CN107123125A - Polarization SAR change detecting method based on scattering signatures and low-rank sparse model - Google Patents

Polarization SAR change detecting method based on scattering signatures and low-rank sparse model Download PDF

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CN107123125A
CN107123125A CN201710195062.6A CN201710195062A CN107123125A CN 107123125 A CN107123125 A CN 107123125A CN 201710195062 A CN201710195062 A CN 201710195062A CN 107123125 A CN107123125 A CN 107123125A
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缑水平
刘舟
刘一舟
焦李成
白静
张丹
刘波
马文萍
马晶晶
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Xidian University
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Abstract

The invention discloses a kind of change detecting method of the Polarimetric SAR Image based on scattered power feature and low-rank sparse model, the problem of mainly solving high loss in the prior art and low disparity map separability.Its implementation process is：1) first phase coherence matrix T1 and the second phase coherence matrix T2 is extracted；2) Freeman decomposition and registration are carried out to T1 and T2 respectively, obtains the input picture I of first phase1With the input picture I of the second phase2；3) I is used1And I2Construct modified-image sequence I；4) modified-image sequence I is decomposed into low-rank image sequence tri- subimage sequence sums of L, sparse image sequence S and noise image sequence G with low-rank sparse decomposition method；5) sparse image sequence S is merged, disparity map is obtained；6) disparity map is clustered with the method for fuzzy C-mean algorithm, obtains the result figure of change detection.The anti-noise sound intensity of the present invention, loss is low, and accuracy of detection is high, available for urban planning, the assessment of natural calamity and the variation monitoring of weather.

Description

Polarization SAR change detecting method based on scattering signatures and low-rank sparse model
Technical field
The invention belongs to the change detecting method of technical field of image processing, more particularly to Polarimetric SAR Image, it can be applied to Urban planning, ecological environment investigation and the evaluation and test of natural calamity.
Background technology
Polarimetric synthetic aperture radar POLSAR Image Change Detections are that a kind of two width from the same place of different time polarize Change information is extracted in SAR image, disparity map is generated, determines the Remote Sensing Image Processing Technology of atural object change information.Polarization SAR energy The echo-signal of four passages is received, it can represent the scattering mechanism of target more fully hereinafter, so what its image was included Information content is much larger than single-channel SAR image.In recent years, Polarimetric SAR Image change detection has turned into one that image procossing is studied Recent studies on direction, is widely used in every field, such as land cover pattern and the variation monitoring, urban planning, the environment that utilize Monitoring analysis, natural calamity estimation etc..
At present, the research of Polarimetric SAR Image change detection is roughly divided into three classes also in the elementary step.
The first kind is characterized with strength information, and traditional change detection techniques are extracted to the different information of polarization SAR image, Such as by the method for principal component analysis, Threshold segmentation and matrix decomposition.But the weak point of this kind of method is to make full use of The scattered information of polarization SAR.
Equations of The Second Kind is the difference letter for extracting polarization SAR using polarization SAR statistical distribution based on polarization SAR data Breath, such as change detecting method of the likelihood ratio test based on polarization covariance matrix.But, the application of this method is on condition that atural object The polarization covariance matrix of target meets Wishart distributions, but actual atural object scattering properties is more complicated, is sometimes difficult to meet this Condition, therefore the general of method be restricted.
3rd class is to carry out feature extraction to polarization SAR data using some Polarization target decomposition models, then looks for closing Suitable method extracts different information.Polarization target decomposition is by some known basic scattering interpretation target scatterings.Typical side Method has Pauli to decompose and Cloude decomposition, and wherein Pauli, which will be decomposed, to be three basic collision matrixes by target scattering mechanism decomposition Linear combination；Cloude decomposes the combination for three basic scattering components by Polarization target decomposition.Then difference letter is carried out again Breath is extracted, and such as difference, ratio, Wavelet Fusion are finally optimized to different information, obtains changing testing result.Due to pole Change the complexity of diversity of the SAR comprising information and Terrain Scattering characteristic.
At present, many research is carried out along the direction of the 3rd class method, and this kind of method is due to utilizing polarization , it is necessary to determine whether polarizing target is concerned with before decomposition during goal decomposition model, so as to the polarization characteristic got well, however, It is to be difficult to judge whether polarizing target is concerned with before decomposition；Simultaneously because such method does not utilize image when extracting disparity map Spatial information, the influence of noise is not considered yet, so that testing result is inaccurate.
