CN113723483A - Image fusion method and system based on robust principal component analysis - Google Patents

Image fusion method and system based on robust principal component analysis Download PDF

Info

Publication number
CN113723483A
CN113723483A CN202110960255.2A CN202110960255A CN113723483A CN 113723483 A CN113723483 A CN 113723483A CN 202110960255 A CN202110960255 A CN 202110960255A CN 113723483 A CN113723483 A CN 113723483A
Authority
CN
China
Prior art keywords
image
domain
sparse model
echo
combined low
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Pending
Application number
CN202110960255.2A
Other languages
Chinese (zh)
Inventor
但波
王明泽
刘瑜
王亮
高山
谭大宁
尉豪轩
卢中原
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Naval Aeronautical University
Original Assignee
Naval Aeronautical University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Naval Aeronautical University filed Critical Naval Aeronautical University
Priority to CN202110960255.2A priority Critical patent/CN113723483A/en
Publication of CN113723483A publication Critical patent/CN113723483A/en
Pending legal-status Critical Current

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/25—Fusion techniques
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
    • G06F18/213—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods
    • G06F18/2135—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods based on approximation criteria, e.g. principal component analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
    • G06F18/213—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods
    • G06F18/2136—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods based on sparsity criteria, e.g. with an overcomplete basis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/02—Neural networks
    • G06N3/04—Architecture, e.g. interconnection topology
    • G06N3/044—Recurrent networks, e.g. Hopfield networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/02—Preprocessing

Landscapes

  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Data Mining & Analysis (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Physics & Mathematics (AREA)
  • General Engineering & Computer Science (AREA)
  • Life Sciences & Earth Sciences (AREA)
  • Artificial Intelligence (AREA)
  • General Physics & Mathematics (AREA)
  • Evolutionary Computation (AREA)
  • Bioinformatics & Cheminformatics (AREA)
  • Evolutionary Biology (AREA)
  • Bioinformatics & Computational Biology (AREA)
  • Health & Medical Sciences (AREA)
  • Biomedical Technology (AREA)
  • Biophysics (AREA)
  • Computational Linguistics (AREA)
  • General Health & Medical Sciences (AREA)
  • Molecular Biology (AREA)
  • Computing Systems (AREA)
  • Mathematical Physics (AREA)
  • Software Systems (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

The invention relates to an image fusion method and system based on robust principal component analysis, wherein the method comprises the following steps: acquiring a through-wall radar echo signal; carrying out robust principal component analysis on the through-wall radar echo signal, and establishing an echo domain combined low-rank sparse model; processing the through-wall radar echo signal by using a BP algorithm to obtain an original image; carrying out robust principal component analysis on the original image, and establishing an image domain combined low-rank sparse model; respectively solving the echo domain combined low-rank sparse model and the image domain combined low-rank sparse model by using a smoothing rapid alternating linearization method, and determining an echo domain target image and an image domain target image; and performing exponential weighting joint multiplication fusion processing on the echo domain target image and the image domain target image to obtain a fusion image. The invention can improve the accuracy of separating the clutter from the target, thereby improving the accuracy of target detection.

