade-off parameter, τ is the minimized Lipschitz constant, ρ 2 Approximating the performance balance parameter, L, for the second Moreau envelope 2 Gradient Lipschitz constant for the second dual objective subfunction, W is the weighting matrix, pi C (. Cndot.) is the projection of real space C, (. Cndot.)>
Figure BDA00029265035500000414
The sequence is buffered for a third iteration.
Further, the third iterative temporal sequence
Figure BDA00029265035500000415
The calculation formula of (2) is as follows:
Figure BDA00029265035500000416
wherein τ is the minimized Lipschitz constant, b (i) For the first iteration temporary storage sequence lambda 1 Lambda is the first sparseness tradeoff parameter 2 For the second sparseness tradeoff parameter ρ 2 Approximating the performance balance parameter, g, for the second Moreau envelope (i) For the image reconstruction sequence of the jth iteration, W is the weighting matrix,
Figure BDA00029265035500000417
the second level buffer sequence for the ith iteration.
Further, in the step S23, a tany weighted norm structure tensor total variation fusion operator
Figure BDA0002926503550000052
The calculation formula of (2) is as follows:
Figure BDA0002926503550000051
wherein ,g(i+1) Image reconstruction sequence for the (i+1) th iteration, g (i) For the image reconstruction sequence of the i-th iteration, I.I 2 Is 2 norms.
In summary, the invention has the following beneficial effects: the sparseness of the reconstructed images is also different in consideration of the difference of the backscattering degree of millimeter waves on the measured object under different frequencies. Aiming at the problem, the invention provides a multi-frequency near-field millimeter wave sparse image reconstruction method, the designed hybrid imaging algorithm can effectively represent sparsity under the condition of multi-frequency near-field millimeter waves, and compared with the multi-frequency imaging algorithm combining the l1 norm and the TV operator hybrid sparse function, the multi-frequency imaging algorithm of the radix weighted norm and the STV (structure tensor) operator hybrid sparse function provided by the invention has better imaging quality.
Drawings
FIG. 1 is a flow chart of a method for sparse reconstruction of images using multi-frequency near-field millimeter waves;
FIG. 2 (a) shows an actual measurement test object;
FIG. 2 (b) is a full sampling reconstructed image of a multi-frequency near-field millimeter wave at a frequency of 36 GHz-44 GHz;
FIG. 3 (a) is a view of the reconstructed image of the radix-weighted l1 norm +STV operator at an undersampling rate of 14%;
FIG. 3 (b) is the reconstructed image of the radix-weighted l1 norm +STV operator at an undersampling rate of 21%;
FIG. 3 (c) is the reconstructed image of the radix-weighted l1 norm +STV operator at an undersampling rate of 28%;
FIG. 3 (d) is the reconstructed image of the radix-weighted l1 norm +TV operator at an undersampling rate of 14%;
FIG. 3 (e) is the reconstructed image of the radix-weighted l1 norm +TV operator at an undersampling rate of 21%;
fig. 3 (f) is the image reconstructed by the base weighted l1 norm + TV operator at an undersampling rate of 28%.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and all the inventions which make use of the inventive concept are protected by the spirit and scope of the present invention as defined and defined in the appended claims to those skilled in the art.
As shown in fig. 1, a method for sparse reconstruction of images by using multi-frequency near-field millimeter waves includes the following steps:
s1, scanning a region to be detected through a multi-frequency near-field millimeter wave device to obtain a multi-frequency sparse observation sequence;
s2, obtaining a reconstructed scanning image of the region to be measured through a mixed imaging algorithm based on a matrix weighted norm structure tensor total variation fusion operator according to the multi-frequency sparse observation sequence.
The step S2 includes the steps of:
s21, setting an iteration mark i, an image reconstruction sequence, a first primary cache sequence, an intermediate factor, a first secondary cache sequence and an initial value of a second secondary cache sequence in a computer system;
in the step S21, the initial value of the iteration flag i is set to 1, and the initial values of the image reconstruction sequence, the first primary buffer sequence, the intermediate factor, the first secondary buffer sequence and the second secondary buffer sequence are set according to the following formulas:
g (i) ＝M # s
y (i) ＝g (i)
γ (i) ＝1
Figure BDA0002926503550000061
Figure BDA0002926503550000062
wherein ,g(i) Image reconstruction sequence for the ith iteration, M # The matrix M is the inverse matrix of the matrix M, the matrix M is the transmission matrix of the multi-frequency near-field millimeter wave device, s is a multi-frequency sparse observation sequence, y (i) For the first level one cache sequence of the ith iteration, gamma (i) As an intermediate factor for the i-th iteration,
Figure BDA0002926503550000063
for the first level two cache sequence of the ith iteration,/i>
Figure BDA0002926503550000064
Second level buffer sequence for ith iteration, J K For the weighting block jacobian, W is the weighting matrix.