The content of the invention
It is an object of the invention to the deficiency for above-mentioned prior art, propose a kind of based on scattered power feature and low-rank The Polarimetric SAR Image change detecting method of sparse model, before decomposition, to judge the coherence of polarizing target, reduction change The loss of detection, improves the accuracy rate of detection.
The technical scheme is that：The multidate polarization SAR data of reading are carried out respectively Freeman decompose obtain compared with Good scattered power feature, and utilize low-rank sparse mould as the input of sparse low-rank model with its construction polarization image sequence Type, which to input decompose, obtains sparse image sequence, and it is merged, and obtains the preferable disparity map of separability, finally makes Split with Fuzzy C-Means Cluster Algorithm, obtain the result figure of change detection, implementation step includes as follows：
(1) extract in the first coherence matrix T1, the second phase polarization data and extract from first phase polarization data respectively Second coherence matrix T2, two inputs decomposed as Freeman；
(2) according to the first coherence matrix T1 and the second coherence matrix T2, the defeated of the first phase that size is c=m × n is obtained Enter image I1With the input picture I of the second phase2；
(3) first phase image I is utilized1, phase images I when second2Construct (k-2) width modified-image Ii；And use I1、I2And Ii Constitute k amplitude variation image sequence I=[i1,…ii,…ik], wherein, i=2,3 ..., k-1, k is of image in image sequence Number, k >=30, i1Correspondence first phase image I1Column vector after transformed, iiCorrespondence structural map is as IiRow after transformed to Amount, ikPhase images I during correspondence second2Column vector after transformed, and i1, ii, ik∈Rc×1, I ∈ Rc×k, Rc×kExpression size is c × k real number space；
(4) image sequence I is decomposed into three subimage sequence sums with low-rank sparse decomposition method：I=L+S+G, wherein, S is sparse image sequence, and L is low-rank image sequence, and G is noise image sequence, L, S, G ∈ Rc×k, and S={ s1,…sl,…, sk, slIt is l-th of column vector in sparse image sequence S, l=1,2 ..., k；
(5) method merged with weighted mean, is merged to sparse image sequence S, obtains disparity map, disparity map it is big Small is c × 1；
(6) fuzzy C-mean algorithm method is used, disparity map is clustered, last change testing result figure is obtained.
The present invention has advantages below compared with prior art：
1. the present invention is directed to the scattering properties of polarization SAR, is decomposed using Freeman and decompose multidate polarization SAR data For three scattered power features, and for different atural objects, select different scattered powers as the input of change detection, improve Change the accuracy rate of detection；
2. the low-rank sparse method used in the present invention, had both considered the neighborhood information in multi-temporal image, it is contemplated that Different information between multi-temporal image, reduces the loss of change detection；
3. the average weighted method used in the present invention, because every piece image in sparse image sequence is only capable of detection The change information of middle part, thus, the separability of disparity map is improved, and then improve the accuracy rate of change detection.
Brief description of the drawings
Fig. 1 is the implementation process figure of the present invention；
Fig. 2 is first phase and the Pauli of the second phase figures in the present invention；
Fig. 3 is Tokyo airfield runway polarimetric SAR image data collection used in present invention emulation；
Fig. 4 is the standards change testing result figure that Fig. 2 is obtained by handmarking；
Fig. 5 is with tradition and change testing result figure of the change detecting method of the present invention to Fig. 2；
Fig. 6 is Tokyo part vegetation region remote sensing image data collection used in present invention emulation；
Fig. 7 is the standards change testing result figure that Fig. 5 is obtained by handmarking；
Fig. 8 is with tradition and change testing result figure of this method change detecting method to Fig. 5.
Embodiment
Below in conjunction with accompanying drawing, embodiments of the invention and effect are described further：
Reference picture 1, the polarization SAR change detecting method of the invention based on scattering signatures and low-rank sparse model, including such as Lower step：
Step 1:From the corresponding two phases coherence matrix of the polarization SAR extracting data of two phases.
This example uses the two phase polarization SAR data obtained from unloaded satellite ALOS, i.e. first phase polarization SAR data With the second phase polarization SAR data；
1a) from first phase polarization SAR the first coherence matrix of extracting data T1；
1b) from second phase polarization SAR the second coherence matrix of extracting data T2.
