CN112946636A - 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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CN112946636A
CN112946636A CN202110141094.4A CN202110141094A CN112946636A CN 112946636 A CN112946636 A CN 112946636A CN 202110141094 A CN202110141094 A CN 202110141094A CN 112946636 A CN112946636 A CN 112946636A
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sparse
image
millimeter wave
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CN112946636B (en
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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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University of Electronic Science and Technology of China
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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 the area to be measured through the multi-frequency near-field millimeter wave device to obtain a multi-frequency sparse observation sequence; s2, obtaining a reconstructed scanning image of the to-be-detected area through a hybrid imaging algorithm based on a Gini weighted norm structure tensor total variation fusion operator according to the multi-frequency sparse observation sequence; the method solves the problem of how to effectively reconstruct the image from the 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, and reconstructed images under various frequencies are subjected to average processing to generate images with more stable quality. For a single-frequency near-field millimeter wave sparse imaging system, a mixed sparse function formed by the norm l1 and a TV operator can represent the sparsity of an image, so that an algorithm can reconstruct the image from sparse observation data acquired under a low undersampling rate. For a multi-frequency near-field millimeter wave sparse imaging system, due to the fact that backscattering degrees of a measured object to millimeter waves with different frequencies are different, sparsity degrees reflected by a reconstructed image are different, and a mixed sparse function more suitable for measuring image sparsity needs to be considered and combined.
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 effectively reconstruct an image from multi-frequency sparse observation data.
In order to achieve the purpose of the invention, the invention adopts the technical scheme that: a multi-frequency near-field millimeter wave sparse image reconstruction method comprises the following steps:
s1, scanning the area to be measured through the multi-frequency near-field millimeter wave device to obtain a multi-frequency sparse observation sequence;
and S2, obtaining a reconstructed scanning image of the region to be detected through a hybrid imaging algorithm based on a Gini weighted norm structure tensor total variation fusion operator according to the multi-frequency sparse observation sequence.
Further, the step S2 includes the following steps:
s21, setting initial values of an iteration mark i, an image reconstruction sequence, a first primary cache sequence, an intermediate factor, a first secondary cache sequence and a second secondary cache sequence in a computer system;
s22, according to the current first primary cache sequence, the intermediate factor, the first secondary cache sequence and the second secondary cache sequence, based on the iteration equation set iteration image reconstruction sequence of the hybrid imaging algorithm of the Gini weighted norm structure tensor total variation fusion operator, and adding 1 to the iteration mark i;
s23, judging the whole variation fusion operator of the Gini weighted norm structure tensor
Figure BDA0002926503550000021
Whether or not greater than the interrupt tolerance
Figure BDA0002926503550000022
If yes, jumping to step S24, otherwise, jumping to step S25;
s24, judging whether the iteration flag i is larger than the iteration upper limit, if so, jumping to the step S25, and if not, jumping to the step S22;
and S25, storing the current image reconstruction sequence to obtain a reconstructed scanning image of the region to be measured.
Further, in 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 middle 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 BDA0002926503550000025
Figure BDA0002926503550000026
wherein ,g(i)For the image reconstruction sequence of the ith iteration, 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 the multi-frequency sparse observation sequence, y(i)For the first primary buffer sequence of the ith iteration, gamma(i)Is an intermediate factor for the ith iteration,
Figure BDA0002926503550000023
for the first secondary cache sequence of the ith iteration,
Figure BDA0002926503550000024
second level buffer sequence for ith iteration, JKW is a weighting matrix.