S22, iterating an image reconstruction sequence according to an iteration equation set of a hybrid imaging algorithm of a full-variation fusion operator of a basis weight norm structure tensor according to a current first-level buffer sequence, an intermediate factor, a first-level buffer sequence and a second-level buffer sequence, and adding an iteration mark i by 1;
the iterative equation set of the hybrid imaging algorithm based on the basis of the matrix weighted norm structure tensor total variation fusion operator in the step S22 comprises the following formulas:
Figure BDA0002926503550000071
Figure BDA0002926503550000072
Figure BDA0002926503550000073
Figure BDA0002926503550000074
Figure BDA0002926503550000075
wherein ,g(i) Pi for the image reconstruction sequence of the ith iteration C (. Cndot.) is the projection of real space C, b (i) For the first iteration temporary storage sequence lambda 1 Lambda is the first sparseness tradeoff parameter 2 For the second sparse trade-off parameter, τ is the minimized Lipschitz constant, x is convolution, W is the weighting matrix, J K For the weighting block jacobian operator,
Figure BDA0002926503550000076
is->
Figure BDA0002926503550000077
Is->
Figure BDA0002926503550000078
Is l ∞ -S q Norm unit sphere space, ++>
Figure BDA0002926503550000079
Is->
Figure BDA00029265035500000710
Is->
Figure BDA00029265035500000711
Ball space in gini index GIN units, y (i+1) First level cache sequence for the i+1st iteration, gamma (i) Intermediate factor for the ith iteration, +.>
Figure BDA00029265035500000712
For the first secondary cache sequence of the ith iteration,
Figure BDA00029265035500000713
the second level buffer sequence for the ith iteration.
First iteration temporary storage sequence b (i) The calculation formula of (2) is as follows:
Figure BDA00029265035500000714
wherein ,y(i) For the first level cache sequence of the ith iteration, τ is the minimized Lipschitz constant, M # The matrix M is an inverse matrix of the matrix M, the matrix M is a transmission matrix of the multi-frequency near-field millimeter wave device, and s is a multi-frequency sparse observation sequence.
The said
Figure BDA0002926503550000081
Projection of +.>
Figure BDA0002926503550000082
The calculation formula of (2) is as follows:
Figure BDA0002926503550000083
wherein ,
Figure BDA0002926503550000084
is->
Figure BDA0002926503550000085
Is->
Figure BDA0002926503550000086
Lambda for the first secondary cache sequence of the ith iteration 1 Lambda is the first sparseness tradeoff parameter 2 For the second sparsity trade-off parameter, τ is the minimized Lipschitz constant, ρ 1 Approximating the performance balance parameter, L, for the first Moreau envelope 1 Gradient Lipschitz constant for first dual objective subfunction, J K For weighting block Jacobian operator, pi C (. Cndot.) is the projection of real space C, (. Cndot.)>
Figure BDA0002926503550000087
The sequence is buffered for a second iteration.
The second iteration temporary storage sequence
Figure BDA0002926503550000088
The calculation formula of (2) is as follows:
Figure BDA0002926503550000089
wherein τ is the minimized Lipschitz constant, b (i) For the first iteration temporary storage sequence lambda 1 Lambda is the first sparseness tradeoff parameter 2 For the second sparseness tradeoff parameter ρ 1 Approximating the performance balance parameter, g, for the first Moreau envelope (i) For the ith iterationImage reconstruction sequence, J K For the weighting block jacobian operator,
Figure BDA00029265035500000810
a first secondary cache sequence for the ith iteration.
The said
Figure BDA00029265035500000811
Projection of +.>
Figure BDA00029265035500000812
The calculation formula of (2) is as follows:
Figure BDA00029265035500000813
wherein ,
Figure BDA00029265035500000814
is->
Figure BDA00029265035500000815
Is->
Figure BDA00029265035500000816
Lambda for the second level buffer sequence of the ith iteration 1 Lambda is the first sparseness tradeoff parameter 2 For the second sparsity trade-off parameter, τ is the minimized Lipschitz constant, ρ 2 Approximating the performance balance parameter, L, for the second Moreau envelope 2 Gradient Lipschitz constant for the second dual objective subfunction, W is the weighting matrix, pi C (. Cndot.) is the projection of real space C, (. Cndot.)>
Figure BDA00029265035500000817
The sequence is buffered for a third iteration.