Step 2:According to the first coherence matrix T1 and the second coherence matrix T2, the first phase that size is c=m × n is obtained Input picture I1With the input picture I of the second phase2。
2a) Freeman points are carried out respectively to the first coherence matrix T1 and the second coherence matrix T2 respectively using equation below Solution：
Pv=8Fv/ 3, wherein FvFor the decomposition coefficient of volume scattering component
Pd=Fd(1+α2), wherein FvFor the decomposition coefficient of dihedral angle scattering component, α is constant
Ps=Fs(1+β2), wherein FsFor the decomposition coefficient of in-plane scatter component, β is constant
Obtain first phase scattered power image Pd1、Pv1、Ps1With the second phase scattered power image Pd2、Pv2、Ps2；
Registration 2b) is carried out respectively to first phase scattered power image and the second phase scattered power image, registration is obtained First phase scattered power image Pd afterwards1'、Pv1'、Ps1' and the second phase scattered power image Pd2'、Pv2'、Ps2'；
Characteristic image selection 2c) is carried out according to the different scattered power characteristics of image of the different atural objects of different zones correspondence：
From the scattered power image Pd of first phase1'、Pv1'、Ps1' in select can reactions change information scattered power it is special Image is levied, the input picture I of first phase is designated as1；
From the scattered power image Pd of the second phase2'、Pv2'、Ps2' in select can reactions change information scattered power it is special Image is levied, the input picture I of the second phase is designated as2。
Step 3:Construct k-2 width modified-images.
Log ratio method 3a) is used, from first phase image I1With phase images I when second2Middle extraction initial change region I0；
3b) utilize first phase image I1, phase images I when second2And initial change region I0, obtain k-2 width variation diagrams As Ii：
Wherein, FiRepresent modified-image IiIn the region that changes, UiRepresent modified-image IiIn do not change Region,Represent initial change region I0Be divided into k equal portions, and take it is therein i parts, in formulaIn,Represent phase images I when second2In part region of variationGray value, move to modified-image IiIn pair Answer on position；Represent first phase image I1In remove and part region of variationOutside the identical region of position All regions, in formulaIn,Represent first phase image I1In remove and part region of variationThe gray value in all regions outside the identical region of position, moves to modified-image IiIn correspondence position on.
Step 4:Utilize first phase image I1, phase images I when second2(k-2) width modified-image Ii, constitute k amplitude variations Image sequence I=[i1,…ii,…ik], wherein, i=2,3 ..., k-1, k is the number of image in image sequence, k >=30, i1 Correspondence first phase image I1Column vector after transformed, iiCorrespondence structural map is as IiColumn vector after transformed, ikCorrespondence second When phase images I2Column vector after transformed, and i1, ii, ik∈Rc×1, I ∈ Rc×k, Rc×kRepresent that size is empty for c × k real number Between.
Step 5:Image sequence I is decomposed into three subimage sequence sums with low-rank sparse decomposition method.
5a) with the method for bilateral accidental projection, low-rank is carried out to image sequence I and approached, iteration low-rank matrix L is obtainedtFor：
Lt=Q1[R1(A2t TY1t)-1R2 T]1/(2q+1)Q2 T,
Wherein, q is convergence coefficient, and t is iterations, A2t=IA1(t-1), as t=1, A1(t-1)It is that initialization order is r Gaussian matrix, Q1,R1Respectively to left projection matrix Y1tCarry out the intermediate parameters that singular value decomposition is obtained：Y1t=IA1t=Q1R1, As t >=2, A1t=ITA2(t-1), T is transposition symbol, Q2,R2It is to right projection matrix Y respectively2tSingular value decomposition is carried out to obtain Intermediate parameters：Y2t=ITA2t=Q2R2；
5b) use image sequence I and iteration low-rank matrix LtGo to approach iteration sparse matrix St：
St=PΩ(I-Lt),
Wherein, Ω representing matrixs (I-Lt) first k maximum nonzero value subset space, PΩRepresent that non-zero is empty from Ω Between project to iteration sparse matrix StOn；
5c) given threshold ε is 3.2e-5, repeat step 5a) arrive 5b), often it is repeated once, iterations t adds 1, until full Untill the following end condition of foot：
||I-Lt-St||2/||I||2<ε, wherein, | | | |22 norms are represented,
The iteration sparse matrix S of end condition will be mettSparse image sequence S is designated as, by iteration low-rank matrix LtIt is designated as low Order image sequence L；
5d) by image sequence I, sparse image sequence S and low-rank image sequence L obtains noise image sequence G：
G=I-S-L,
Wherein, L, S, G ∈ Rc×k, S={ s1,…sl,…,sk, slIt is l-th of column vector, l=in sparse image sequence S 1,2,…,k；
Step 6:Obtained changing testing result figure according to sparse image sequence S.