Further, the iterative equation set of the hybrid imaging algorithm based on the kini weighted norm structure tensor total variation fusion operator in step S22 includes the following formulas:
Figure BDA0002926503550000031
Figure BDA0002926503550000032
Figure BDA0002926503550000033
Figure BDA0002926503550000034
Figure BDA0002926503550000035
wherein ,g(i)For the image reconstruction sequence of the ith iteration,. piC(. is a projection of real space C, b(i)For the first iteration of the temporary storage sequence, lambda1For the first sparse tradeoff parameter, λ2For the second sparse trade-off parameter, τ is the minimized Lipschitz constant,. tau.is the convolution, W is the weighting matrix, JKIn order to weight the block-Jacobian operator,
Figure BDA0002926503550000036
is composed of
Figure BDA0002926503550000037
The projection of (a) is performed,
Figure BDA0002926503550000038
is 1∞-SqThe norm is in the unit sphere space of the norm,
Figure BDA0002926503550000039
is composed of
Figure BDA00029265035500000310
The projection of (a) is performed,
Figure BDA00029265035500000311
is the Gini index GIN unit sphere space, y(i+1)For the first primary buffer sequence of the (i + 1) th iteration, gamma(i)Is an intermediate factor for the ith iteration,
Figure BDA00029265035500000312
for the first secondary cache sequence of the ith iteration,
Figure BDA00029265035500000313
second level buffer sequence for ith iteration。
Further, the first iterative temporal storage sequence b(i)The calculation formula of (2) is as follows:
Figure BDA00029265035500000314
wherein ,y(i)For the first one-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
Figure BDA00029265035500000315
Projection of
Figure BDA00029265035500000316
The calculation formula of (2) is as follows:
Figure BDA00029265035500000317
wherein ,
Figure BDA0002926503550000041
is composed of
Figure BDA0002926503550000042
The projection of (a) is performed,
Figure BDA0002926503550000043
for the first secondary buffer sequence of the ith iteration, λ1For the first sparse tradeoff parameter, λ2For the second sparsity tradeoff parameter, τ is the minimized Lipschitz constant, ρ1Approximating the Performance Balancing parameter for the first Moreau envelope, L1Gradient Lipschitz constant for the first even objective sub-function, JKIs a weighted block Jacobian operator, nC(. cndot.) is a projection of the real space C,
Figure BDA0002926503550000044
the sequence is temporarily stored for the second iteration.
Further, the second iterative scratch pad sequence
Figure BDA0002926503550000045
The calculation formula of (2) is as follows:
Figure BDA0002926503550000046
wherein, tau is a minimized Lipschitz constant, b(i)For the first iteration of the temporary storage sequence, lambda1For the first sparse tradeoff parameter, λ2For the second sparsity tradeoff parameter, ρ1Approximating the Performance Balancing parameter, g, for the first Moreau envelope(i)Reconstruction sequence of images for the ith iteration, JKIn order to weight the block-Jacobian operator,
Figure BDA0002926503550000047
the sequence is cached for the first level two of the ith iteration.
Further, the
Figure BDA0002926503550000048
Projection of
Figure BDA0002926503550000049
The calculation formula of (2) is as follows:
Figure BDA00029265035500000410
wherein ,
Figure BDA00029265035500000411
is composed of
Figure BDA00029265035500000412
The projection of (a) is performed,
Figure BDA00029265035500000413
is the ith timeIterative second level buffer sequence, lambda1For the first sparse tradeoff parameter, λ2For the second sparsity tradeoff parameter, τ is the minimized Lipschitz constant, ρ2Approximating the performance balance parameter for a second Moreau envelope, L2Is the second dual objective sub-function gradient Lipschitz constant, W is the weighting matrix, piC(. cndot.) is a projection of the real space C,
Figure BDA00029265035500000414
the sequence is temporarily stored for the third iteration.
Further, the third iterative scratch pad sequence
Figure BDA00029265035500000415
The calculation formula of (2) is as follows:
Figure BDA00029265035500000416
wherein, tau is a minimized Lipschitz constant, b(i)For the first iteration of the temporary storage sequence, lambda1For the first sparse tradeoff parameter, λ2For the second sparsity tradeoff parameter, ρ2Approximating the performance balance parameter, g, for a second Moreau envelope(i)For the image reconstruction sequence of the jth iteration, W is the weighting matrix,
Figure BDA00029265035500000417
the sequence is cached for the second level of the ith iteration.