Description

Image fusion method and system based on robust principal component analysis
Technical Field
The invention relates to the field of clutter suppression, in particular to an image fusion method and system based on robust principal component analysis.
Background
Unlike other radars in free space, a Through-The Wall Imaging Radar (TWIR) needs to detect and image a target behind a Wall. In this process, clutter signals caused by wall reflections can "mask" the target signal with a large amplitude or interleave and overlap with the target signal in the time domain. Therefore, the method effectively inhibits the wall clutter and is an important precondition for accurate imaging of the TWIR on the target behind the wall.
Classical clutter suppression algorithms such as Singular Value Decomposition (SVD) can only achieve elimination of the clutter of the main wall, and the residual clutter can significantly reduce the imaging quality of the target. With the wide application and deep research of the TWIR, the requirements of the work such as target detection, target identification and the like on early-stage imaging are more and more strict, and the existing clutter suppression algorithm is difficult to achieve the conditions of real-time performance and accuracy of through-wall imaging.
In recent years, machine learning theories have been gradually introduced into the TWIR field, such as Compressive Sensing (CS), Matrix Completion (MC), and Robust Principal Component Analysis (RPCA). The RPCA can be used as a common tool for research directions such as foreground extraction in hyperspectral image denoising and video monitoring, and can uniquely decompose a data matrix into a low-rank clutter matrix and a sparse target matrix, namely, the accurate separation of clutter and a target is realized at the same time. Therefore, a method is needed to accurately separate clutter from targets using RPCA.
Disclosure of Invention
The invention aims to provide an image fusion method and system based on robust principal component analysis to improve accuracy of clutter and target separation.
In order to achieve the purpose, the invention provides the following scheme:
an image fusion method based on robust principal component analysis comprises the following steps:
acquiring a through-wall radar echo signal;
carrying out robust principal component analysis on the through-wall radar echo signal, and establishing an echo domain combined low-rank sparse model;
processing the through-wall radar echo signal by using a BP algorithm to obtain an original image;
carrying out robust principal component analysis on the original image, and establishing an image domain combined low-rank sparse model;
respectively solving the echo domain combined low-rank sparse model and the image domain combined low-rank sparse model by using a smoothing rapid alternating linearization method, and determining an echo domain target image and an image domain target image;
and performing exponential weighting joint multiplication fusion processing on the echo domain target image and the image domain target image to obtain a fusion image.
Optionally, the echo domain joint low-rank sparse model is:
Figure BDA0003222031650000021
wherein, UwAs a matrix of clutter signals, UtgFor the target signal matrix, γ is a regularization parameter that balances the low rank term and the sparse term.
Optionally, the image domain joint low-rank sparse model is:
Figure BDA0003222031650000022
wherein, IwAs a matrix of clutter components, ItgFor the target component matrix, γ is a regularization parameter that balances the low rank term and the sparse term.
Optionally, the using a smoothing rapid alternating linearization method to respectively solve the echo domain combined low-rank sparse model and the image domain combined low-rank sparse model to determine an echo domain target image and an image domain target image specifically includes:
inputting the through-wall radar echo signal into the echo domain combined low-rank sparse model, and inputting the original image into the image domain combined low-rank sparse model;
respectively initializing a smooth parameter and a penalty parameter of a combined low-rank sparse model, wherein the combined low-rank sparse model comprises an echo domain combined low-rank sparse model and an image domain combined low-rank sparse model;
smoothing the initialized combined low-rank sparse model to obtain a smoothed combined low-rank sparse model;
and iterating the smoothed combined low-rank sparse model to obtain an echo domain target image and an image domain target image.
Optionally, the performing an exponential weighting, joint multiplication and fusion process on the echo domain target image and the image domain target image to obtain a fusion image specifically includes:
setting a first weighting index;
determining a second weighting index according to the first weighting index and the pixel mean value;
and performing exponential weighted joint multiplication multi-domain image fusion processing on the target image according to the first weighted index and the second weighted index to obtain a fused image.
An image fusion system based on robust principal component analysis, comprising:
the acquisition module is used for acquiring through-wall radar echo signals;
the first robust principal component analysis module is used for carrying out robust principal component analysis on the through-wall radar echo signal and establishing an echo domain combined low-rank sparse model;
the original image determining module is used for processing the through-wall radar echo signal by using a BP algorithm to obtain an original image;
the second robust principal component analysis module is used for carrying out robust principal component analysis on the original image and establishing an image domain combined low-rank sparse model;
the solving module is used for respectively solving the echo domain combined low-rank sparse model and the image domain combined low-rank sparse model by using a smoothing rapid alternating linearization method to determine an echo domain target image and an image domain target image;
and the index weighting joint multiplication fusion processing module is used for performing index weighting joint multiplication fusion processing on the echo domain target image and the image domain target image to obtain a fusion image.
Optionally, the echo domain joint low-rank sparse model is:
Figure BDA0003222031650000031
wherein, UwAs a matrix of clutter signals, UtgFor the target signal matrix, γ is a regularization parameter that balances the low rank term and the sparse term.
Optionally, the image domain joint low-rank sparse model is:
Figure BDA0003222031650000041