6a) the method merged with weighted mean, is merged to sparse image sequence S, obtains disparity map, disparity map it is big Small is c × 1；
Fuzzy C-mean algorithm method 6b) is used, disparity map is clustered, the corresponding class label of each pixel is obtained, obtains most Whole change testing result figure.
The effect of the present invention can be further illustrated by following emulation experiment：
1. experiment condition
Experimental situation is：Window 7, CPU Intel i3, fundamental frequency are 3.2GHz, and software platform is Matlab R2012b.
It is the two four L-band polarization SAR data regarded to emulate the data set used, and this data set was shot in 2006 respectively Abundant atural object, such as sea, city and vegetation are included in the Tokyo area in July and in April, 2009, the data set.For It is easy to observation, has synthesized the RGB image of two phase polarization SAR data from data set:Fig. 2 (a) and Fig. 2 (b), they Size is 2300 × 1048, and wherein R is represented | HH-VV |, G is represented | HV |+| VH |, B is represented | HH+VV |, H represents that satellite level is sent out Reception mode is sent, V represents vertically to send reception mode, HV represents that level is sent, vertical reception.
Fig. 2 region 1 and region 2 is selected to be analyzed.Change, institute caused by airport runways are mainly built in region 1 The size for selecting region of variation is 600 × 500；Region 2 is mainly vegetation and changed with caused by seasonal variations, and selected region of variation is big Small is 318 × 230.
Using the corresponding polarization SAR data in region 1 as first data set, as shown in figure 3, wherein Fig. 3 (a) is new airport The volume scattering power image of the first phase of runway, Fig. 3 (b) is the volume scattering power image of the new phase of airfield runway second.Figure As size is 600 × 500 pixels, gray level is 256, and it includes 290420 non-changing pixels and 9580 change pixels.
Airfield runway new to above-mentioned Tokyo carries out handmarking, obtains this runway standard drawing as shown in Figure 4.
Using the corresponding polarization SAR data in region 2 as second data set, as shown in fig. 6, wherein Fig. 6 (a) is Tokyo portion Divide the first phase dihedral angle scattered power image of vegetation area, Fig. 6 (b) is the face of the second phase two in Tokyo part vegetation area Angle scattered power image, these image sizes are 318 × 230, and gray level is 256, it include 69627 non-changing pixels and 3513 change pixels.
Handmarking is carried out to above-mentioned Tokyo part vegetation area, the standard drawing for obtaining this region is as shown in Figure 7.
2. experiment content and experimental result
Experiment 1：With the inventive method and existing differential technique SM and existing log ratio method LR, detection is changed to Fig. 3. Experimental result is as shown in figure 5, wherein 5 (a) is the result figure that SM differential techniques are changed detection to Fig. 3, and 5 (b) is LR logarithm ratios Value method is changed the result figure of detection to Fig. 3, and 5 (c) is the result figure that the inventive method is changed detection to Fig. 3.
Experiment 2：With the inventive method and two kinds of traditional change detecting methods：Differential technique SM and log ratio method LR is right Fig. 6 is changed detection, and experimental result is as shown in Figure 8.Wherein 8 (a) is the result that differential technique SM is changed detection to Fig. 6 Figure, 8 (b) is the result figure that log ratio method LR is changed detection to Fig. 6, and 8 (c) is that the inventive method is changed to Fig. 6 The result figure of detection.
As can be seen that SD differential techniques are changed in the experimental result of detection to image and had very from Fig. 5 (a) and Fig. 8 (a) Many miscellaneous points；
As can be seen that the experimental result of LR log ratio methods generates many details and lost from Fig. 5 (b) and Fig. 8 (b) Lose, edge is very fuzzy, and Fig. 5 (b) lost most region of variation；
From Fig. 5 (c) and Fig. 8 (c) as can be seen that in the case where preferably keeping edge details, the present invention can reduce miscellaneous The number of point, and then reduce loss.