The third iteration temporary storage sequence
Figure BDA00029265035500000818
The calculation formula of (2) is as follows:
Figure BDA0002926503550000091
wherein τ is the minimized Lipschitz constant, b (i) For the first iteration temporary storage sequence lambda 1 Lambda is the first sparseness tradeoff parameter 2 For the second sparseness tradeoff parameter ρ 2 Approximating the performance balance parameter, g, for the second Moreau envelope (i) For the image reconstruction sequence of the ith iteration, W is the weighting matrix,
Figure BDA0002926503550000092
the second level buffer sequence for the ith iteration.
S23, judging a matrix weighted norm structure tensor total variation fusion operator
Figure BDA0002926503550000093
Whether or not it is greater than the interrupt tolerance->
Figure BDA0002926503550000094
If yes, jumping to the step S24, if not, jumping to the step S25;
the step S23 is that the tensor total variation fusion operator of the basis weight norm structure
Figure BDA0002926503550000095
The calculation formula of (2) is as follows:
Figure BDA0002926503550000096
wherein ,g(i+1) Image reconstruction sequence for the (i+1) th iteration, g (i) For the image reconstruction sequence of the i-th iteration, I.I 2 Is 2 norms.
S24, judging whether the iteration mark i is larger than the iteration upper limit, if so, jumping to the step S25, and if not, jumping to the step S22;
s25, storing the current image reconstruction sequence to obtain a reconstructed scanning image of the region to be detected.
Experiment:
in a multi-frequency near-field millimeter wave sparse imaging actual measurement experiment, an imaging system scans a measured object at about 60mm below a 128mm multiplied by 128mm sampling plane in a grid step of about 2mm through an antenna probe working in a frequency band of 36 GHz-44 GHz, and the scanning frequency interval is 0.1GHz (N f =61). Fig. 2 shows a full-sampling reconstructed image of a measured object and a near-field millimeter wave system operating at a working frequency of 36GHz to 44GHz reconstructed after data acquisition of the measured object. The measured object in fig. 2 (a) is a metal scissors, and fig. 2 (b) is a multi-frequency near-field millimeter wave full-sampling reconstructed image in the frequency range of 36 GHz-44 GHz, where the multi-frequency full-sampling reconstructed image can be used as a reference image of image quality evaluation standards SSIM and PSNR.
In this experiment, the radix weighted l1 norm selects the Daubechies wavelet with 8 th order vanishing moment and the STV operator selects the 3 x 3 size gaussian convolution kernel with standard deviation of 0.5. Furthermore, the sparse trade-off parameter λ given in the algorithm 1 ＝4×10 -4 ，λ 2 ＝2×10 -4 The method comprises the steps of carrying out a first treatment on the surface of the Moreau envelope approximation performance balance parameter ρ 1 ＝1，ρ 2 =1; optimization minimisation Lipschitz constant τ=8; dual objective subfunction gradient Lipschitz constant:
Figure BDA0002926503550000101
interrupt tolerance->
Figure BDA0002926503550000102
Fig. 3 shows the effect of reconstructing an image by a multi-frequency near-field millimeter wave sparse imaging algorithm combined with different hybrid sparse functions at different undersampling rates (14%, 21%, 28%). Wherein, fig. 3 (a) to 3 (c) are images reconstructed by a multi-frequency imaging algorithm combined with a matrix weighted l1 norm+stv operator mixed sparse function, and fig. 3 (d) to 3 (f) are images reconstructed by a multi-frequency imaging algorithm combined with a l1 norm+tv operator mixed sparse function. As can be seen from comparing fig. 3 (a) and fig. 3 (d), when the undersampling rate is 14%, the multi-frequency imaging algorithm of the keni weighted l1 norm+stv operator is selected to reconstruct the screw pattern of the axis of the scissors, but the multi-frequency imaging algorithm of the l1 norm+tv operator is selected to not reconstruct successfully. And when the undersampling rate is 21% and 28%, the reconstruction effect of the multi-frequency imaging algorithm of the base weighted l1 norm plus STV operator on the right lower angle scissor handle is better than that of the multi-frequency imaging algorithm of the l1 norm plus TV operator.
