CN105405100A - Sparse drive SAR image reconstruction regularization parameter automatic selection method - Google Patents
Sparse drive SAR image reconstruction regularization parameter automatic selection method Download PDFInfo
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- CN105405100A CN105405100A CN201510762325.8A CN201510762325A CN105405100A CN 105405100 A CN105405100 A CN 105405100A CN 201510762325 A CN201510762325 A CN 201510762325A CN 105405100 A CN105405100 A CN 105405100A
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- 238000010187 selection method Methods 0.000 title abstract 3
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- 238000009394 selective breeding Methods 0.000 abstract description 2
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- G—PHYSICS
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T3/00—Geometric image transformations in the plane of the image
- G06T3/40—Scaling of whole images or parts thereof, e.g. expanding or contracting
- G06T3/4053—Scaling of whole images or parts thereof, e.g. expanding or contracting based on super-resolution, i.e. the output image resolution being higher than the sensor resolution
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- G06T2207/00—Indexing scheme for image analysis or image enhancement
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Abstract
The invention discloses a sparse drive SAR image reconstruction regularization parameter automatic selection method. Selection of regularization parameters is a quite important issue in regularization image reconstruction. Conventional selection methods are limited in the capacity of selection of non-quadratic regularization parameters, and artificial selection of the regularization parameters is often required in order to obtain high-quality reconstruction images. In order the solve the problem, the invention provides the sparse drive SAR image reconstruction regularization parameter automatic selection numerical computation method on the basis of the research of an L curve method. The beneficial effects of the method are that automatic selection of the sparse drive SAR image reconstruction regularization parameters is realized. Computational amount is low in solving the sparse drive SAR image reconstruction regularization parameters through the method, and noise suppression and feature preservation are greatly balanced so that the more reasonable reconstruction images can be obtained.
Description
Technical field
The present invention relates to a kind of sparse driving SAR(Syntheticapertureradar, synthetic-aperture radar) image reconstruction regularization parameter automatic selecting method.
Background technology
Tradition SAR imaging technique resolution is low, there is coherent speckle noise and secondary lobe impact, has a strong impact on the application of SAR image in the tasks such as Automatic Targets and target identification.In recent years, researchist proposes some new SAR image method for reconstructing in succession, and wherein based on the SAR image method for reconstructing of sparse driving, its basic thought is solved by regularization, reaches the object of enhanced SAR characteristics of image.In general, the image rebuilding method based on regularization all obtains required problem stable solution by managing equilibrium criterion fidelity and priori, and its stability is realized by a scalar parameter and regularization parameter.Therefore, in regularized image is rebuild, the selection of regularization parameter is a very important problem.At present, researchist proposes the regularization parameter system of selection of several Corpus--based Method thought, as Stein without inclined evaluation of risk method, Generalized Cross Validation method, bayes method and
lcurve method, wherein the most famous and widely used be Tikhonov regularization method.Tikhonov regularization method is a kind of secondary regularization method.In Tikhonov regularization method, quadratic form optimization problem is made up of one group of linear equation, has to close to separate, and can realize the automatic selection of regularization parameter, greatly reduce the operand of image reconstruction.In view of image sparse represents had advantage, at present regularization constraint is introduced sparse graph and become more and more general as Problems of Reconstruction.Non-secondary regularization constraint is introduced Sparse Problems and can improve the openness of required problem.But the introducing of non-quadratic form constraint can cause optimization problem to close solution, thus need to use iterations and numerical simulation method to solve problem.Therefore, compared with quadratic form, the selection of the lower regularization parameter of non-quadratic form constraint is more complicated.For the selection of non-quadratic form regularization parameter, conventional Stein without inclined evaluation of risk method, Generalized Cross Validation method and
lcurve method limited in one's ability, rebuilding image to obtain high-quality sparse driving SAR, often needing to carry out artificial selection to regularization parameter.In order to solve the problem, the present invention is in research
lon the basis of curve method, propose the numerical computation method that a kind of sparse driving SAR image reconstruction regularization parameter is selected automatically.
(1) sparse driving SAR image rebuilds principle
SAR image based on regularization is rebuild mainly based on following SAR observation process:
（1）
Wherein
hfor discrete complex value SAR image rebuilds operator,
wfor additive white Gaussian noise,
gwith
fbe respectively measured data and truly reflect scene.In order to emphasize to reflect the openness of scene, SAR image Problems of Reconstruction is expressed as following optimization problem by us:
（2）
Wherein
regularization parameter,
expression is asked
f's
l p norm, it is defined as
, here
f i be
f?
iindividual element,
nbe
fthe number of middle element.(2) Section 1 in formula is called data fidelity item, and it comprises SAR observation model (1) and observes geological information.Section 2 is called regularization term or boundary constraint item, and we utilize it prior imformation can be incorporated in image reconstruction.When in regularization term
pwhen=2, it is exactly famous Tikhonov regularization method.Different from Tikhonov regularization method, boundary constraint item is herein intended to introduce sparse prior information, therefore except
p=2, we also can select other
pvalue.When
time, minimum
l p norm is reconstituted in reconstructed results image and can produces local energy gathering, thus improves and rebuilds the openness of image.Use the object of boundary constraint item to be suppress image artifacts, increase the resolving power of scattering, thus the result images that generation one is sparse.Test verified, this sparse constraint can produce the reconstructed results image of super-resolution.