Further, the total variation fusion operator of the kini weighted norm structure tensor in the step S23
Figure BDA0002926503550000052
The calculation formula of (2) is as follows:
Figure BDA0002926503550000051
wherein ,g(i+1)For the image reconstruction sequence of the (i + 1) th iteration, g(i)Is the ith timeIterative image reconstruction sequence (| · |) non-woven phosphor2Is a 2 norm.
In conclusion, the beneficial effects of the invention are as follows: the sparsity degree of the reconstructed image is different in consideration of the difference of the backscattering degree of the millimeter wave to the measured object under different frequencies. Aiming at the problem, the invention provides a multi-frequency near-field millimeter wave sparse image reconstruction method, a designed hybrid imaging algorithm can effectively represent sparsity under the condition of multi-frequency near-field millimeter waves, and compared with a multi-frequency imaging algorithm combining l1 norm + TV operator hybrid sparse functions, the multi-frequency imaging algorithm combining the Kernel weighted norm + STV (Structure tensor) operator hybrid sparse functions has better imaging quality.
Drawings
FIG. 1 is a flow chart of a multi-frequency near-field millimeter wave sparse image reconstruction method;
FIG. 2(a) shows an actually measured test object;
FIG. 2(b) is a multi-frequency near-field millimeter wave full-sampling reconstructed image at a frequency of 36 GHz-44 GHz;
FIG. 3(a) is an image reconstructed with a Kearny weighted l1 norm + STV operator at an undersampling rate of 14%;
FIG. 3(b) is an image reconstructed by the Keyny weighted l1 norm + STV operator at an undersampling rate of 21%;
FIG. 3(c) is an image reconstructed with a Gini weighted l1 norm + STV operator at an undersampling rate of 28%;
FIG. 3(d) is an image reconstructed by the Keyny weighted l1 norm + TV operator at an undersampling rate of 14%;
FIG. 3(e) is an image reconstructed by the Keyny weighted l1 norm + TV operator at an undersampling rate of 21%;
FIG. 3(f) is an image reconstructed by the Keyny 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 the 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 it will be apparent to those skilled in the art that various changes may be made without departing from the spirit and scope of the invention as defined and defined in the appended claims, and all matters produced by the invention using the inventive concept are protected.
As shown in fig. 1, a multi-frequency near-field millimeter wave sparse image reconstruction method includes the following steps:
s1, scanning the area to be measured through the multi-frequency near-field millimeter wave device to obtain a multi-frequency sparse observation sequence;
and S2, obtaining a reconstructed scanning image of the region to be detected through a hybrid imaging algorithm based on a Gini 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 initial values of an iteration mark i, an image reconstruction sequence, a first primary cache sequence, an intermediate factor, a first secondary cache sequence and a second secondary cache sequence in a computer system;
in 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)For the image reconstruction sequence of the ith iteration, 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 the multi-frequency sparse observation sequence, y(i)For the first primary buffer sequence of the ith iteration, gamma(i)Is an intermediate factor for the ith iteration,
Figure BDA0002926503550000063
for the first secondary cache sequence of the ith iteration,
Figure BDA0002926503550000064
second level buffer sequence for ith iteration, JKW is a weighting matrix.
