CN112731395B - SAR imaging method based on non-convex and total variation regularization - Google Patents
SAR imaging method based on non-convex and total variation regularization Download PDFInfo
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Abstract
Based on non-protruding&Full-variation regularized SAR imaging partyA method comprising the steps of: constructing an SAR observation model; construction based on non-convex&A full variational regularized SAR imaging model; non-convex based solution using variable separation and generalized threshold iterative contraction algorithm&And (3) a full-variance regularized SAR imaging model, and completing SAR imaging. Compared with L 1 &The TV regularization method can accurately reconstruct the scattering intensity amplitude information of the target, and avoid underestimation of the scattering intensity amplitude information of the target; compared with the traditional matched filtering algorithm, the method provided by the invention can not only effectively inhibit additive noise and clutter, but also inhibit speckle noise, maintain the continuity and uniformity of the backward scattering coefficient of the surface target, and can realize the simultaneous enhancement of the characteristics of the point target and the surface target.
Description
Technical Field
The invention relates to the technical field of radar imaging, in particular to a SAR imaging method based on non-convex and total variation regularization (Nonconvex & total variation regularization).
Background
The synthetic aperture radar (Synthetic aperture radar, SAR) is an active microwave imaging system, has the characteristics of all-day, all-weather and high-resolution imaging, and is widely applied to the aspects of military reconnaissance, environmental monitoring, land resource management and the like. With the development of SAR technology, the resolution and mapping bandwidth of radar systems are required to be continuously improved, and the bottleneck of large data volume is also becoming more apparent.
Based on L 1 The regularized SAR imaging method can effectively inhibit noise and clutter under the condition of full sampling, and improve the image quality; and under the condition of downsampling rate, the SAR image is effectively reconstructed, and target details are kept. L (L) 1 Regularization can enhance point target features in SAR images; total Variation (TV) regularization can enhance the surface target characteristics in SAR images, and maintain the continuity and uniformity of the surface target backscattering coefficients. Will L 1 The simple linear combination of the norm penalty term and the TV norm penalty term generates a compound penalty function, and L can be obtained 1 &A TV regularization model that can enhance both point target features and face target features. But L is 1 The regularization method is a convex optimization methodThe method inevitably underestimates the amplitude of the SAR reconstruction target, so that errors of a signal processing end are caused, and the SAR calibration precision is influenced.
Disclosure of Invention
Accordingly, a primary object of the present invention is to provide a SAR imaging method based on non-convex and total variation regularization, so as to partially solve at least one of the above technical problems.
In order to achieve the above object, as an aspect of the present invention, there is provided a SAR imaging method based on non-convex & total variation regularization, comprising the steps of:
constructing an SAR observation model;
constructing an SAR imaging model based on non-convex and total variation regularization;
and solving the SAR imaging model based on non-convex and total variation regularization by using a variable separation and generalized threshold iterative shrinkage algorithm to finish SAR imaging.
According to the SAR geometric relationship, a SAR two-dimensional observation model is constructed as follows:
Y＝ΞA+N；
wherein Y is SAR two-dimensional echo, A is SAR two-dimensional scene, xi is observation matrix constructed according to SAR observation geometry, and N is two-dimensional additive noise.
Vectorizing the SAR two-dimensional observation model to obtain a one-dimensional observation model as follows:
y＝Φα+n；
wherein y is a two-dimensional echo vectorization result, alpha is a two-dimensional scene vectorization result, phi is a corresponding observation matrix after vectorizing the echo and the scene, and n is vectorized additive noise.
The SAR imaging model based on non-convex and total variation regularization is as follows:
wherein lambda is 1 ，λ 2 For regularization parameters, p (α) is a non-convex penalty term, and TV (|α|) is a total variationA norm penalty term.
Wherein the non-convex penalty term includes L q A norm penalty term, a log and penalty term, a minimum maximum concave penalty term, and a smooth clipping absolute deviation penalty term.