wherein, IwAs a matrix of clutter components, ItgFor the target component matrix, γ is a regularization parameter that balances the low rank term and the sparse term.
Optionally, the solving module specifically includes:
the input unit is used for inputting the through-wall radar echo signals to the echo domain combined low-rank sparse model and inputting the original images to the image domain combined low-rank sparse model;
the initialization unit is used for respectively initializing a smooth parameter and a penalty parameter of a combined low-rank sparse model, wherein the combined low-rank sparse model comprises an echo domain combined low-rank sparse model and an image domain combined low-rank sparse model;
the smoothing unit is used for smoothing the initialized combined low-rank sparse model to obtain a smoothed combined low-rank sparse model;
and the iteration unit is used for iterating the smoothed combined low-rank sparse model to obtain an echo domain target image and an image domain target image.
Optionally, the exponentially weighted joint multiplication fusion processing module specifically includes:
a setting unit for setting a first weighting index;
a second weighting index determining unit, configured to determine a second weighting index according to the first weighting index and the pixel mean;
and the exponential weighting joint multiplication multi-domain image fusion processing unit is used for performing exponential weighting joint multiplication multi-domain image fusion processing on the target image according to the first weighting index and the second weighting index to obtain a fusion image.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
according to the image fusion method and system based on robust principal component analysis, multi-domain joint processing is achieved by establishing the echo domain joint low-rank sparse model and the image domain joint low-rank sparse model, meanwhile, robust principal component analysis is conducted in the echo domain and the image domain, index weighting joint multiplication fusion processing is conducted on the echo domain target image and the image domain target image, clutter and target division precision is improved, and when the echo domain joint low-rank sparse model and the image domain joint low-rank sparse model are solved, the processing speed of the whole image fusion method is improved through a smoothing rapid alternating linearization method.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments 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 to obtain other drawings without inventive exercise.
FIG. 1 is a flowchart of an image fusion method based on robust principal component analysis according to the present invention;
FIG. 2 is a simplified flowchart of the image fusion method based on robust principal component analysis according to the present invention;
FIG. 3 is a schematic diagram of an image fusion system based on robust principal component analysis provided by the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. 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 invention aims to provide an image fusion method and system based on robust principal component analysis to improve accuracy of clutter and target separation.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
In order to meet the requirements of real-time performance and accuracy of through-wall imaging, the invention respectively designs and improves the speed and the precision of an algorithm: firstly, a smoothing rapid alternate linearization method is provided to shorten the solving time of the RPCA problem, thereby accelerating the speed of the algorithm; and secondly, multi-domain combined processing is carried out, an RPCA theory is applied to an echo domain and an image domain, and the precision of the algorithm is improved by carrying out exponential weighting combined multiplication fusion processing on the obtained target image.
As shown in fig. 1, the image fusion method based on robust principal component analysis provided by the present invention includes:
step 101: and acquiring a through-wall radar echo signal.
Step 102: and carrying out robust principal component analysis on the through-wall radar echo signal, and establishing an echo domain combined low-rank sparse model. Wherein the echo domain joint low-rank sparse model is as follows:
Figure BDA0003222031650000061
wherein, UwAs a matrix of clutter signals, UtgFor the target signal matrix, γ is a regularization parameter that balances the low rank term and the sparse term.
The robust Principal Component Analysis is a polynomial time algorithm generated to enhance the robustness of Principal Component Analysis (PCA). Compared with the classical PCA, the RPCA expands the slight disturbance of the low-rank matrix into a sparse error matrix with any size, and breaks through the limitation of additive one-dimensional Gaussian noise. Briefly, RPCA maps a data matrix D ∈ Rl×sExpressed as a low rank matrix A ∈ Rl×sAnd the sparse matrix E ∈ Rl×sSumming and decomposing the two. Wherein R isl×sFor l is the number of rows of the matrix and s is the number of columns of the matrix. As an optimization problem, its mathematical expression is
Figure BDA0003222031650000062
Wherein rank (A) represents the rank of matrix A, | E | | Y0L representing the matrix E0Norm, γ > 0, γ is a regularization parameter that balances the low rank term and the sparse term. Meanwhile, in order to guarantee the unique decomposition of the matrix, the following conditions need to be satisfied:
Figure BDA0003222031650000063
where ρ > 0 is a constant coefficient.
However, formula (1) contains both MC and l0Norm minimization of thisTwo sub-problems of Non-deterministic Polynomial difficulties (NP-Hard), so this discontinuous Non-convex optimization problem does not exist as a theoretically valid solution. However, in combination with the results of the relevant studies, in1Norm instead of l0Norm, the rank of which replaces the matrix with the nuclear norm, so that the optimization problem after convex relaxation can be obtained as
Figure BDA0003222031650000064
Wherein | A | Y phosphor*Representing the kernel norm of the matrix A, | E | | non-woven cells1L representing the matrix E1And (4) norm. Here, matrices a and E are to meet the rank sparse incoherent condition to ensure a correct solution of the convex optimization problem. Obviously, in a rather broad range of cases, this condition is true, i.e. matrices a and E can be accurately recovered with a high probability.