S22, according to the current first primary cache sequence, the intermediate factor, the first secondary cache sequence and the second secondary cache sequence, based on the iteration equation set iteration image reconstruction sequence of the hybrid imaging algorithm of the Gini weighted norm structure tensor total variation fusion operator, and adding 1 to the iteration mark i;
in step S22, the iterative equation set of the hybrid imaging algorithm based on the kini weighted norm structure tensor total variation fusion operator includes the following formulas:
Figure BDA0002926503550000071
Figure BDA0002926503550000072
Figure BDA0002926503550000073
Figure BDA0002926503550000074
Figure BDA0002926503550000075
wherein ,g(i)Reconstructing a sequence of images for the ith iteration, ΠC(. is a projection of real space C, b(i)For the first iteration of the temporary storage sequence, lambda1Is the first dilutionSparse trade-off parameter, λ2For the second sparse trade-off parameter, τ is the minimized Lipschitz constant,. tau.is the convolution, W is the weighting matrix, JKIn order to weight the block-Jacobian operator,
Figure BDA0002926503550000076
is composed of
Figure BDA0002926503550000077
The projection of (a) is performed,
Figure BDA0002926503550000078
is 1∞-SqThe norm is in the unit sphere space of the norm,
Figure BDA0002926503550000079
is composed of
Figure BDA00029265035500000710
The projection of (a) is performed,
Figure BDA00029265035500000711
is the Gini index GIN unit sphere space, y(i+1)For the first primary buffer sequence of the (i + 1) th iteration, gamma(i)Is an intermediate factor for the ith iteration,
Figure BDA00029265035500000712
for the first secondary cache sequence of the ith iteration,
Figure BDA00029265035500000713
the sequence is cached for the second level of the ith iteration.
First iterative temporal sequence b(i)The calculation formula of (2) is as follows:
Figure BDA00029265035500000714
wherein ,y(i)For the first one-level cache sequence of the ith iteration, τ is the minimized Lipschitz constant, M#Is an inverse matrix of the matrix M, which is a multifrequency near-field millimeterAnd s is a multi-frequency sparse observation sequence.
The above-mentioned
Figure BDA0002926503550000081
Projection of
Figure BDA0002926503550000082
The calculation formula of (2) is as follows:
Figure BDA0002926503550000083
wherein ,
Figure BDA0002926503550000084
is composed of
Figure BDA0002926503550000085
The projection of (a) is performed,
Figure BDA0002926503550000086
for the first secondary buffer sequence of the ith iteration, λ1For the first sparse tradeoff parameter, λ2For the second sparsity tradeoff parameter, τ is the minimized Lipschitz constant, ρ1Approximating the Performance Balancing parameter for the first Moreau envelope, L1Gradient Lipschitz constant for the first even objective sub-function, JKFor weighting block Jacobian operators, ΠC(. cndot.) is a projection of the real space C,
Figure BDA0002926503550000087
the sequence is temporarily stored for the second iteration.
The second iterative temporal sequence
Figure BDA0002926503550000088
The calculation formula of (2) is as follows:
Figure BDA0002926503550000089
wherein τ is extremely smallChemical Lipschitz constant, b(i)For the first iteration of the temporary storage sequence, lambda1For the first sparse tradeoff parameter, λ2For the second sparsity tradeoff parameter, ρ1Approximating the Performance Balancing parameter, g, for the first Moreau envelope(i)Reconstruction sequence of images for the ith iteration, JKIn order to weight the block-Jacobian operator,
Figure BDA00029265035500000810
the sequence is cached for the first level two of the ith iteration.
The above-mentioned
Figure BDA00029265035500000811
Projection of
Figure BDA00029265035500000812
The calculation formula of (2) is as follows:
Figure BDA00029265035500000813
wherein ,
Figure BDA00029265035500000814
is composed of
Figure BDA00029265035500000815
The projection of (a) is performed,
Figure BDA00029265035500000816
second level buffer sequence for ith iteration, lambda1For the first sparse tradeoff parameter, λ2For the second sparsity tradeoff parameter, τ is the minimized Lipschitz constant, ρ2Approximating the performance balance parameter for a second Moreau envelope, L2Is the second dual objective sub-function gradient Lipschitz constant, W is the weighting matrix, piC(. cndot.) is a projection of the real space C,
Figure BDA00029265035500000817
the sequence is temporarily stored for the third iteration.
The thirdIterative temporal storage sequence
Figure BDA00029265035500000818
The calculation formula of (2) is as follows:
Figure BDA0002926503550000091
wherein, tau is a minimized Lipschitz constant, b(i)For the first iteration of the temporary storage sequence, lambda1For the first sparse tradeoff parameter, λ2For the second sparsity tradeoff parameter, ρ2Approximating the performance balance parameter, g, for a second Moreau envelope(i)For the image reconstruction sequence of the ith iteration, W is the weighting matrix,
Figure BDA0002926503550000092
the sequence is cached for the second level of the ith iteration.