Wherein, the definition of the minimum maximum concave penalty term is:
the definition of the smooth clipping absolute deviation penalty term is:
wherein the total variation norm penalty term is defined as:
wherein, the liquid crystal display device comprises a liquid crystal display device,
D h |A| i，j ＝|A[i+1，j]|-|A[i，j]|；
D v |A| i，j ＝|A[i，j+1]|-|A[i，j]|。
the method for solving the SAR imaging model based on non-convex and total variation regularization by using the variable separation and generalized threshold iterative shrinkage algorithm specifically comprises the following steps:
initializing iteration parameters: the radar echo is y, the observation matrix is phi, and the radar scene is initialized to alpha 0 =0, intermediate variable z 1 0 ＝0，z 2 0 ＝0，p 0 = (0, 0), regularization parameter λ 1 ，λ 2 Lagrange multiplier is l 1 ，l 2 Full variation regularization iteration step τ=0.248, noiseAcoustic variance sigma; let the maximum iteration step number be T max Let iteration step number initial value t=0, iteration termination condition epsilon;
performing iteration;
and calculating iteration parameters.
The formula adopted in the iteration is as follows:
λ 1 (t+1) ＝2l 1 (|α (t+1) | K+1 )；
z 2 (t+1) ＝α (t+1) -λ TV div(p (t+1) )；
wherein, the liquid crystal display device comprises a liquid crystal display device,
wherein sign (·) represents the sign function.
Wherein the calculation of the iteration parameters
res＝||α( t+1) -α (t) || 2 /||α (t) || 2 ；
t＝t+1；
Judging whether res > epsilon and T < T are satisfied at the same time max And if the conditions are not met, continuing iteration.
Based on the above technical solution, compared with the prior art, the SAR imaging method of the present invention has at least some of the following advantages:
compared with L 1 &The TV regularization method can accurately reconstruct the scattering intensity amplitude information of the target, and avoid underestimation of the scattering intensity amplitude information of the target; compared with the traditional matched filtering algorithm, the method provided by the invention can not only effectively inhibit additive noise and clutter, but also inhibit speckle noise, maintain the continuity and uniformity of the backward scattering coefficient of the surface target, and can realize the simultaneous enhancement of the characteristics of the point target and the surface target.
Drawings
FIG. 1 is a process flow diagram of synthetic aperture radar imaging based on non-convex & full-variational regularization;
FIG. 2 is a matched filtering algorithm, L 1 &TV regularization and non-convex&Reconstruction results of the full variance regularization on the simulation surface target, wherein fig. 2 (a) is the reconstruction results of the matched filtering algorithm, and fig. 2 (b) is L 1 &FIG. 2 (c) is the reconstruction result of the TV regularization, the method of the invention employing MC penalty term, and FIG. 2 (d) is the reconstruction result of the method of the invention employing SCAD;
FIG. 3 is a matched filtering algorithm, L 1 &TV regularization and non-convex&The reconstruction result of the full variance regularization on the face object in the Gaofen-3 scene is shown in FIG. 3 (a) which is the reconstruction result of the matching filter algorithm on the face object in the Gaofen-3 scene, and FIG. 3 (b) which is L 1 &TV regularization results on reconstruction of face targets in Gaofen-3 scene, FIG. 3 (c) is the result of reconstruction of face targets in Gaofen-3 scene by MC penalty term, and FIG. 3 (d) is the result of reconstruction of face targets in Gaofen-3 scene by SCAD.
Detailed Description
Comparison with L 1 The pattern and properties of the norm penalty term, the non-convex penalty term, are closer to L 0 Norm numberThe penalty term, therefore, is that the non-convex regularization can both get a sparse solution and avoid underestimation of the reconstructed sparse vector magnitude. Common non-convex penalty terms are: l (L) q A norm penalty term, a Log sum penalty term (LSP), a minimum maximum concave penalty term (Minimax concave penalty, MCP), and a smooth clipping absolute deviation penalty term (Smoothly clipped absolute deviation, SCAD). The non-convex penalty term and the TV regular term are simply and linearly combined to generate a compound penalty function, thus obtaining the non-convex penalty&A total variation regularization model. The imaging model has the following advantages: 1. comparison with L 1 &TV regularization, the method avoids underestimation of the amplitude of the reconstruction sparse vector, and improves the reconstruction precision; 2. compared with a Matched Filter (MF) algorithm, the method can effectively inhibit additive noise and clutter, can inhibit speckle noise, keeps the continuity and uniformity of the backward scattering coefficient of the surface target, and can realize the simultaneous enhancement of the characteristics of the point target and the surface target.