For the solution of the RPCA problem in equation (3), there are several common first-order methods: the method comprises the steps of firstly, accelerating an approximate Gradient (APG) method, and realizing local approximation of a target function by a linearization function, so that the calculated amount of single iteration is small, but the convergence speed is slow; secondly, a precise Augmented Lagrange Multipliers (EALM) method obtains matrixes A and E by alternately iterating and augmenting Lagrange functions, high-order linear convergence can be realized, however, the SVD times of each iteration are more, and the calculation speed is greatly influenced; and thirdly, an Inaccurate Augmented Lagrange Multipliers (IALMs) method, which minimizes the alternation of multiple rounds in the EALM to one round, and can effectively reduce SVD times on the basis of keeping the original convergence speed.
Echo domain modeling
First, the imaging scene is set as follows: the TWIR detects and images a target behind a wall by a uniform antenna array which is arranged at the same time of receiving and transmitting, the number of the array elements is N, the antenna array is parallel to the surface of the uniform wall, and echo signals received by the nth antenna array element are
u(n,t)＝uw(n,t)+utg(n,t)+uno(n,t)+uant(n,t) (4)
Wherein u isw(n, t) is a wall clutter signal, utg(n, t) is a target echo signal, uno(n, t) is a noise signal, uantAnd (n, t) is an antenna coupling signal. In the invention, the antenna coupling wave is eliminated after being preprocessed, and the influence of a noise signal is relatively weak due to pulse accumulation, so that an echo signal can be further simplified into a signal
u(n,t)＝uw(n,t)+utg(n,t) (5)
The result in equation (5) is then extended to the entire antenna array, with a two-dimensional echo matrix
U＝Uw+Utg,U∈RT×N (6)
Wherein T is the number of sampling points of each antenna channel signal, UwAs a matrix of clutter signals, UtgIs a target signal matrix.
In the imaging scene, the wall reflection coefficients and the signal transmission paths corresponding to the antenna elements are the same, and the wall reflection echoes received by the antenna elements are the same, namely, the U-shaped reflection echoes are the same, as for the wall clutter signals alonewIs a low rank matrix. From the space, the targets behind the wall are sparse relative to the whole detection area; similarly, in the echo domain, the target sampling points are also sparse with respect to all sampling points, i.e., UtgIs a sparse matrix. Then, according to equation (3), a Joint Low-Rank Sparse (JLRS) model is established in the echo domain, including
Figure BDA0003222031650000081
Step 103: and processing the through-wall radar echo signal by using a BP algorithm to obtain an original image.
Step 104: and carrying out robust principal component analysis on the original image, and establishing an image domain combined low-rank sparse model. Wherein the image domain joint low-rank sparse model is as follows:
Figure BDA0003222031650000082
wherein, IwAs a matrix of clutter components, ItgFor the target component matrix, γ is a regularization parameter that balances the low rank term and the sparse term.
In practical applications, the steps 102 and 103-104 are performed simultaneously.
Compared with an echo domain, the image domain is visual representation of the detection region, and the effect of applying the RPCA theory is better. For the two-dimensional echo matrix in equation (6), if the imaging process is performed by the Back Projection (BP) algorithm, the amplitude of any pixel in the image is
i(p,q)＝iW(p,q)+itg(p,q) (8)
Wherein iW(p, q) is the pixel clutter component at position (p, q), itg(p, q) is the pixel target component at position (p, q). Extending this representation to the entire image, there is a two-dimensional image matrix
I＝Iw+Itg,I∈RP×Q (9)
P, Q represents the number of longitudinally and transversely divided pixels in the image, IwAs a matrix of clutter components, ItgIs the target component matrix.
In practice, the BP algorithm is to add the channel signals coherently after time compensation. In this way, the signal is focused at the target location and the sparsity of the target is greatly enhanced, obviously ItgIs a sparse matrix; while the otherwise "aligned" clutter signals become "scattered" and the low rank nature of the clutter is reduced, but I can still be consideredwIs a low rank matrix. Similarly, a JLRS model is built in the image domain, which has
Figure BDA0003222031650000091
Step 105: and respectively solving the echo domain combined low-rank sparse model and the image domain combined low-rank sparse model by using a smoothing rapid alternating linearization method, and determining an echo domain target image and an image domain target image.
Wherein, the 105 specifically comprises:
and inputting the through-wall radar echo signal to the echo domain combined low-rank sparse model, and inputting the original image to the image domain combined low-rank sparse model.
Respectively initializing smooth parameters and penalty parameter of a combined low-rank sparse model, wherein the combined low-rank sparse model comprises the echo domain combined low-rank sparse model and the image domain combined low-rank sparse model.
And smoothing the initialized combined low-rank sparse model to obtain a smoothed combined low-rank sparse model.
And iterating the smoothed combined low-rank sparse model to obtain an echo domain target image and an image domain target image.
From the analysis of the solution method to the RPCA problem, one can obtain: the linearized approximation reduces the computational complexity of a single iteration, while the alternate iterations speed up convergence and reduce the iteration complexity. In order to increase the RPCA problem solving speed, an SFAL (Smoothing Fast Alternating Linearization) method is proposed.
Taking the image domain JLRS model as an example, take definite | | | Iw||*＝f(x)，γ||I-Iw||1The RPCA problem in equation (10) can be converted into a minimization problem of the sum of convex functions, i.e., P ═ l, Q ═ s
Figure BDA0003222031650000107
However, considering that the convex functions f (x), g (x) are all non-smooth, the smoothing process is performed sequentially for the convenience of solving the minimization.
In order to enhance the scalability of the smoothing process and reduce the smoothing parameter adjustments, a smooth proximity function is preferably chosen, as distinguished from classical smoothing techniquesc (v). c (v) is Rl×s Convexity parameter κ c1, its gradient
Figure BDA0003222031650000105
Satisfying the Lipschitz continuity and the Lipschitz constant Lc≥κc. Order to
Figure BDA0003222031650000101
And given a smoothness parameter α > 0, the smooth approximation function of f (x) is
Figure BDA0003222031650000102