In order to avoid working as
f i the problem of objective function non-differentiability when being zero, we are right
l p norm is similar to, and is revised as by objective function (2):
（3）
Wherein
it is a very little scalar.In an experiment, we rule of thumb compromise consideration, select
.
Our target obtains estimated value
.When
p>1, required problem is a convex optimization problem.Ask
right
fgradient, have:
（4）
Wherein
a diagonal weight matrix, its
iindividual diagonal element is
.If gradient equals zero, for any
pvalue, the solution of this optimization problem is a stationary point, therefore meets following equation:
（5）
?
iindividual diagonal element according to the penalty term with spatial variations to
ithe intensity of individual pixel is weighted.Because weighting matrix depends on
, but equation (5) for
be not linear, therefore (5) formula is closed and is separated, but we can utilize fixed point iteration method to solve, and each step of iterative process all comprises and solves following linear problem:
（6）
Wherein
?
kthe solution that secondary iteration obtains.Although (6) formula for
can produce one in principle to close and separate, but this needs to solve the inverse matrix of a very large matrix.Therefore we utilize gradient descent method to adopt Numerical Methods Solve system of equations (6).
(2)
lcurve method
A scalar parameter and regularization parameter is comprised in objective function (3)
, it has vital role in scene rebuilding.Work as parameter
time less, data fidelity item, the Section 1 namely in objective function (3), plays dominating role to the solution of objective function (3); Work as parameter
time larger, the Section 2 in objective function (3), namely based on
l p the penalty term of norm increases the effect of the solution of objective function (3).In order to obtain the SAR image of high-quality Exact Reconstruction, must select one suitable
value, makes data fidelity item and this effect of two of penalty term be balanced preferably.The present invention will based on data-driven version, and employing improves
lcurve method (L-curve) is to regularization parameter
automatically select.
lthe definition of curve method is: in log-log coordinate system, norm
its corresponding residual norm
ratio, wherein with regularization parameter
for its parameter.In actual applications,
lcurve is usually expressed as shown in Figure 1
ltype curve.It is generally acknowledged,
lthe corner location of type curve is Selection parameter
good area, select the parameter in this region to realize
balance between middle regularization error and agitation error.Utilize
lcurve method selects regularization parameter just based on this characteristic.Although seem directly perceived simple,
lthe calculating of curved corner position is also not easy.Determine that the method for corner location mainly contains that to calculate the maximum point of curvature, calculate closest to the point of reference position (such as initial point) and slope calculations be the point of contact etc. of the straight line of-1 at present.We will adopt below
loptimization of profile method for solving is selected automatically to the regularization parameter that sparse driving SAR image is rebuild, and provides implementation step.
Summary of the invention
Rebuilding the deficiency of regularization parameter system of selection in order to overcome above-mentioned sparse driving SAR image, the invention provides one
loptimization of profile method for solving, gives implementation step, thus realizes the automatic selection that sparse driving SAR image rebuilds regularization parameter.
Concrete technical scheme of the present invention and regularization parameter Optimization Solution algorithm as follows:
(1) establish
the region of search be
i=(
i 1,
i 2);
(2) initial lower bound and the upper bound of getting the region of search are respectively
with
;
(3) calculate
value
,
,
with
, wherein
kwith
lfor iterations,
for the step-length preset;
(4) calculate
lmistake on curve
,
,
with
the tangent slope of point
,
,
with
, wherein differential adopts numerical method to calculate;
(5) if
So
,
k=
k+ 1
Otherwise
Similarly,
If
So
,
l=
l+ 1
Otherwise
Repeat step (3)-(5), reduce the region of search further;
(6) get reference point (
x 0,
y 0), it is
with
the intersection point of place's tangent line;
(7) two test values are determined according to golden section ratio
;
(8) residual norm is calculated
conciliate norm
, wherein
i=1,2;
(9) calculation level (
) and reference point (
x 0,
y 0) between distance
;
(10) golden section search is utilized to determine a new interval
, namely
If
d 1>
d 2
So
Otherwise
;
(11)
, repeat step (7)-(11), until interval
ienough little.
Compared with prior art, the invention has the beneficial effects as follows the automatic selection achieving sparse driving SAR image reconstruction regularization parameter.Not only calculated amount is little to utilize the method to solve sparse driving SAR image reconstruction regularization parameter, and between squelch and feature keep, this method provides a balance preferably, can obtain more reasonably rebuilding image.Although it is pointed out that the present invention is mainly devoted to solve sparse driving SAR image Problems of Reconstruction, it can be applied to other complex value completely
l p norm regularization image reconstruction problem.
Accompanying drawing explanation
Figure of description 1 is
lcurve and regularization parameter search schematic diagram.
Embodiment
Reach object to make technological means of the present invention, creation characteristic, workflow, using method and effect is easy to understand, below in conjunction with Figure of description 1, the present invention is further described.
