CN105405100B - A kind of sparse driving SAR image rebuilds regularization parameter automatic selecting method - Google Patents
A kind of sparse driving SAR image rebuilds regularization parameter automatic selecting method Download PDFInfo
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Abstract
The invention discloses the automatic selecting methods that a kind of sparse driving SAR image rebuilds regularization parameter.In regularized image reconstruction, the problem of selection of regularization parameter is one extremely important.Selection for non-quadratic form regularization parameter, Conventional methods of selection ability is limited, in order to obtain the reconstruction image of high quality, it is often necessary to carry out artificial selection to regularization parameter.To solve the above-mentioned problems, the present invention is studyingLOn the basis of curve method, it is proposed that a kind of sparse driving SAR image rebuilds the numerical computation method that regularization parameter automatically selects.The beneficial effects of the invention are as follows realize sparse driving SAR image to rebuild automatically selecting for regularization parameter.Solving sparse driving SAR image reconstruction regularization parameter using this method, not only calculation amount is small, but also a preferable balance is provided between noise suppressed and feature are kept, and can obtain more rational reconstruction image.
Description
Technical field
The present invention relates to a kind of sparse driving SAR（Synthetic aperture radar, synthetic aperture radar）Image
Rebuild regularization parameter automatic selecting method.
Background technology
Traditional SAR imaging techniques resolution ratio is low, and there are coherent speckle noises and secondary lobe to influence, and seriously affects SAR image certainly
Application in the tasks such as moving-target detection and target identification.In recent years, researcher proposes some new SAR image weights in succession
Construction method wherein the SAR image method for reconstructing based on sparse driving, basic thought are solved by regularization, reaches enhancing
The purpose of SAR image feature.In general, the image rebuilding method based on regularization is all by trying equilibrium criterion fidelity
With priori obtain required by problem stable solution, stability realized by a scalar parameter, that is, regularization parameter.Cause
This is in regularized image reconstruction, the problem of selection of regularization parameter is one extremely important.At present, researcher proposes
Several regularization parameter selection methods based on statistical thinking, such as Stein unbiased evaluation of risk method, Generalized Cross Validation method, shellfish
This method of leaf andLCurve method, wherein most famous and be widely used that Tikhonov regularization methods.Tikhonov regularizations
Method is a kind of secondary regularization method.In Tikhonov regularization methods, quadratic form optimization problem is by one group of linear equation
Composition, with closing solution, it can be achieved that regularization parameter automatically selects, greatly reduce the operand of image reconstruction.In view of
Advantage possessed by image sparse expression, introduces sparse image Problems of Reconstruction by regularization constraint at present and becomes increasingly prevalent.
Non- secondary regularization constraint is introduced Sparse Problems can improve the openness of required problem.However, non-quadratic form constraint is drawn
Membership causes optimization problem not close solution, so as to need that problem is solved using iterations and numerical simulation method.Therefore, with
Quadratic form is compared, and the selection of the non-lower regularization parameter of quadratic form constraint is more complicated.Choosing for non-quadratic form regularization parameter
Select, conventional Stein unbiased evaluation of risk method, Generalized Cross Validation method andLThe ability of curve method is limited, in order to obtain high quality
Sparse driving SAR reconstruction images, generally require to regularization parameter carry out artificial selection.To solve the above-mentioned problems, this hair
It is bright to studyLOn the basis of curve method, it is proposed that a kind of sparse driving SAR image rebuilds the numerical value that regularization parameter automatically selects
Computational methods.
（One）Sparse driving SAR image rebuilds principle
SAR image reconstruction based on regularization is based primarily upon following SAR observation process：
（1）
WhereinHOperator is rebuild for discrete complex value SAR image,wFor additive white Gaussian noise,gWithfRespectively measured data and
True reflection scene.In order to emphasize the openness of reflection scene, we ask the optimization that SAR image Problems of Reconstruction is expressed as
Topic：
（2）
WhereinIt is regularization parameter,Expression is askedf'sl p Norm is defined as, heref i
It isf iA element,nIt isfThe number of middle element.（2）First item in formula is known as data fidelity item, it includes SAR and observes mould
Type（1）And observation geological information.Section 2 is known as regularization term or boundary constraint item, we can be introduced prior information using it
Into image reconstruction.When in regularization termp It is exactly famous Tikhonov regularization methods when=2.With Tikhonov just
Then change method difference, the present invention in boundary constraint item be intended to introduce sparse prior information, therefore in addition top=2, we can also
Selection is otherpValue.WhenWhen, it is minimuml p Norm, which is reconstituted in reconstructed results image, can generate local energy aggregation, thus
Improve the openness of reconstruction image.Purpose using boundary constraint item is to inhibit image artifacts, increases the resolving power of scattering, from
And generate a sparse result images.Experiment is it has been proved that this sparse constraint can generate the reconstructed results of super-resolution
Image.