The change testing result of the inventive method and above two conventional method on two region of variation is counted, As shown in table 1.There are four kinds of evaluation indexes in table 1：Respectively false-alarm number FA, missing inspection number MA, error number OE and accuracy PCC, its In, false-alarm number FA is the pixel that reality does not change but is taken as change to detect, and missing inspection number MA is not detect The next pixel for having actually occurred change, error number OE=FA+MA, accuracy PCC=error numbers/image pixel number, wherein Error number is the result figure of method therefor and the difference of standard drawing.
The experimental result data of table 1
As it can be seen from table 1 the present invention is compared with two kinds of traditional change detecting methods：
First, as can be seen that detection of the present invention to region 2 has of a relatively high void to examine from the empty inspection number index of table 1 Number, quality is decomposed in this selection and low-rank sparse with the scattered power feature in the present invention certain relation；
Secondly, as can be seen that the inventive method is in the data set of region 1 and the data set of region 2 from the missing inspection index of table 1 On compared with two kinds of traditional change detecting methods, obtain higher accuracy rate, and obtain less missing inspection number.And this Inventive method is on the data set of region 1 compared with differential technique, and missing inspection number reduces by 128 pixels, on the data set of region 2； Missing inspection number reduces by 457 pixels.
To sum up, the inventive method has less missing inspection number, less mistake compared with two kinds of traditional change detecting methods Number, and higher accuracy rate is either obtained in the data set of region 1 and the data set of region 2, improve change detection essence Degree.

Claims (4)

1. a kind of polarization SAR change detecting method based on scattering signatures and low-rank sparse model, including：
(1) the first coherence matrix T1 and second is extracted from first phase polarization data and the second phase polarization data respectively to be concerned with Two inputs that matrix T2 is decomposed as Freeman；
(2) according to the first coherence matrix T1 and the second coherence matrix T2, the input figure for the first phase that size is c=m × n is obtained As I1With the input picture I of the second phase2；
(3) first phase image I is utilized1, phase images I when second2Construct (k-2) width modified-image Ii；And use I1、I2And IiComposition K width image sequence I=[i1,…ii,…ik], wherein, i=2,3 ..., k-1, k be image sequence in image number, k >=30, i1Correspondence first phase image I1Column vector after transformed, iiCorrespondence structural map is as IiColumn vector after transformed, ikCorrespondence the Phase images I when two2Column vector after transformed, and i1, ii, ik∈Rc×1, I ∈ Rc×k, Rc×kRepresent that size is empty for c × k real number Between；
(4) image sequence I is decomposed into three subimage sequence sums with low-rank sparse decomposition method：I=L+S+G, wherein, S is Sparse image sequence, L is low-rank image sequence, and G is noise image sequence, L, S, G ∈ Rc×k, and S={ s1,…sl,…,sk, slIt is l-th of column vector in sparse image sequence S, l=1,2 ..., k；
(5) method merged with weighted average, is merged to sparse image sequence S, obtains disparity map, and the size of disparity map is c×1；
(6) fuzzy C-mean algorithm method is used, disparity map is clustered, obtains finally changing testing result figure.
