CN105405100B - A kind of sparse driving SAR image rebuilds regularization parameter automatic selecting method - Google Patents

Abstract

The invention discloses a method for automatically selecting regularization parameters for sparsely driven SAR image reconstruction. In regularized image reconstruction, the choice of regularization parameters is a very important issue. For the selection of non-quadratic regularization parameters, conventional selection methods have limited capabilities. In order to obtain high-quality reconstructed images, it is often necessary to manually select regularization parameters. In order to solve the above problems, the present invention proposes a numerical calculation method for automatic selection of regularization parameters for sparsely driven SAR image reconstruction on the basis of studying the L -curve method. The beneficial effect of the present invention is that the automatic selection of the regularization parameter for sparsely driven SAR image reconstruction is realized. Using this method to solve the regularization parameters of sparsely driven SAR image reconstruction not only has a small amount of calculation, but also provides a better balance between noise suppression and feature preservation, and a more reasonable reconstructed image can be obtained.

Description

An Automatic Selection Method of Regularization Parameters for Sparse-Driven SAR Image Reconstruction

technical field

The invention relates to a method for automatically selecting regularization parameters for sparse-driven SAR (Synthetic aperture radar, synthetic aperture radar) image reconstruction.

Background technique

Traditional SAR imaging technology has low resolution, coherent speckle noise and side lobe effects, which seriously affect the application of SAR images in tasks such as automatic target detection and target recognition. In recent years, researchers have successively proposed some new SAR image reconstruction methods. Among them, the SAR image reconstruction method based on sparseness drive, its basic idea is to achieve the purpose of enhancing the characteristics of SAR image through regularization solution. In general, image reconstruction methods based on regularization obtain a stable solution to the problem by trying to balance data fidelity and prior knowledge, and its stability is achieved by a scalar parameter, the regularization parameter. Therefore, in regularized image reconstruction, the selection of regularization parameters is a very important issue. At present, researchers have proposed several regularization parameter selection methods based on statistical ideas, such as Stein unbiased risk estimation method, generalized cross-validation method, Bayesian method and L -curve method, among which the most famous and widely used is Tikhonov regularization method. The Tikhonov regularization method is a quadratic regularization method. In the Tikhonov regularization method, the quadratic optimization problem is composed of a set of linear equations with closed solutions, which can realize the automatic selection of regularization parameters and greatly reduce the computational load of image reconstruction. Given the advantages afforded by image sparse representations, it is becoming increasingly common to introduce regularization constraints into sparse image reconstruction problems. Introducing non-quadratic regularization constraints to sparse problems can improve the sparsity of the desired problem. However, the introduction of non-quadratic constraints will lead to no closed solution to the optimization problem, so iterative numerical calculation methods are required to solve the problem. Therefore, the choice of regularization parameters under non-quadratic constraints is more complicated than quadratic. For the selection of non-quadratic regularization parameters, the conventional Stein unbiased risk estimation method, generalized cross-validation method and L -curve method have limited capabilities. In order to obtain high-quality sparsely driven SAR reconstruction images, regularization parameters are often required artificial selection. In order to solve the above problems, the present invention proposes a numerical calculation method for automatic selection of regularization parameters for sparsely driven SAR image reconstruction on the basis of studying the L -curve method.

(1) Sparse-driven SAR image reconstruction principle

SAR image reconstruction based on regularization is mainly based on the following SAR observation process:

(1)

Where H is the discrete complex-valued SAR image reconstruction operator, w is the additive Gaussian white noise, g and f are the measured data and the real reflection scene, respectively. To emphasize the sparsity of reflective scenes, we formulate the SAR image reconstruction problem as the following optimization problem:

(2)

in is the regularization parameter, Indicates to find the l _p norm of f , which is defined as , where f _i is the ith element of f , and n is the number of elements in f . The first item in the formula (2) is called the data fidelity item, which includes the SAR observation model (1) and observation geometry information. The second term is called the regularization term or bounding constraint term, and we use it to introduce prior information into image reconstruction. When p = 2 in the regularization term, it is the famous Tikhonov regularization method. Different from the Tikhonov regularization method, the boundary constraint term in the present invention aims to introduce sparse prior information, so we will choose other p values besides p = 2. when When , the minimum l _p norm reconstruction will produce local energy accumulation in the reconstructed result image, thus improving the sparsity of the reconstructed image. The purpose of using the Boundary Constraints item is to suppress image artifacts and increase the resolution of the scatter, resulting in a sparse resulting image. Experiments have demonstrated that this sparsity constraint can produce super-resolution reconstructed resulting images.