S23, judging the whole variation fusion operator of the Gini weighted norm structure tensor
Figure BDA0002926503550000093
Whether or not greater than the interrupt tolerance
Figure BDA0002926503550000094
If yes, jumping to step S24, otherwise, jumping to step S25;
the total variation fusion operator of the kini weighted norm structure tensor in the step S23
Figure BDA0002926503550000095
The calculation formula of (2) is as follows:
Figure BDA0002926503550000096
wherein ,g(i+1)For the image reconstruction sequence of the (i + 1) th iteration, g(i)For the image reconstruction sequence of the ith iteration, | ·| purple2Is a 2 norm.
S24, judging whether the iteration flag i is larger than the iteration upper limit, if so, jumping to the step S25, and if not, jumping to the step S22;
and S25, storing the current image reconstruction sequence to obtain a reconstructed scanning image of the region to be measured.
Experiment:
in a multi-frequency near-field millimeter wave sparse imaging actual measurement experiment, an imaging system scans a measured object about 60mm below a 128mm multiplied by 128mm sampling plane in a grid stepping mode of about 2mm by an antenna probe working at a frequency band of 36 GHz-44 GHz, and the frequency sweep interval is 0.1GHz (N is Nf61). Fig. 2 shows a measured object and a reconstructed full-sampling reconstructed image obtained after data acquisition is carried out on the measured object by a near-field millimeter wave system operating at an operating frequency of 36 GHz-44 GHz. The measured object in fig. 2(a) is a metal scissors, the measured object in fig. 2(b) is a multi-frequency near-field millimeter wave full-sampling reconstructed image in a frequency band of 36GHz to 44GHz, and 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 kini weighted l1 norm selected Daubechies wavelets with vanishing moments of order 8, and the STV operator selected a gaussian convolution kernel of size 3 × 3 with a standard deviation of 0.5. Furthermore, the sparse trade-off parameter λ given in the algorithm1＝4×10-4，λ2＝2×10-4(ii) a Moreau envelope approximation performance balance parameter ρ1＝1，ρ21 is ═ 1; optimizing and minimizing a Lipschitz constant tau of 8; dual objective subfunction gradient Lipschitz constant:
Figure BDA0002926503550000101
interrupt tolerance
Figure BDA0002926503550000102
Fig. 3 shows the image reconstruction effect of the multi-frequency near-field millimeter wave sparse imaging algorithm combined with different mixed sparse functions at different undersampling rates (14%, 21%, 28%). Fig. 3(a) to 3(c) are images reconstructed by the multi-frequency imaging algorithm combining the mixed sparse function of the kini weighted l1 norm + STV operator, and fig. 3(d) to 3(f) are images reconstructed by the multi-frequency imaging algorithm combining the mixed sparse function of the l1 norm + TV operator. As can be seen from comparing fig. 3(a) and fig. 3(d), when the undersampling rate is 14%, the multi-frequency imaging algorithm using the kiney weighted l1 norm + STV operator can reconstruct the screw pattern of the axis of the scissors, whereas the multi-frequency imaging algorithm using the l1 norm + TV operator has not been successfully reconstructed. And when the undersampling rate is 21% and 28%, the effect of the multifrequency imaging algorithm of selecting the Kernel weighted l1 norm + STV operator on the reconstruction of the scissor handle at the lower right corner is better than that of the multifrequency imaging algorithm of selecting the l1 norm + TV operator.
To further illustrate the comparison of imaging effects under two mixed sparse functions, table 1 gives the margins of interruption
Figure BDA0002926503550000103
After the experiment is independently repeated for 50 times, the multi-frequency near-field millimeter wave sparse imaging algorithm of the mixed sparse function has the average effect and the comparison of all indexes when the algorithm converges under different undersampling rates (14%, 21% and 28%). It can be known from the comparison in table 1 that, at different undersampling rates, the proposed imaging algorithm of the mixed sparse function of the kini weighted norm l1 + STV operator has better image reconstruction capability than the imaging algorithm of the mixed sparse function of the norm l1 + TV operator, which explains the effectiveness of the proposed mixed sparse function in the actual measurement experiment.