The invention discloses a non-convex based&Synthetic aperture radar imaging method based on total variation regularization, which is established based on non-convex first&The model is then solved using a variable separation (Variable splitting, VS) and generalized threshold iterative contraction (Generalized iterative shrinkage and thresholding, GIST) algorithm. Compared with L 1 &The TV regularization method can accurately reconstruct the scattering intensity amplitude information of the target, and avoid underestimation of the scattering intensity amplitude information of the target; compared with the traditional matched filtering algorithm, the method can effectively inhibit additive noise and clutter, can inhibit speckle noise, keeps the continuity and uniformity of the backward scattering coefficient of the surface target, and can realize the simultaneous enhancement of the characteristics of the point target and the surface target.
The present invention will be further described in detail below with reference to specific embodiments and with reference to the accompanying drawings, in order to make the objects, technical solutions and advantages of the present invention more apparent.
As shown in fig. 1, a process flow diagram of synthetic aperture radar imaging based on non-convex & total variation regularization; the method specifically comprises the following steps:
step S1: construction of SAR observation model
Constructing an SAR two-dimensional observation model according to the SAR geometric relationship
Y＝ΞA+N
Wherein Y is SAR two-dimensional echo, A is SAR two-dimensional scene, xi is observation matrix constructed according to SAR observation geometry, and N is two-dimensional additive noise.
Vectorizing the two-dimensional observation model to obtain a one-dimensional observation model
y＝Φα+n
y is a two-dimensional echo vectorization result, alpha is a two-dimensional scene vectorization result, phi is a corresponding observation matrix after vectorizing the echo and the scene, and n is vectorized additive noise.
Step S2: building SAR imaging model based on non-convex and total variation regularization
Where p (α) is a non-convex penalty term, and here two typical non-convex penalty terms of MC and SCAD are defined:
and TV (|α|) is a total variation norm penalty term defined as:
wherein, the liquid crystal display device comprises a liquid crystal display device,
D h |A| i，j ＝|A[i+1，j]|-|A[i，j]|，
D v |A| i，j ＝|A[i，j+1]|-|A[i，j]|.
step S3: SAR imaging models based on non-convex & total variation regularization are solved using a generalized threshold iterative contraction (Generalized iterative shrinkage and thresholding, GIST) algorithm with variable separation (Variable splitting, VS).
Step S31: initializing iteration parameters: the radar echo is y, the observation matrix is phi, and the radar scene is initialized to alpha 0 =0, intermediate variable z 1 0 ＝0，z 2 0 ＝0，p 0 = (0, 0), regularization parameter λ 1 ，λ 2 Lagrange multiplier is l 1 ，l 2 The full variance regularization iteration step τ=0.248, noise variance σ. Setting the maximum iteration step number as T max Let iteration step number initial value t=0, iteration termination condition epsilon.
Step S32: iteration is performed using the following formula
λ 1 (t+1) ＝2l 1 (|α (t+1) | K+1 )
z 2 (t+1) ＝α (t+1) -λ TV div(p (t+1) ).
Wherein, the liquid crystal display device comprises a liquid crystal display device,
in the formula, sign (·) represents a sign function.
Step S33: calculating iteration parameters
res＝||α (t+1) -α (t) || 2 /||α (t) || 2
t＝t+1
Judging whether res > epsilon and T < T are satisfied at the same time max Otherwise, step S32 is entered.
The SAR imaging method based on non-convex and total variation regularization provided by the invention is verified by a simulation experiment and a Gaofen-3 actual measurement data experiment.
FIG. 2 is a matched filtering algorithm, L 1 &TV regularization and non-convex&Reconstruction results of the full variance regularization on the simulation surface target, wherein fig. 2 (a) is the reconstruction results of the matched filtering algorithm, and fig. 2 (b) is L 1 &The reconstruction result of TV regularization, fig. 2 (c) is the reconstruction result of the method of the present invention using the MC penalty term, and fig. 2 (d) is the reconstruction result of the method of the present invention using SCAD.
Table 1 shows the mean and variance of the face target magnitudes in the results of three methods (where the non-convex & total variation regularization method uses two typical non-convex penalty terms: MC and SCAD) reconstruction.