To avoid the problem that the objective function is not differentiable when fi is zero, we approximate the _lp norm and _modify the objective function (2) as:

(3)

in is a small scalar. In the experiment, we consider a compromise based on experience, choose .

Our goal is to find an estimate . When p > 1, the desired problem is a convex optimization problem. beg For the gradient of f , there are:

(4)

in is a diagonal weighting matrix whose ith diagonal element is . Let the gradient equal to zero, for any value of p , the solution of the optimization problem is a stagnation point, so the following equation is satisfied:

(5)

The i -th diagonal element of y weights the intensity of the i -th pixel according to a penalty term that varies with space. Since the weighting matrix depends on , but equation (5) for is not linear, so formula (5) has no closed solution, but we can use the fixed-point iterative method to solve it, and each step of the iterative process includes solving the following linear problem:

(6)

in is the solution obtained at the kth iteration. Although (6) for In principle a closed solution can be produced, but this requires solving the inverse of a very large matrix. Therefore, we use the gradient descent method to numerically solve the equations (6).

(2) L -curve method

The objective function (3) contains a scalar parameter, the regularization parameter , which plays an important role in scene reconstruction. when parameter When is small, the data fidelity term, namely the first term in the objective function (3), plays a dominant role in the solution of the objective function (3); when the parameter When is larger, the second item in the objective function (3), that is, the penalty item based on the l _p norm, has a greater effect on the solution of the objective function (3). In order to obtain high-quality and accurately reconstructed SAR images, it is necessary to choose a suitable value, so that the effects of the data fidelity item and the penalty item can be better balanced. The present invention will use the improved L -curve method (L-curve) to adjust the regularization parameters based on the data-driven approach. Make an automatic selection.

The definition of the L -curve method is: in the log-logarithmic coordinate system, the norm The corresponding residual norm The ratio of , where the regularization parameter as its parameter. In practical applications, the L -curve usually appears as an L -shaped curve as shown in FIG. 1 . It is generally believed that the corner position of the L -shaped curve is a selection parameter A good area of , choosing the parameters of this area can achieve The balance between regularization error and perturbation error. The choice of regularization parameters using the L -curve method is based on this property. Although it seems intuitive and simple, the calculation of the corner position of the L -curve is not easy. The current method of determining the corner position mainly includes calculating the point with the largest curvature, calculating the point closest to the reference position (such as the origin), and calculating the tangent point of a straight line with a slope of -1, etc. In the following, we will use the L -curve optimization solution method to automatically select the regularization parameters for sparse-driven SAR image reconstruction, and give its implementation steps.

Contents of the invention

In order to overcome the shortcomings of the method for selecting regularization parameters for sparsely driven SAR image reconstruction, the present invention provides an L -curve optimization solution method, and provides its implementation steps, so as to realize the automatic selection of regularization parameters for sparsely driven SAR image reconstruction.

The specific technical scheme adopted in the present invention is the regularization parameter optimization solution algorithm as follows:

(1) Set regularization parameters The search interval for ;

(2) Take the initial lower bound and upper bound of the search interval as and ;

(3) calculation the value of , , and , where k and l are the number of iterations, is a preset step size;

(4) Calculate the L curve , , and the slope of the tangent to the point , , and , where the differential is calculated numerically;

(5) if

So , k = k +1

otherwise

Similarly,

if

So , l = l +1

otherwise

Repeat steps (3)-(5) to further narrow the search interval;

(6) Take the reference point ( x ₀ , y ₀ ), which is and the intersection of the tangent lines at;

(7) According to the golden ratio Determine the two test values ;

(8) Calculate the residual norm Reconciliation norm , where i =1, 2; H is the discrete complex-valued SAR image reconstruction operator, g and f are the measured data and the real reflection scene, respectively, the superscript 2 and p represent the power of 2 and the power of p respectively, and the subscripts 2 and p represents the 2 - norm and p- norm of the matrix, respectively;

(9) Calculation point and the distance between the reference point ( x ₀ , y ₀ ) , where ln represents natural logarithm, whose base is e ;

(10) Use the golden section search method to determine a new interval ,Right now

if d ₁ > d ₂

So

otherwise ;

(11) , repeat steps (7)-(11) until the interval I is small enough.