TABLE 1
Figure BDA0002926503550000111

Claims (10)

1. A multi-frequency near-field millimeter wave sparse image reconstruction method is characterized by comprising the following steps:
s1, scanning the area to be measured through the multi-frequency near-field millimeter wave device to obtain a multi-frequency sparse observation sequence;
and S2, obtaining a reconstructed scanning image of the region to be detected through a hybrid imaging algorithm based on a Gini weighted norm structure tensor total variation fusion operator according to the multi-frequency sparse observation sequence.
2. The multi-frequency near-field millimeter wave sparse reconstruction image method of claim 1, wherein the step S2 comprises the steps of:
s21, setting initial values of an iteration mark i, an image reconstruction sequence, a first primary cache sequence, an intermediate factor, a first secondary cache sequence and a second secondary cache sequence in a computer system;
s22, according to the current first primary cache sequence, the intermediate factor, the first secondary cache sequence and the second secondary cache sequence, based on the iteration equation set iteration image reconstruction sequence of the hybrid imaging algorithm of the Gini weighted norm structure tensor total variation fusion operator, and adding 1 to the iteration mark i;
s23, judging the whole variation fusion operator of the Gini weighted norm structure tensor
Figure FDA0002926503540000012
Whether or not greater than the interrupt tolerance
Figure FDA0002926503540000013
If yes, jumping to step S24, otherwise, jumping to step S25;
s24, judging whether the iteration flag i is larger than the iteration upper limit, if so, jumping to the step S25, and if not, jumping to the step S22;
and S25, storing the current image reconstruction sequence to obtain a reconstructed scanning image of the region to be measured.
3. The multi-frequency near-field millimeter wave sparse image reconstruction method of claim 2, wherein in step S21, an initial value of the iteration flag i is set to 1, and initial values of the image reconstruction sequence, the first primary buffer sequence, the middle 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 FDA0002926503540000011
Figure FDA0002926503540000021
wherein ,g(i)For the image reconstruction sequence of the ith iteration, 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 the multi-frequency sparse observation sequence, y(i)For the first primary buffer sequence of the ith iteration, gamma(i)Is an intermediate factor for the ith iteration,
Figure FDA0002926503540000022
for the first secondary cache sequence of the ith iteration,
Figure FDA0002926503540000023
second level buffer sequence for ith iteration, JKW is a weighting matrix.
4. The method for sparsely reconstructing an image according to claim 2, wherein the iterative equation set of the hybrid imaging algorithm based on the kini weighted norm structure tensor total variation fusion operator in the step S22 includes the following formulas:
Figure FDA0002926503540000024
Figure FDA0002926503540000025
Figure FDA0002926503540000026
Figure FDA0002926503540000027
Figure FDA0002926503540000028
wherein ,g(i)Reconstructing a sequence of images for the ith iteration, ΠC(. is a projection of real space C, b(i)For the first iteration of the temporary storage sequence, lambda1For the first sparse tradeoff parameter, λ2For the second sparse trade-off parameter, τ is the minimized Lipschitz constant,. tau.is the convolution, W is the weighting matrix, JKIn order to weight the block-Jacobian operator,
Figure FDA0002926503540000029
is composed of
Figure FDA00029265035400000210
The projection of (a) is performed,
Figure FDA00029265035400000211
is 1∞-SqThe norm is in the unit sphere space of the norm,
Figure FDA00029265035400000212
is composed of
Figure FDA00029265035400000213
The projection of (a) is performed,
Figure FDA00029265035400000214
is the Gini index GIN unit sphere space, y(i+1)For the first primary buffer sequence of the (i + 1) th iteration, gamma(i)Is an intermediate factor for the ith iteration,
Figure FDA00029265035400000215
for the first secondary cache sequence of the ith iteration,
Figure FDA00029265035400000216
the sequence is cached for the second level of the ith iteration.