In order to avoid working asf i When being zero the problem of object function non-differentiability, we are rightl p Norm carries out approximation, by object function
（2）It is revised as：
（3）
WhereinIt is the scalar of a very little.In an experiment, we rule of thumb compromise consideration, selection。
Our target is that estimated value is obtained.Whenp>1, required problem is that a convex optimization is asked
Topic.It asksIt is rightfGradient, have：
（4）
WhereinIt is a diagonal weight matrix, itsiA diagonal element is.If
Gradient is equal to zero, for anypValue, the solution of the optimization problem is a stationary point, therefore meet following equation：
（5）
iA diagonal element is according to the penalty term with spatial variations toiThe intensity of a pixel is added
Power.Since weighting matrix depends on, but equation（5）ForBe not it is linear, therefore（5）Formula does not close solution, but we
It can be solved using fixed point iteration method, each step of iterative process is all comprising the following linear problem of solution：
（6）
WhereinIt iskThe solution that secondary iteration is obtained.Although（6）Formula forA closing can be generated in principle
Solution, but this needs to solve one very big inverse of a matrix matrix.Therefore we use Numerical Methods Solve side using gradient descent method
Journey group（6）.
（Two）LCurve method
Object function（3）In include a scalar parameter, that is, regularization parameter, it has important work in scene rebuilding
With.Work as parameterWhen smaller, data fidelity item, i.e. object function（3）In first item, to object function（3）Solution rise dominate
Effect；Work as parameterWhen larger, object function（3）In Section 2, that is, be based onl p The penalty term of norm is to object function（3）'s
The effect increase of solution.In order to obtain the SAR image of high quality Exact Reconstruction, it is necessary to select one suitablyValue, protects data
True item and penalty term this two effect are preferably balanced.The present invention will be based on data-driven version, and use is improvedLIt is bent
Collimation method（L-curve）To regularization parameterIt is automatically selected.
LThe definition of curve method is：In log-log coordinate system, normIts corresponding residual norm
Ratio, wherein with regularization parameterFor its parameter.In practical applications,LCurve is usually expressed as shown in Figure 1L
Type curve.It is generally believed thatLThe corner location of type curve is selection parameterGood area, select the parameter in the region can be with
It realizesBalance between middle regularization error and agitation error.It utilizesLCurve method selection regularization parameter is based on this
Characteristic.While it appear that it is intuitive simple, butLThe calculating of curved corner position is not easy to.The method of determining corner location at present
Mainly have and calculate the point of maximum curvature, calculate closest to reference position（Such as origin）Point and straight line that calculating slope is -1
Point of contact etc..We will use belowLThe regularization parameter that optimization of profile method for solving rebuilds sparse driving SAR image carries out certainly
Dynamic selection, and provide implementation step.
Invention content
In order to overcome the shortcomings of that above-mentioned sparse driving SAR image rebuilds regularization parameter selection method, the present invention provides
It is a kind ofLOptimization of profile method for solving, gives implementation step, and regularization parameter is rebuild so as to fulfill sparse driving SAR image
Automatically select.
Specific technical solution of the present invention, that is, regularization parameter Optimization Solution algorithm is as follows：
（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 iteration time
Number,For preset step-length；
（4）It calculatesLMistake on curve,,WithThe tangent slope of point,,With
, wherein differential 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, here 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.
Compared with prior art, the beneficial effects of the invention are as follows realize sparse driving SAR image to rebuild regularization parameter
Automatically select.Solving sparse driving SAR image reconstruction regularization parameter using this method, not only calculation amount is small, but also in noise
Inhibit between feature holding, this method provides a preferable balances, can obtain more rational reconstruction image.It needs to refer to
Go out, although present invention is primarily directed to solve sparse driving SAR image Problems of Reconstruction, it can be completely applied to other
Complex valuel p Norm regularization image reconstruction problem.
Description of the drawings
Figure of description 1 isLCurve and regularization parameter search schematic diagram.
Specific embodiment
In order to which technological means, creation characteristic, workflow, application method reached purpose and effect for making the present invention are easy to bright
White to understand, 1 the present invention is further described with reference to the accompanying drawings of the specification.
Present invention determine that the optimization algorithm step that sparse driving SAR image rebuilds regularization parameter is as follows：
（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 iteration time
Number,For preset step-length；
（4）It calculatesLMistake on curve,,WithThe tangent slope of point,,With
, wherein differential 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, here 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.
The basic principles, main features and the advantages of the invention have been shown and described above.The technology of the industry
Personnel are it should be appreciated that the present invention is not limited to the above embodiments, and the above embodiments and description only describe this
The principle of invention, without departing from the spirit and scope of the present invention, various changes and improvements may be made to the invention, these changes
Change and improvement all fall within the protetion scope of the claimed invention.The claimed scope of the invention by appended claims and its
Equivalent thereof.
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.
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| CN107765225A (en) * | 2017-10-27 | 2018-03-06 | 中国人民解放军国防科技大学 | Sparse regularization SAR image sidelobe suppression method based on log measurement |
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