Wherein f is*Fenchel conjugation function of f, dom (f)*) As a function f*Definition of (a)-1f*(α-1x) represents the parameter α-1Lower convex function f*The Moreau envelope, | · | | non-woven phosphor2Is represented by2Norm, v is an auxiliary variable. Due to the strong convexity of the proximity function, the optimization problem in equation (12) has a unique optimal solution, i.e.
Jα(x)＝α-1(x-proxαf(x)) (13)
Wherein the neighbor operators
Figure BDA0003222031650000103
r is an auxiliary variable
For smooth function fα(x) In other words, the gradient thereof
Figure BDA0003222031650000106
Satisfying the Lipschitz continuity and the Lipschitz constant Lfα＝α-1. Similarly, for the function g (x), there is a smooth approximation function of
Figure BDA0003222031650000104
Wherein beta > 0 is a smoothing parameter, g*Fenchel conjugation function of gAnd (4) counting. Function gβ(x) Gradient of (2)
Figure BDA0003222031650000111
Satisfy Lipschitz continuity, and Lipschitz constant
Figure BDA00032220316500001113
At this time, equation (11) can be transformed into the following smooth convex optimization problem:
Figure BDA0003222031650000112
considering fα(x) And gβ(x) Is a linearized differentiable function, which in its regularized form constitutes a quadratic approximation of the objective function F (x), respectively, of
Figure BDA0003222031650000113
Figure BDA0003222031650000114
Wherein, muf、μgIs a penalty parameter, y, z are iteration variables, k is the number of iterations, zkIs the z variable at the kth iteration,
Figure BDA0003222031650000115
and
Figure BDA0003222031650000116
are all quadratic approximations of the objective function. Neglecting the constant term, the minimum values of the equations (16) and (17) are respectively
Figure BDA0003222031650000117
Figure BDA0003222031650000118
Due to fα(x) And gβ(x) The calculation of the minimum value can be simplified to solve the one-dimensional minimization problem for a separable function, and the calculation amount is small. At the same time, to accelerate convergence, η is introduced to update the operator z, having
Figure BDA0003222031650000119
Figure BDA00032220316500001110
It can be easily demonstrated that the above method has an iterative complexity of
Figure BDA00032220316500001111
Wherein the content of the first and second substances,
Figure BDA00032220316500001112
epsilon represents the order of the optimal solution, and the iterative complexity reaches the theoretical limit of the first-order method[. Finally, a flow chart summarizing the SFAL method is shown in table 1.
TABLE 1 SFAL methods
Figure BDA0003222031650000121
When the JLRS model in the echo domain is solved by the SFAL method, only the input is required to be changed into a two-dimensional echo matrix U epsilon RT ×N、
Figure BDA0003222031650000122
The remaining parameters need not be adjusted.
Step 106: and performing exponential weighting joint multiplication fusion processing on the echo domain target image and the image domain target image to obtain a fusion image.
Step 106 specifically includes:
a first weighting index is set.
And determining a second weighting index according to the first weighting index and the pixel mean value.
And performing exponential weighted joint multiplication multi-domain image fusion processing on the target image according to the first weighted index and the second weighted index to obtain a fused image.
From the JLRS model established above, it is easy to find that clutter and targets are not always strictly low rank or strictly sparse in each domain. In the echo domain, clutter is low rank, sparsity of the target is weak, and the opposite is true in the image domain. The two display a 'complementary relation' in nature, and the relation is particularly obvious in the target image obtained from each domain. In order to improve the algorithm precision and the target imaging quality, the target image is subjected to exponential weighting joint multiplication multi-domain image fusion processing.
First, the target image in the echo domain and the image domain is analyzed as follows: in an echo domain, a target signal matrix in the JLRS model is a real matrix, phase information of a target is hidden, an obtained target image is equivalent to an incoherent BP imaging result, and the azimuth resolution and the focusing effect are reduced by the influence of residual clutter, but main clutter of a wall body is suppressed relatively thoroughly; in an image domain, original echo imaging is directly decomposed, a target image at the moment is a coherent BP imaging result, the target focusing effect is relatively good, clutter separation is not thorough enough, and a certain 'shielding' effect is formed on a target.
Through the analysis, compared with multi-channel or multi-angle sub-image fusion, the target images in the echo domain and the image domain have certain difference, and the basic joint multiplication fusion has limited improvement on the target imaging quality. Thereby, an exponential weighting joint multiplication fusion idea is provided, namely
Figure BDA0003222031650000131
Wherein imf(p, q) is the pixel point amplitude at position (p, q) in the fused image, i1(p,q)、i2(p, q) are eachThe pixel point amplitudes of the target image in the echo domain and the image domain at the position (p, q), and a and b are weighting indexes of corresponding sub-images.
The values of the weighted indices are discussed further. Considering the difference of target images in each domain, an excessive weighting index can cause target loss, and a, b E [0,1] can be preliminarily defined. On the basis, in order to conveniently and quickly determine the optimal weighting index pair, the image domain target image with better target focusing effect is not used as the fused main image, the contribution of the echo domain target image in the joint multiplication is adjusted to suppress clutter and a focusing target to the maximum extent, namely a proper a epsilon [0,1] is searched under the condition that b is equal to 1. In the process, the speed requirement of the algorithm and the joint multiplication value experience are comprehensively considered, and the value of a can be accurate to 0.05.
Subsequently, an evaluation index is determined to represent the improvement effect of different weighted index values on the imaging quality of the target in the fused image. Generally, the pixel mean is a common image domain index, which is defined as
Figure BDA0003222031650000132