The present invention determines that the optimized algorithm of sparse driving SAR image reconstruction regularization parameter is as follows:
(1) establish
the region of search be
i=(
i 1,
i 2);
(2) initial lower bound and the upper bound of getting the region of search are respectively
with
;
(3) calculate
value
,
,
with
, wherein
kwith
lfor iterations,
for the step-length preset;
(4) calculate
lmistake on curve
,
,
with
the tangent slope of point
,
,
with
, wherein differential adopts numerical method to calculate;
(5) if
So
,
k=
k+ 1
Otherwise
Similarly,
If
So
,
l=
l+ 1
Otherwise
Repeat step (3)-(5), reduce the region of search further;
(6) get reference point (
x 0,
y 0), it is
with
the intersection point of place's tangent line;
(7) two test values are determined according to golden section ratio
;
(8) residual norm is calculated
conciliate norm
, wherein
i=1,2;
(9) calculation level (
) and reference point (
x 0,
y 0) between distance
;
(10) golden section search is utilized to determine a new interval
, namely
If
d 1>
d 2
So
Otherwise
;
(11)
, repeat step (7)-(11), until interval
ienough little.
More than show and describe ultimate principle of the present invention and principal character and advantage of the present invention.The technician of the industry should understand; the present invention is not restricted to the described embodiments; what describe in above-described embodiment and instructions just illustrates principle of the present invention; without departing from the spirit and scope of the present invention; the present invention also has various changes and modifications, and these changes and improvements all fall in the claimed scope of the invention.Application claims protection domain is defined by appending claims and equivalent thereof.
Claims (2)
1. sparse driving SAR image rebuilds a regularization parameter automatic selecting method, it is characterized in that: the selection that sparse driving SAR image rebuilds regularization parameter is a very important problem during regularized image is rebuild; For the selection of non-quadratic form regularization parameter, existing Conventional methods of selection is limited in one's ability, usually needs to carry out human assistance selection to regularization parameter; In order to solve the problem, the present invention is in research
lon the basis of curve method, propose the numerical computation method that a kind of sparse driving SAR image reconstruction regularization parameter is selected automatically.
2. the present invention determines that the algorithm realization step of sparse driving SAR image reconstruction regularization parameter is as follows:
(1) establish
the region of search be
i=(
i 1,
i 2);
(2) initial lower bound and the upper bound of getting the region of search are respectively
with
;
(3) calculate
value
,
,
with
, wherein
kwith
lfor iterations,
for the step-length preset;
(4) calculate
lmistake on curve
,
,
with
the tangent slope of point
,
,
with
, wherein differential adopts numerical method to calculate;
(5) if
So
,
k=
k+ 1
Otherwise
Similarly,
If
So
,
l=
l+ 1
Otherwise
Repeat step (3)-(5), reduce the region of search further;
(6) get reference point (
x 0,
y 0), it is
with
the intersection point of place's tangent line;
(7) two test values are determined according to golden section ratio
;
(8) residual norm is calculated
conciliate norm
, wherein
i=1,2;
(9) calculation level (
) and reference point (
x 0,
y 0) between distance:
;
(10) golden section search is utilized to determine a new interval
, namely
If
d 1>
d 2
So
Otherwise
;
(11)
, repeat step (7)-(11), until interval
ienough little, so far complete the selection of regularization parameter.
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Cited By (5)
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| CN106023085A (en) * | 2016-06-12 | 2016-10-12 | 西南科技大学 | SURE golden section automatic search algorithm for sparsely constrained SAR image reconstruction regularization parameters |
| CN106056538A (en) * | 2016-06-12 | 2016-10-26 | 西南科技大学 | Sparse constraint SAR image reconstruction regularization parameter GCV golden section automatic search algorithm |
| 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 |
| CN107942326A (en) * | 2017-11-14 | 2018-04-20 | 西南交通大学 | A kind of two-dimentional active MMW imaging method with high universalizable |
| CN110082764A (en) * | 2019-04-26 | 2019-08-02 | 西安电子科技大学 | SAR image imaging method based on steady regularization chromatography method |
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| US20120294543A1 (en) * | 2009-12-04 | 2012-11-22 | Pradeep Sen | System and methods of compressed sensing as applied to computer graphics and computer imaging |
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Cited By (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106023085A (en) * | 2016-06-12 | 2016-10-12 | 西南科技大学 | SURE golden section automatic search algorithm for sparsely constrained SAR image reconstruction regularization parameters |
| CN106056538A (en) * | 2016-06-12 | 2016-10-26 | 西南科技大学 | Sparse constraint SAR image reconstruction regularization parameter GCV golden section automatic search algorithm |
| 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 |
| CN107942326A (en) * | 2017-11-14 | 2018-04-20 | 西南交通大学 | A kind of two-dimentional active MMW imaging method with high universalizable |
| CN107942326B (en) * | 2017-11-14 | 2021-02-02 | 西南交通大学 | Two-dimensional active millimeter wave imaging method with high universality |
| CN110082764A (en) * | 2019-04-26 | 2019-08-02 | 西安电子科技大学 | SAR image imaging method based on steady regularization chromatography method |
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