TABLE 1
| Reconstruction method | Mean mu | Variance sigma 2 |
| Matched filtering | 1.7579 | 0.4968 |
| L 1 &TV regularization | 1.2450 | 0.0973 |
| MC&TV regularization | 1.7020 | 0.0974 |
| SCAD&TV regularization | 1.7019 | 0.0975 |
FIG. 3 is a matched filtering algorithm, L 1 &TV regularization and non-convex&The reconstruction result of the full variance regularization on the face object in the Gaofen-3 scene is shown in FIG. 3 (a) which is the reconstruction result of the matching filter algorithm on the face object in the Gaofen-3 scene, and FIG. 3 (b) which is L 1 &TV regularization results on reconstruction of face targets in Gaofen-3 scene, FIG. 3 (c) is the result of reconstruction of face targets in Gaofen-3 scene by MC penalty term, and FIG. 3 (d) is the result of reconstruction of face targets in Gaofen-3 scene by SCAD.
Three rectangular areas in the target island are selected, as shown in fig. 3 (a), the mean and variance of the complex image amplitude are respectively settled, and the statistical result is shown in table 2.
TABLE 2
From the above results, it can be seen that compared with L 1 &The TV regularization method can accurately reconstruct the scattering intensity amplitude information of the target, and avoid underestimation of the scattering intensity amplitude information of the target; compared with the traditional matched filtering algorithm, the method based on the invention can not only effectively inhibit additive noise and clutter, but also inhibit speckle noise, maintain the continuity and uniformity of the backward scattering coefficient of the surface target, and can realize the simultaneous enhancement of the characteristics of the point target and the surface target.
The foregoing description of the embodiments has been provided for the purpose of illustrating the general principles of the invention, and is not meant to limit the invention thereto, but to limit the invention thereto, and any modifications, equivalents, improvements and equivalents thereof may be made without departing from the spirit and principles of the invention.
Claims (6)
1. The SAR imaging method based on non-convex and total variation regularization is characterized by comprising the following steps of:
constructing an SAR observation model;
constructing an SAR imaging model based on non-convex and total variation regularization;
solving an SAR imaging model based on non-convex and total variation regularization by utilizing a variable separation and generalized threshold iterative shrinkage algorithm to finish SAR imaging;
the SAR imaging model based on non-convex and total variation regularization is as follows:
wherein y is a two-dimensional echo vectorization result, alpha is a two-dimensional scene vectorization result, phi is an observation matrix corresponding to the vectorized echo and scene, and lambda 1 ,λ 2 For regularization parameters, p (α) is a non-convex penalty, and TV (|α|) is a full variation norm penalty.
2. The SAR imaging method according to claim 1, wherein the construction of the SAR two-dimensional observation model from the SAR geometric relationship is as follows:
Y＝ΞA+N；
wherein Y is SAR two-dimensional echo, A is SAR two-dimensional scene, xi is observation matrix constructed according to SAR observation geometry, and N is two-dimensional additive noise.
3. The SAR imaging method according to claim 2, wherein the SAR two-dimensional observation model is vectorized to obtain a one-dimensional observation model as follows:
y＝Φα+n；
wherein y is a two-dimensional echo vectorization result, alpha is a two-dimensional scene vectorization result, phi is a corresponding observation matrix after vectorizing the echo and the scene, and n is vectorized additive noise.
4. The SAR imaging method of claim 1, wherein the non-convex penalty term comprises L q A norm penalty term, a log and penalty term, a minimum maximum concave penalty term, and a smooth clipping absolute deviation penalty term.
5. The SAR imaging method according to claim 1, wherein the solving the SAR imaging model based on non-convex & total variation regularization using variable separation and generalized threshold iterative contraction algorithm specifically comprises:
initializing iteration parameters: the radar echo is y, the observation matrix is phi, and the radar scene is initialized to alpha 0 =0, intermediate variable z 1 0 ＝0，z 2 0 ＝0，p 0 = (0, 0), regularization parameter λ 1 ,λ 2 Lagrange multiplier is l 1 ,l 2 The full variance regularization iteration step τ=0.248, noise variance σ; let the maximum iteration step number be T max Let iteration step number initial value t=0, iteration termination condition epsilon;
performing iteration;
and calculating iteration parameters.
6. The SAR imaging method of claim 5, wherein the calculated iteration parameters
res＝||α (t+1) -α (t) || 2 /||α (t) || 2 ；
t＝t+1；
Judging whether res > epsilon and T < T are satisfied at the same time max If the conditions are not met, continuing iteration;
wherein t is the number of iterative steps.
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