With the increase of the weighting index a, the contribution of the echo domain target image in the fusion image is correspondingly increased, and the clutter is gradually eliminated; after the clutter basically disappears, the weighting index is continuously increased, so that the loss of the target pixel is caused, and therefore, it is important to find a node where the clutter disappears. However, in this process, the pixel mean value continues to decrease, and the rate of decrease does not have a significant change point. Based on the above teaching, the index of the number of pixels in the super-mean value can be considered, and if the set of all the pixel points in the image is S, the index is defined as
Figure BDA0003222031650000141
Wherein the set of pixel points whose amplitude exceeds the pixel mean
Figure BDA0003222031650000142
crad (B) indicates the number of elements in set B.
Also during the weighted exponential increase, the number of pixels in the super-mean value shows a regular change: from the beginning, the number of pixels exceeding the average value is continuously reduced at a higher speed along with the elimination of the clutter pixels with larger amplitude; after the clutter basically disappears, the target pixel becomes the main body of the pixel to be eliminated in the image, and the reduction speed of the index can be obviously slowed down. Compared with the pixel mean value, the index describes the pixel change more carefully and comprehensively, so that the node with the deceleration change is easy to find. Therefore, the number of pixels in the super-average value is used as an evaluation index, and the first point at which the deceleration is slowed is used as a weighting index a.
As shown in fig. 2, the main steps of the method provided by the present invention can be summarized as follows:
the first stage is as follows: and obtaining target images in each domain by using an SFAL method, wherein the steps comprise 1 and 2.
Step 1: directly establishing an echo domain JLRS model according to the through-wall radar echo signal; meanwhile, the echo signals are processed by a BP algorithm to obtain an original image, and an image domain JLRS model is established according to the original image.
Step 2: and sequentially solving the JLRS model in each domain by using an SFAL method to respectively obtain the target images in each domain.
And a second stage: and performing exponential weighted joint multiplication fusion processing on the target images in each domain, wherein the processing comprises steps 3 and 4.
And step 3: given b ═ 1, and plot the change curve of the number of pixels over the mean in steps of 0.05 over a range of a ∈ [0,1], with the first point where the curve deceleration is significantly slowed down as the weighting index a.
And 4, step 4: and performing exponential weighted joint multiplication multi-domain image fusion processing according to the selected weighted indexes a and b to obtain a final fusion image.
As shown in fig. 3, the image fusion system based on robust principal component analysis provided by the present invention includes:
and the obtaining module 301 is configured to obtain a through-wall radar echo signal.
And the first robust principal component analysis module 302 is used for performing robust principal component analysis on the through-wall radar echo signal and establishing an echo domain combined low-rank sparse model.
And the original image determining module 303 is configured to process the through-wall radar echo signal by using a BP algorithm to obtain an original image.
And the second robust principal component analysis module 304 is configured to perform robust principal component analysis on the original image, and establish an image domain combined low-rank sparse model.
And the solving module 305 is configured to respectively solve the echo domain combined low-rank sparse model and the image domain combined low-rank sparse model by using a smoothing fast alternative linearization method, and determine an echo domain target image and an image domain target image.
And an exponential weighting, joint multiplication and fusion processing module 306, configured to perform exponential weighting, joint multiplication and fusion processing on the echo domain target image and the image domain target image to obtain a fusion image.
Wherein the echo domain joint low-rank sparse model is as follows:
Figure BDA0003222031650000151
wherein, UwAs a matrix of clutter signals, UtgFor the target signal matrix, γ is a regularization parameter that balances the low rank term and the sparse term.
Wherein the image domain joint low-rank sparse model is as follows:
Figure BDA0003222031650000152
wherein, IwAs a matrix of clutter components, ItgFor the target component matrix, γ is a regularization parameter that balances the low rank term and the sparse term.
In practical applications, the solving module 305 specifically includes:
and the input unit is used for inputting the through-wall radar echo signals to the echo domain combined low-rank sparse model and inputting the original images to the image domain combined low-rank sparse model.
And the initialization unit is used for respectively initializing a smooth parameter and a penalty parameter of a combined low-rank sparse model, wherein the combined low-rank sparse model comprises the echo domain combined low-rank sparse model and the image domain combined low-rank sparse model.
And the smoothing unit is used for smoothing the initialized combined low-rank sparse model to obtain the smoothed combined low-rank sparse model.
And the iteration unit is used for iterating the smoothed combined low-rank sparse model to obtain an echo domain target image and an image domain target image.
In practical application, the exponentially weighted joint-multiplication fusion processing module 306 specifically includes:
a setting unit for setting the first weighting index.
And the second weighting index determining unit is used for determining a second weighting index according to the first weighting index and the pixel mean value.
And the exponential weighting joint multiplication multi-domain image fusion processing unit is used for performing exponential weighting joint multiplication multi-domain image fusion processing on the target image according to the first weighting index and the second weighting index to obtain a fusion image.
The invention provides a multi-domain combined suppression algorithm based on an RPCA theory aiming at the clutter suppression problem of a through-wall radar, the algorithm enables target imaging to be focused accurately through multi-domain image fusion, and the real-time performance of the process is enhanced by utilizing an SFAL method. Simulation proves that the algorithm has good speed and precision, can realize sufficient suppression on clutter, and can quickly provide accurate target information for subsequent processing such as target detection, identification and the like.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.