Compared with the prior art, the beneficial effect of the present invention is that the automatic selection of the regularization parameter for sparsely driven SAR image reconstruction is realized. Using this method to solve the regularization parameters of sparsely driven SAR image reconstruction not only has a small amount of calculation, but also provides a better balance between noise suppression and feature preservation, and a more reasonable reconstructed image can be obtained. It should be pointed out that although the present invention is mainly dedicated to solving the problem of sparsely driven SAR image reconstruction, it can be fully applied to other complex-valued l _p norm regularized image reconstruction problems.

Description of drawings

Attached Figure 1 of the specification is a schematic diagram of L curve and regularization parameter search.

Detailed ways

In order to make the technical means, creative features, work flow, and use methods of the present invention achieve the purpose and effect easy to understand, the present invention will be further described below in conjunction with accompanying drawing 1 of the description.

The present invention determines the optimization algorithm steps of sparsely driven SAR image reconstruction regularization parameters as follows:

(1) Set regularization parameters The search interval for ;

(2) Take the initial lower bound and upper bound of the search interval as and ;

(3) calculation the value of , , and , where k and l are the number of iterations, is a preset step size;

(4) Calculate the L curve , , and the slope of the tangent to the point , , and , where the differential is calculated numerically;

(5) if

So , k = k +1

otherwise

Similarly,

if

So , l = l +1

otherwise

Repeat steps (3)-(5) to further narrow the search interval;

(6) Take the reference point ( x ₀ , y ₀ ), which is and the intersection of the tangent lines at;

(7) According to the golden ratio Determine the two test values ;

(8) Calculate the residual norm Reconciliation norm , where i =1, 2; H is the discrete complex-valued SAR image reconstruction operator, g and f are the measured data and the real reflection scene, respectively, the superscript 2 and p represent the power of 2 and the power of p respectively, and the subscripts 2 and p represents the 2 - norm and p- norm of the matrix, respectively;

(9) Calculation point and the distance between the reference point ( x ₀ , y ₀ ) , where ln represents natural logarithm, whose base is e ;

(10) Use the golden section search method to determine a new interval ,Right now

if d ₁ > d ₂

So

otherwise ;

(11) , repeat steps (7)-(11) until the interval I is small enough.

The basic principles and main features of the present invention and the advantages of the present invention have been shown and described above. Those skilled in the industry should understand that the present invention is not limited by the above-mentioned embodiments, and what described in the above-mentioned embodiments and the description only illustrates the principles of the present invention, and the present invention will also have other functions without departing from the spirit and scope of the present invention. Variations and improvements are possible, which fall within the scope of the claimed invention. The protection scope of the present invention is defined by the appended claims and their equivalents.

Claims (1)

1. a kind of sparse driving SAR image rebuilds regularization parameter automatic selecting method, which is characterized in that this method includes as follows The step of determining regularization parameter：

（1）If regularization parameterThe region of search be；

（2）The initial lower bound and the upper bound for taking the region of search be respectivelyWith；

（3）It calculatesValue,,With, whereinkWithlFor iterations,For preset step-length；

（4）It calculatesLMistake on curve,,WithThe tangent slope of point,,With, Middle differential is calculated using numerical method；

（5）If

So,k=k+1

Otherwise

Similarly,

If

So,l=l+1

Otherwise

Repeat step（3）-（5）, further reduce the region of search；

（6）Take reference point（x ₀, y ₀）, it isWithLocate the intersection point of tangent line；

（7）According to golden section ratioDetermine two test values；

（8）Calculate residual normConciliate norm, whereini=1, 2；HIt is discrete multiple It is worth SAR image and rebuilds operator,gWithfRespectively measured data and true reflection scene, 2 He of subscriptpRepresent respectively 2 power andpIt is secondary Power, 2 He of subscriptpIt represents to ask the 2 of matrix respectively-Norm andp-Norm；

（9）Calculate pointAnd reference point（x ₀, y ₀）The distance between , wherein ln expression take natural logrithm, the truth of a matter ise；

（10）A new section is determined using golden section search, i.e.,

Ifd ₁ >d ₂

So

Otherwise；

（11）, repeat step（7）-（11）, until sectionIIt is sufficiently small, so far complete the selection of regularization parameter.