2. according to the first coherence matrix T1 and the second coherence matrix in the method according to claim 1, wherein step (2) T2, obtains the input picture I for the first phase that size is c=m × n1With the input picture I of the second phase2；Enter as follows OK：
Freeman decomposition 2a) is carried out respectively to the first coherence matrix T1 and the second coherence matrix T2 respectively using equation below：
Pv=8Fv/ 3, wherein FvFor the decomposition coefficient of volume scattering component
Pd=Fd(1+α2), wherein FvFor the decomposition coefficient of dihedral angle scattering component, α is constant
Ps=Fs(1+β2), wherein FsFor the decomposition coefficient of in-plane scatter component, β is that constant obtains first phase scattered power image Pd1、Pv1、Ps1With the second phase scattered power image Pd2、Pv2、Ps2；
Registration 2b) is carried out respectively to first phase scattered power image and the second phase scattered power image, obtained after registration One phase scattered power image Pd1'、Pv1'、Ps1' and the second phase scattered power image Pd2'、Pv2'、Ps2'；
2c) according to the different scattered power characteristics of image of the different atural objects of different zones correspondence, by feature selecting, from first when The scattered power image Pd of phase1'、Pv1'、Ps1' in select can reactions change information scattered power characteristic image, be designated as first The input picture I of phase1；From the scattered power image Pd of the second phase2'、Pv2'、Ps2' in select can reactions change information Scattered power characteristic image, is designated as the input picture I of the second phase2。
3. according to the method described in claim 1, the utilization first phase image I wherein described in step (3)1, phase images when second I2Construct (k-2) width modified-image Ii, i=2,3 ..., k-1 are carried out as follows：
Log ratio method 3a) is used, from first phase image I1With phase images I when second2Middle extraction initial change region I0；
3b) utilize first phase image I1, phase images I when second2And initial change region I0, obtain k-2 width modified-images Ii：
<mrow> <msub> <mi>I</mi> <mi>i</mi> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <msub> <mi>F</mi> <mi>i</mi> </msub> </mtd> <mtd> <mrow> <msub> <mi>F</mi> <mi>i</mi> </msub> <mover> <mo>&amp;LeftArrow;</mo> <mi>F</mi> </mover> <mfrac> <mi>i</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>2</mn> </mrow> </mfrac> <msub> <mi>I</mi> <mn>0</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>U</mi> <mi>i</mi> </msub> </mtd> <mtd> <mrow> <msub> <mi>U</mi> <mi>i</mi> </msub> <mover> <mo>&amp;LeftArrow;</mo> <mi>U</mi> </mover> <msub> <mi>I</mi> <mn>1</mn> </msub> <mo>-</mo> <mfrac> <mi>i</mi> <mrow> <mi>k</mi> <mo>-</mo> <mn>2</mn> </mrow> </mfrac> <msub> <mi>I</mi> <mn>0</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> </mrow>
Wherein, FiRepresent modified-image IiIn the region that changes, UiRepresent modified-image IiIn the region that does not change,Represent initial change region I0Be divided into k equal portions, and take it is therein i parts, in formulaIn, Represent phase images I when second2In part region of variationGray value, move to modified-image IiIn corresponding position Put；Represent first phase image I1In remove and part region of variationInstitute outside the identical region of position There is region, in formulaIn,Represent first phase image I1In remove and part region of variationThe gray value in all regions outside the identical region of position, moves to modified-image IiIn correspondence position on.
4. according to the method described in claim 1, image sequence I is decomposed with GODEC low-rank sparses and calculated wherein in step (4) Method carries out low-rank sparse decomposition, carries out as follows：
4a) with the method for bilateral accidental projection, low-rank is carried out to image sequence I and approached, iteration low-rank matrix L is obtainedtFor：
Lt=Q1[R1(A2t TY1t)-1R2 T]1/(2q+1)Q2 T,
Wherein, q is convergence coefficient, and t is iterations, A2t=IA1(t-1), as t=1, A1(t-1)It is to initialize the Gauss that order is r Matrix, Q1,R1Respectively to left projection matrix Y1tCarry out the intermediate parameters that singular value decomposition is obtained：Y1t=IA1t=Q1R1, work as t When >=2, A1t=ITA2(t-1), T is transposition symbol, Q2,R2It is to right projection matrix Y respectively2tDuring progress singular value decomposition is obtained Between parameter：Y2t=ITA2t=Q2R2；
4b) with image sequence I and iteration low-rank matrix LtGo to approach iteration sparse matrix St：
St=PΩ(I-Lt),
Wherein, Ω representing matrixs (I-Lt) first k maximum nonzero value subset space, PΩRepresent to throw non-zero from Ω spaces Shadow is to iteration sparse matrix StOn；
4c) repeat step 4a) arrive 4b), often it is repeated once, iterations t adds 1, untill end condition is met, the termination bar Part is：
||I-Lt-St||2 F/||I||2 F<ε,
Wherein, | | | |2 F2 norms are represented, ε is the threshold value of setting, and value is 3.2e-5；
The iteration sparse matrix S of end condition will be mettWith low-rank matrix LtSparse image sequence S and low-rank image are designated as respectively Sequence L；
4d) by image sequence I, sparse image sequence S and low-rank image sequence L, noise image sequence G is obtained：
G=I-S-L.
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CN113609898A (en) * 2021-06-23 2021-11-05 国网山东省电力公司泗水县供电公司 Power transmission line icing monitoring method and system based on SAR image
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