5. The method for sparse reconstruction of images of multi-frequency near-field millimeter waves of claim 4, wherein the first iterative temporal storage sequence b(i)The calculation formula of (2) is as follows:
Figure FDA0002926503540000031
wherein ,y(i)For the first one-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.
6. The method for multi-frequency near-field millimeter wave sparse reconstruction of an image according to claim 4, wherein the method is characterized in that
Figure FDA0002926503540000032
Projection of
Figure FDA0002926503540000033
The calculation formula of (2) is as follows:
Figure FDA0002926503540000034
wherein ,
Figure FDA0002926503540000035
is composed of
Figure FDA0002926503540000036
The projection of (a) is performed,
Figure FDA0002926503540000037
for the first secondary buffer sequence of the ith iteration, λ1For the first sparse tradeoff parameter, λ2For the second sparsity tradeoff parameter, τ is the minimized Lipschitz constant, ρ1Approximating the Performance Balancing parameter for the first Moreau envelope, L1Gradient Lipschitz constant for the first even objective sub-function, JKFor weighting block Jacobian operators, ΠC(. cndot.) is a projection of the real space C,
Figure FDA0002926503540000038
the sequence is temporarily stored for the second iteration.
7. The method of claim 6, wherein the second iterative temporal storage sequence is configured to perform sparse reconstruction of the image
Figure FDA0002926503540000039
The calculation formula of (2) is as follows:
Figure FDA00029265035400000310
wherein, tau is a minimized Lipschitz constant, b(i)For the first iteration of the temporary storage sequence, lambda1For the first sparse tradeoff parameter, λ2For the second sparsity tradeoff parameter, ρ1Approximating the Performance Balancing parameter, g, for the first Moreau envelope(i)Reconstruction sequence of images for the ith iteration, JKIn order to weight the block-Jacobian operator,
Figure FDA00029265035400000311
the sequence is cached for the first level two of the ith iteration.
8. The multi-frequency near-field millimeter wave sparse reconstruction image space of claim 4Method characterized in that
Figure FDA00029265035400000312
Projection of
Figure FDA00029265035400000313
The calculation formula of (2) is as follows:
Figure FDA0002926503540000041
wherein ,
Figure FDA0002926503540000042
is composed of
Figure FDA0002926503540000043
The projection of (a) is performed,
Figure FDA0002926503540000044
second level buffer sequence for ith iteration, lambda1For the first sparse tradeoff parameter, λ2For the second sparsity tradeoff parameter, τ is the minimized Lipschitz constant, ρ2Approximating the performance balance parameter for a second Moreau envelope, L2Is the second dual objective sub-function gradient Lipschitz constant, W is the weighting matrix, piC(. cndot.) is a projection of the real space C,
Figure FDA0002926503540000045
the sequence is temporarily stored for the third iteration.
9. The method of claim 8, wherein the third iterative temporal storage sequence is configured to perform sparse reconstruction on the image
Figure FDA0002926503540000046
The calculation formula of (2) is as follows:
Figure FDA0002926503540000047
wherein, tau is a minimized Lipschitz constant, b(i)For the first iteration of the temporary storage sequence, lambda1For the first sparse tradeoff parameter, λ2For the second sparsity tradeoff parameter, ρ2Approximating the performance balance parameter, g, for a second Moreau envelope(i)For the image reconstruction sequence of the ith iteration, W is the weighting matrix,
Figure FDA0002926503540000048
the sequence is cached for the second level of the ith iteration.
10. The method for sparsely reconstructing an image according to claim 2, wherein in the step S23, the kini weighted norm structure tensor full-variation fusion operator
Figure FDA00029265035400000410
The calculation formula of (2) is as follows:
Figure FDA0002926503540000049
wherein ,g(i+1)For the image reconstruction sequence of the (i + 1) th iteration, g(i)For the image reconstruction sequence of the ith iteration, | ·| purple2Is a 2 norm.
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