Claims (10)

1. An image fusion method based on robust principal component analysis is characterized by comprising the following steps:
acquiring a through-wall radar echo signal;
carrying out robust principal component analysis on the through-wall radar echo signal, and establishing an echo domain combined low-rank sparse model;
processing the through-wall radar echo signal by using a BP algorithm to obtain an original image;
carrying out robust principal component analysis on the original image, and establishing an image domain combined low-rank sparse model;
respectively solving the echo domain combined low-rank sparse model and the image domain combined low-rank sparse model by using a smoothing rapid alternating linearization method, and determining an echo domain target image and an image domain target image;
and performing exponential weighting joint multiplication fusion processing on the echo domain target image and the image domain target image to obtain a fusion image.
2. The image fusion method based on robust principal component analysis according to claim 1, wherein the echo domain joint low-rank sparse model is:
Figure FDA0003222031640000011
wherein, UwAs a matrix of clutter signals, UtgIs a target messageThe number matrix, γ, is the regularization parameter that balances the low rank term and the sparse term.
3. The robust principal component analysis based image fusion method of claim 1, wherein the image domain combined low rank sparse model is:
Figure FDA0003222031640000012
wherein, IwAs a matrix of clutter components, ItgFor the target component matrix, γ is a regularization parameter that balances the low rank term and the sparse term.
4. The image fusion method based on robust principal component analysis according to claim 1, wherein the solving of the echo domain combined low-rank sparse model and the image domain combined low-rank sparse model by using a smoothing fast alternative linearization method respectively determines an echo domain target image and an image domain target image, and specifically comprises:
inputting the through-wall radar echo signal into the echo domain combined low-rank sparse model, and inputting the original image into the image domain combined low-rank sparse model;
respectively initializing a smooth parameter and a penalty parameter of a combined low-rank sparse model, wherein the combined low-rank sparse model comprises an echo domain combined low-rank sparse model and an image domain combined low-rank sparse model;
smoothing the initialized combined low-rank sparse model to obtain a smoothed combined low-rank sparse model;
and iterating the smoothed combined low-rank sparse model to obtain an echo domain target image and an image domain target image.
5. The image fusion method based on robust principal component analysis according to claim 1, wherein the exponentially weighted joint multiplication fusion processing is performed on the echo domain target image and the image domain target image to obtain a fusion image, and specifically includes:
setting a first weighting index;
determining a second weighting index according to the first weighting index and the pixel mean value;
and performing exponential weighted joint multiplication multi-domain image fusion processing on the target image according to the first weighted index and the second weighted index to obtain a fused image.
6. An image fusion system based on robust principal component analysis, comprising:
the acquisition module is used for acquiring through-wall radar echo signals;
the first robust principal component analysis module is used for carrying out robust principal component analysis on the through-wall radar echo signal and establishing an echo domain combined low-rank sparse model;
the original image determining module is used for processing the through-wall radar echo signal by using a BP algorithm to obtain an original image;
the second robust principal component analysis module is used for carrying out robust principal component analysis on the original image and establishing an image domain combined low-rank sparse model;
the solving module is used for respectively solving the echo domain combined low-rank sparse model and the image domain combined low-rank sparse model by using a smoothing rapid alternating linearization method to determine an echo domain target image and an image domain target image;
and the index weighting joint multiplication fusion processing module is used for performing index weighting joint multiplication fusion processing on the echo domain target image and the image domain target image to obtain a fusion image.
7. The robust principal component analysis based image fusion system of claim 6, wherein the echo domain joint low rank sparse model is:
Figure FDA0003222031640000031
wherein, UwAs a matrix of clutter signals, UtgFor the target signal matrix, γ is a regularization parameter that balances the low rank term and the sparse term.
8. The robust principal component analysis based image fusion system of claim 6, wherein the image domain in combination with the low rank sparse model is:
Figure FDA0003222031640000032
wherein, IwAs a matrix of clutter components, ItgFor the target component matrix, γ is a regularization parameter that balances the low rank term and the sparse term.
9. The image fusion system based on robust principal component analysis according to claim 6, wherein the solving module specifically comprises:
the input unit is used for inputting the through-wall radar echo signals to the echo domain combined low-rank sparse model and inputting the original images to the image domain combined low-rank sparse model;
the initialization unit is used for respectively initializing a smooth parameter and a penalty parameter of a combined low-rank sparse model, wherein the combined low-rank sparse model comprises an echo domain combined low-rank sparse model and an image domain combined low-rank sparse model;
the smoothing unit is used for smoothing the initialized combined low-rank sparse model to obtain a smoothed combined low-rank sparse model;
and the iteration unit is used for iterating the smoothed combined low-rank sparse model to obtain an echo domain target image and an image domain target image.
10. The image fusion system based on robust principal component analysis according to claim 6, wherein the exponentially weighted joint-multiplication fusion processing module specifically comprises:
a setting unit for setting a first weighting index;
a second weighting index determining unit, configured to determine a second weighting index according to the first weighting index and the pixel mean;
and the exponential weighting joint multiplication multi-domain image fusion processing unit is used for performing exponential weighting joint multiplication multi-domain image fusion processing on the target image according to the first weighting index and the second weighting index to obtain a fusion image.
CN202110960255.2A 2021-08-20 2021-08-20 Image fusion method and system based on robust principal component analysis Pending CN113723483A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110960255.2A CN113723483A (en) 2021-08-20 2021-08-20 Image fusion method and system based on robust principal component analysis