To further illustrate the comparison of imaging effects under two mixed sparsity functions, table 1 shows the tolerance to discontinuity
Figure BDA0002926503550000103
After the experiment is independently repeated 50 times, the multi-frequency near-field millimeter wave sparse imaging algorithm of the mixed sparse function has the average effect and comparison of all indexes when the algorithm converges at different undersampling rates (14%, 21%, 28%). As can be seen from comparison of Table 1, the imaging algorithm combining the proposed radix weighted l1 norm and STV operator mixed sparse function has better image reconstruction capability than the imaging algorithm combining the l1 norm and TV operator mixed sparse function at different undersampling rates, and the effectiveness of the proposed mixed sparse function in actual measurement experiments is demonstrated.
TABLE 1
Figure BDA0002926503550000111

Claims (8)

1. The multi-frequency near-field millimeter wave sparse image reconstruction method is characterized by comprising the following steps of:
s1, scanning a region to be detected through a multi-frequency near-field millimeter wave device to obtain a multi-frequency sparse observation sequence;
s2, obtaining a reconstructed scanning image of the region to be measured through a mixed imaging algorithm based on a matrix weighted norm structure tensor total variation fusion operator according to the multi-frequency sparse observation sequence;
the step S2 includes the steps of:
s21, setting an iteration mark i, an image reconstruction sequence, a first primary cache sequence, an intermediate factor, a first secondary cache sequence and an initial value of a second secondary cache sequence in a computer system;
s22, iterating an image reconstruction sequence according to an iteration equation set of a hybrid imaging algorithm of a full-variation fusion operator of a basis weight norm structure tensor according to a current first-level buffer sequence, an intermediate factor, a first-level buffer sequence and a second-level buffer sequence, and adding an iteration mark i by 1;
s23, judging a matrix weighted norm structure tensor total variation fusion operator
Figure FDA0004232755900000015
Whether or not it is greater than the interrupt tolerance->
Figure FDA0004232755900000016
If yes, jumping to the step S24, if not, jumping to the step S25;
s24, judging whether the iteration mark i is larger than the iteration upper limit, if so, jumping to the step S25, and if not, jumping to the step S22;
s25, saving a current image reconstruction sequence to obtain a reconstructed scanning image of the region to be detected;
the iterative equation set of the hybrid imaging algorithm based on the basis of the matrix weighted norm structure tensor total variation fusion operator in the step S22 includes the following formulas:
Figure FDA0004232755900000011
Figure FDA0004232755900000012
Figure FDA0004232755900000013
Figure FDA0004232755900000014
Figure FDA0004232755900000021
wherein ,g(i) Pi for the image reconstruction sequence of the ith iteration C (. Cndot.) is the projection of real space C, b (i) For the first iteration temporary storage sequence lambda 1 Lambda is the first sparseness tradeoff parameter 2 For the second sparse trade-off parameter, τ is the minimized Lipschitz constant, x is convolution, W is the weighting matrix, J K For the weighting block jacobian operator,
Figure FDA0004232755900000022
is->
Figure FDA0004232755900000023
Is->
Figure FDA0004232755900000024
Is l ∞ -S q Norm unit sphere space, ++>
Figure FDA0004232755900000025
Is->
Figure FDA0004232755900000026
Is->
Figure FDA0004232755900000027
Ball space in gini index GIN units, y (i+1) First level cache sequence for the i+1st iteration, gamma (i) Intermediate factor for the ith iteration, +.>
Figure FDA0004232755900000028
For the first level two cache sequence of the ith iteration,/i>
Figure FDA0004232755900000029
The second level buffer sequence for the ith iteration.
2. The method for sparse reconstruction of images by multi-frequency near-field millimeter wave according to claim 1, wherein the initial value of the iteration flag i in step S21 is set to 1, and the initial values of the image reconstruction sequence, the first primary buffer sequence, the intermediate factor, the first secondary buffer sequence and the second secondary buffer sequence are set according to the following formulas:
g (i) ＝M # s
y (i) ＝g (i)
γ (i) ＝1
Figure FDA00042327559000000210
Figure FDA00042327559000000211
wherein ,g(i) Image reconstruction sequence for the ith iteration, M # The matrix M is the inverse matrix of the matrix M, the matrix M is the transmission matrix of the multi-frequency near-field millimeter wave device, s is a multi-frequency sparse observation sequence, y (i) For the first level one cache sequence of the ith iteration, gamma (i) As an intermediate factor for the i-th iteration,
Figure FDA00042327559000000212
for the first level two cache sequence of the ith iteration,/i>
Figure FDA00042327559000000213
Second level buffer sequence for ith iteration, J K For the weighting block jacobian, W is the weighting matrix.
3. The multi-frequency near-field millimeter wave sparse reconstruction of claim 1An image method, characterized in that the first iterative temporary sequence b (i) The calculation formula of (2) is as follows:
Figure FDA0004232755900000031
wherein ,y(i) For the first level cache sequence of the ith iteration, τ is the minimized Lipschitz constant, M # The matrix M is an inverse matrix of the matrix M, the matrix M is a transmission matrix of the multi-frequency near-field millimeter wave device, and s is a multi-frequency sparse observation sequence.
4. The method for multi-frequency near-field millimeter wave sparse reconstruction of images of claim 1, wherein the method comprises
Figure FDA0004232755900000032
Projection of +.>
Figure FDA0004232755900000033
The calculation formula of (2) is as follows:
Figure FDA0004232755900000034
wherein ,
Figure FDA0004232755900000035
is->
Figure FDA0004232755900000036
Is->
Figure FDA0004232755900000037
Lambda for the first secondary cache sequence of the ith iteration 1 Lambda is the first sparseness tradeoff parameter 2 For the second sparsity trade-off parameter, τ is the minimized Lipschitz constant, ρ 1 Approximating the performance balance parameter, L, for the first Moreau envelope 1 For the first pair of purposesThe standard function gradient Lipschitz constant, J K For weighting block Jacobian operator, pi C (. Cndot.) is the projection of real space C, (. Cndot.)>
Figure FDA0004232755900000038
The sequence is buffered for a second iteration.
5. The method for multi-frequency near-field millimeter wave sparse image reconstruction of claim 4, wherein said second iterative temporary sequence
Figure FDA0004232755900000039
The calculation formula of (2) is as follows:
Figure FDA00042327559000000310
wherein τ is the minimized Lipschitz constant, b (i) For the first iteration temporary storage sequence lambda 1 Lambda is the first sparseness tradeoff parameter 2 For the second sparseness tradeoff parameter ρ 1 Approximating the performance balance parameter, g, for the first Moreau envelope () Image reconstruction sequence for the ith iteration, J K For the weighting block jacobian operator,
Figure FDA00042327559000000311
a first secondary cache sequence for the ith iteration.
6. The method for multi-frequency near-field millimeter wave sparse reconstruction of images of claim 1, wherein the method comprises
Figure FDA00042327559000000312
Projection of +.>
Figure FDA00042327559000000313
The calculation formula of (2) is as follows:
Figure FDA0004232755900000041
wherein ,
Figure FDA0004232755900000042
is->
Figure FDA0004232755900000043
Is->
Figure FDA0004232755900000044
Lambda for the second level buffer sequence of the ith iteration 1 Lambda is the first sparseness tradeoff parameter 2 For the second sparsity trade-off parameter, τ is the minimized Lipschitz constant, ρ 2 Approximating the performance balance parameter, L, for the second Moreau envelope 2 For the second dual objective subfunction gradient Lipschitz constant, W is the weighting matrix, pi C (. Cndot.) is the projection of real space C, (. Cndot.)>
Figure FDA0004232755900000045
The sequence is buffered for a third iteration.
7. The method for multi-frequency near-field millimeter wave sparse image reconstruction of claim 6, wherein the third iterative temporary sequence
Figure FDA0004232755900000046
The calculation formula of (2) is as follows:
Figure FDA0004232755900000047
wherein τ is the minimized Lipschitz constant, b (i) For the first iteration temporary storage sequence lambda 1 Lambda is the first sparseness tradeoff parameter 2 For the second sparseness tradeoff parameter ρ 2 Approximating the performance balance parameter, g, for the second Moreau envelope (i) For the ith iterationLike the reconstruction sequence, W is the weighting matrix,
Figure FDA0004232755900000048
the second level buffer sequence for the ith iteration.
8. The method for multi-frequency near-field millimeter wave sparse reconstruction of images according to claim 2, wherein the step S23 is a matrix weighted norm structure tensor total variation fusion operator
Figure FDA00042327559000000410
The calculation formula of (2) is as follows:
Figure FDA0004232755900000049
wherein ,g(i+1) Image reconstruction sequence for the (i+1) th iteration, g (i) For the image reconstruction sequence of the i-th iteration, I.I 2 Is 2 norms.
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