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110960255.2A CN113723483A (en) 2021-08-20 2021-08-20 Image fusion method and system based on robust principal component analysis

Publications (1)

Publication Number Publication Date
CN113723483A true CN113723483A (en) 2021-11-30

Family

ID=78677104

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110960255.2A Pending CN113723483A (en) 2021-08-20 2021-08-20 Image fusion method and system based on robust principal component analysis

Country Status (1)

Country Link
CN (1) CN113723483A (en)

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116794624A (en) * 2022-12-26 2023-09-22 南京航空航天大学 ResNet-based data domain and image domain combined SAR target recognition method
CN117289262A (en) * 2023-11-27 2023-12-26 中南大学 Method and system for detecting through-wall radar target

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116794624A (en) * 2022-12-26 2023-09-22 南京航空航天大学 ResNet-based data domain and image domain combined SAR target recognition method
CN117289262A (en) * 2023-11-27 2023-12-26 中南大学 Method and system for detecting through-wall radar target
CN117289262B (en) * 2023-11-27 2024-02-06 中南大学 Method and system for detecting through-wall radar target

Similar Documents

Publication Publication Date Title
Wang et al. ISAR imaging of maneuvering target based on the local polynomial Wigner distribution and integrated high-order ambiguity function for cubic phase signal model
CN113567985B (en) Inverse synthetic aperture radar imaging method, device, electronic equipment and storage medium
CN113723483A (en) Image fusion method and system based on robust principal component analysis
Cao et al. Infrared dim target detection via mode-k1k2 extension tensor tubal rank under complex ocean environment
CN110726992B (en) SA-ISAR self-focusing method based on structure sparsity and entropy joint constraint
CN109669182B (en) Passive bistatic SAR moving/static target joint sparse imaging method
CN110135344B (en) Infrared dim target detection method based on weighted fixed rank representation
JP7297164B2 (en) Image reconstruction using an artificial intelligence (AI) module that is agnostic to image acquisition settings
CN109298420B (en) Moving target iteration minimum entropy imaging method and device of synthetic aperture radar
CN111551928A (en) Through-wall radar imaging method based on wall low-rank sparse constraint
CN110554384A (en) imaging method based on microwave signal
EP2817655B1 (en) Systems and methods for image sharpening
CN112147608A (en) Rapid Gaussian gridding non-uniform FFT through-wall imaging radar BP method
CN111781595A (en) Complex maneuvering group target imaging method based on matching search and Doppler ambiguity resolution
Han et al. Refocusing of moving targets based on low-bit quantized SAR data via parametric quantized iterative hard thresholding
Kulik et al. Multichannel deconvolution with long range dependence: Upper bounds on the Lp-risk (1≤ p<∞)
CN113589287A (en) Synthetic aperture radar sparse imaging method and device, electronic equipment and storage medium
Li et al. An Unsupervised CNN-Based Multichannel Interferometric Phase Denoising Method Applied to TomoSAR Imaging
CN111308436B (en) Radar space-time adaptive processing method and device based on volume correlation function
CN110045374B (en) Chirp Scaling-based multi-angle ultra-long bunching SAR super-resolution imaging algorithm
CN113885026A (en) SAR sparse imaging method and device of moving target, electronic equipment and storage medium
Zhou et al. HPHR-SAR-Net: Hyper-pixel High-resolution SAR Imaging Network Based on Nonlocal Total Variation
CN111708028A (en) SAR image secondary imaging method based on multi-fractal spectrum
Jiang et al. Research on multiplicative speckle noise denoising method of side-scan sonar image based on analysis sparse decomposition
Gao et al. Three-dimensional array SAR sparse imaging based on hybrid regularization

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination