CN103605119A - Method for restraining azimuth ambiguities of spaceborne synthetic aperture radar in strip mode - Google Patents

Abstract

The invention discloses a method for restraining azimuth ambiguities of a spaceborne synthetic aperture radar in a strip mode. The method comprises a first step of determining positions of azimuth ambiguity areas in a synthetic aperture radar (SAR) image and classifying the azimuth ambiguities; a second step of removing isolate ambiguities by employing a compressed sensing method; and a third step of removing area ambiguities by employing an exemplar-based image inpainting method. Compared with traditional methods such as band-pass filtering and the like, the method provided by the invention can directly determine the positions where the azimuth ambiguities are, and pointedly and directly act on ambiguity areas, and influence on normal areas is reduced. By employing the traditional methods such as band-pass filtering and the like, the signal to noise ratio (SNR) is reduced, even speckle noise is increased. Furthermore, by employing the traditional methods, ambiguities are hard to completely remove, and a part of ambiguity signals are still residual in the image. The above problems do not exist in the method provided by the invention.

Description

A kind of satellite-borne synthetic aperture radar band pattern azimuth ambiguity inhibition method

Technical field

The present invention relates to a kind of satellite-borne synthetic aperture radar band pattern azimuth ambiguity inhibition method, belong to signal processing technology field.Background technology

Synthetic-aperture radar (synthetic aperture radar, SAR) is a kind of high-definition remote sensing detection radar of the earth being observed based on spatial altitude.Due to satellite-borne SAR satellite can overcome cloud and mist sleet and dark night condition difficulty carry out on a surface target imaging, realize round-the-clock, round-the-clock, high resolving power, wide cut earth observation, therefore in military affairs, ocean, forestry and the field such as agriculture, have broad application prospects.The application demand day by day increasing is had higher requirement to High Resolution SAR Images quality, yet the working mechanism of satellite-borne SAR itself has determined that it exists blooming, causes picture quality to reduce, and affects target decomposition and identification.

Fuzzy range ambiguity and azimuth ambiguity two classes of mainly comprising of satellite-borne SAR.Range ambiguity is caused at time domain aliasing to target echo and confusion region echo by distance, azimuth ambiguity be by satellite-borne SAR in motion process to echo samples, cause azimuth spectrum side-lobe signal to enter causing in processor bandwidth.Azimuth ambiguity is particularly evident in the very large region of the image dynamic changes such as land and sea junction, on the sea that the azimuth ambiguity image of the strong target in land can be weak at echo strength, brightness of image is lower, show, this " ghost " phenomenon makes image visual effect variation.For the azimuth ambiguity inhibition method of image area, conventionally adopt bandpass filter method and phase place elimination method etc., but that these methods are all difficult to blurred signal filtering is clean, even can reduce image resolution ratio, strengthen speckle noise effect.

Summary of the invention

The object of the invention is in order to suppress the azimuth ambiguity of spaceborne band pattern SAR image, propose a kind of satellite-borne synthetic aperture radar band pattern azimuth ambiguity inhibition method.The SAR image orientation that the method can be removed the regions such as land and sea junction is effectively fuzzy, improves picture quality, and then strengthens the interpretability of image.

A kind of satellite-borne synthetic aperture radar band pattern azimuth ambiguity inhibition method of the present invention, comprises following step:

Step 1: determine position the classification of fuzzy region in SAR image

First, according to SAR operational factor, determine the side-play amount of azimuth ambiguity; Secondly, in conjunction with antenna radiation pattern, determine azimuth ambiguity present position in image; Last according to the size of blurred block, be divided into isolated fuzzyly and region is fuzzy, process respectively.

Step 2: adopt compression sensing method to remove isolated fuzzy

Two dimensional image is changed into a dimensional vector, utilize wavelet transformation and Gauss's sharpening matrix to obtain the rarefaction representation of image, re-use orthogonal matching pursuit (Orthogonal Matching Pursuit, OMP) method is rebuild image, finally isolated blurred block in original image is substituted with rebuilding image, remove isolated fuzzy.

Step 3: adopt the image mending method removal region based on masterplate fuzzy

Fuzzy for region, first calculate on fuzzy region border filling relative importance value a little, and determine the highest relative importance value region.Secondly, at source region, find immediate patch piece and fill fuzzy region.By that analogy, the filling that progressively extends internally along blurred block border, until complete the processing of All Ranges blurred block.

The invention has the advantages that:

(1) specific aim.Than traditional methods such as bandpass filtering, the method that the present invention proposes is directly judged azimuth ambiguity position, directly acts on targetedly fuzzy region, has reduced the impact on normal region.

(2) validity.Traditional methods such as bandpass filtering can reduce signal to noise ratio (S/N ratio) (signal-to-noise ratio, SNR), even can strengthen speckle noise.In addition, classic method is also difficult to remove completely fuzzy, still has part blurred signal residual on image.There are not the problems referred to above in the method that the present invention proposes.

Accompanying drawing explanation

Fig. 1 is the inventive method flow chart of data processing figure.

Fig. 2 is the image mending method schematic diagram based on masterplate.

Fig. 3 is treatment effect comparison diagram.

Embodiment

Below in conjunction with drawings and Examples, the present invention is described in further detail.

The present invention is a kind of satellite-borne synthetic aperture radar band pattern azimuth ambiguity inhibition method, and flow process as shown in Figure 1, comprises following step:

Step 1: determine position the classification of fuzzy region in SAR image

Be specially:

(1) by haplopia complex pattern (Single-Look-Complex, SLC), obtain local average image, establishing former haplopia complex pattern is S, and the local average image obtaining is S _μ:

$S_{\mathrm{\μ}}(a,r)=\frac{1}{m_a{n}_r}\underset{(x,y)\∈L}{\mathrm{\Σ}}S(a,r)$

Wherein, S and S _μbe the complex matrix of m * n, m be orientation to always counting, n is for distance is to always counting, a be orientation to variable, r be apart to variable.L is the rectangle local average window centered by impact point, and the size of window is m _a* n _r, m _afor counting to window in orientation, n _rfor distance, to window, count, can choose m _a=40, n _r=15

(2) obtain fuzzy orientation to distance to skew

$\mathrm{\Δa}=\frac{f_p}{f_r}{V}_g$

$\mathrm{\Δr}=\frac{\mathrm{\λ}}{2}(f_D+\frac{f_p}{2})\frac{f_p}{f_r}$

Wherein, Δ a be blurred signal orientation to skew, Δ r be blurred signal distance to skew, f _ddoppler centroid, f _rdoppler frequency rate, V _gsatellite ground speed, f _pbe pulse repetition rate, λ is SAR operation wavelength.

(3) obtain fuzzy ratio

$G\left(f_d\right)=\sin c\left(\frac{V_g\·(f_d-f_D)\·L_a}{f_r\·R_{\mathrm{ref}}\·\mathrm{\λ}}\right)$

$\mathrm{\ξ}=\frac{{\∫}_{-\frac{f_p}{2}}^{\frac{f_p}{2}}{\left|G\left(f_d\right)\right|}^{4}d{f}_d}{{\∫}_{\frac{f_p}{2}}^{\frac{{3f}_p}{2}}{\left|G\left(f_d\right)\right|}^{4}d{f}_d}$

Wherein, G (f _d) be antenna radiation pattern, f _dinstantaneous Doppler frequency, L _abe orientation to antenna length, R _refbe center constantly with reference to oblique distance, ξ is fuzzy ratio.

(4) obtain fuzzy judgment matrix B ₁(a, r):

Wherein, Δ a be orientation to side-play amount, Δ r be distance to side-play amount, " 1 " representative exist fuzzy, " 0 " representative be not fuzzy.

(5) obtain fuzzy judgment matrix B ₂(a, r):

Wherein, " 1 " representative exists fuzzy, and " 0 " representative is not fuzzy.

(6) obtain fuzzy judgment matrix B (a, r):

B(a,r)＝B ₁(a,r)∪B ₂(a,r)

B (a, r) is B ₁(a, r) and B ₂the union of (a, r)." 1 " representative exists fuzzy, and " 0 " representative is not fuzzy.Fuzzy judgment matrix B (a, r) and former haplopia complex pattern S, local average image S _μon location of pixels, be one to one.So far, all lituras in image have been judged.

(7) according to fuzzy judgment matrix, carry out blurred picture classification.If have, surpass 49 fuzzy elements adjacent (noting: an element is adjacent with its 8 elements around), judge that these fuzzy elements belong to region fuzzy, and these fuzzy elements are all set to 2.At this moment " 0 " indicates without fuzzy, and " 1 " represents isolated fuzzy, and " 2 " represent that region is fuzzy.

Isolated fuzzy employing compressed sensing (Compressed Sensing, CS) method is removed (step 2), and image mending (the Exemplar-Based Image Inpainting) method of the fuzzy employing in region based on model removed (step 3).

Step 2: use compression sensing method to remove isolated fuzzy

Be specially:

(1) former haplopia complex pattern S is N=m * n mono-dimensional vector S' by row generate length:

S'＝S(a,1)∪S(a,2)∪…∪S(a,n)

Wherein, a is that orientation is to variable.

(2) to S', sampling obtains the dimensional vector y that length is M _s:

y _s＝ΦS'

Wherein, Φ is sampling matrix, only contains " 0 " and " 1 ".Every row only has 1 " 1 ", altogether M " 1 ".Obviously the column number of " 1 " has determined the position of sampled point in original image.If column number is y, sample coordinate position is

noting, do not sample isolated ambiguous location, is the element position of " 1 " in fuzzy judgment matrix B (a, r).

(3) build sparse property

Order:

S'＝Γ ^-1Ψ ^TS _w

:

y _s＝ΦΓ ^-1Ψ ^TS _w＝ΘS _w

Θ＝ΦΓ ^-1Ψ ^T

Wherein, Γ is Gauss's sharpening matrix (diagonal matrix, diagonal entry meets Gaussian distribution), and Ψ is wavelet transformation base.Θ can be obtained fom the above equation, Θ is called sensing matrix, S _wfor treating restructuring matrix.

(4) solve l ₁norm minimum problem:

${\hat{S}}_w=\arg \min {\left|\right|S_w\left|\right|}_{1}s.t{y}_s=\mathrm{\Θ}{S}_w$

Also, meeting y _s=Θ S _wprerequisite under, reconstruct l ₁the S of Norm minimum _w;

(5) adopt orthogonal matching pursuit algorithm to be reconstructed, concrete grammar is as follows:

(a) known vector of samples y _s, sensing matrix Θ.Making t is the circulation moment, r _t, Λ _t, Β _t, S _wtbe respectively t residual error constantly, indexed set, rebuilds atom set, treats restructuring matrix.Initialization r ₀=y _s, order circulation is t=1 constantly;

(b) find out residual error r _t-1respectively be listed as θ with sensing matrix Θ _jinner product the maximum, record the corresponding footmark λ of maximum column _t, that is:

λ _t＝j _max＝argmax _j＝1…N|<r _t-1,θ _j>|

(c) upgrade indexed set Λ _t=Λ _t-1∪ { λ _t, the reconstruction atom set in the sensing matrix that record finds

(d) by least square method, obtain immediate S _wt,

(e) upgrade residual error $r_t=y_s-B_t{\hat{S}}_{\mathrm{wt}},t=t+1;$

(f) if || rt|| ₂< δ (wherein δ is for stopping thresholding, generally, can choose δ=0.1 * || y _s|| ₂), stop iteration, output end product

if do not meet, return to step (b), continue iterative computation;

(g) by S'=Γ ^-1Ψ ^ts _wsolve S';

(6) the isolated fuzzy pixel in former haplopia complex pattern S is substituted with corresponding element in S'.So far, obtain removing isolated fuzzy image S ₁.

Step 3: adopt the image mending method based on masterplate, removal region is fuzzy

Be specially:

(1) by S ₁middle region vague image vegetarian refreshments (correspondence position is that 2 element is determined in fuzzy matrix) is whole 0, obtains X piece white space.Fig. 2 has provided the schematic diagram of a typical white space.

(2) establish the confidence level that in C (p) token image, p is ordered.Initialization C (p), order

and point on the δ Ω of border, makes confidence level (Ψ as shown in Figure 2, _pfor next step rectangular area centered by p point that is about to fill up, | Ψ | _pfor region Ψ _parea).Make weighted direction

(as shown in Figure 2,

for linear trend vector, be Ψ _pthe interior image gradient maximal value direction of ∩ (I-Ω), n _pfor the normal vector of p Dian Chu border δ Ω, α is quantizing factor, typical gray-scale map α=255).Make relative importance value see intuitively, confidence level C (p) is in rectangular area to be filled up, and non-NULL part confidence level sum, divided by rectangular area.Weighted direction D (p) is the projection of the maximum direction of gradient on normal, divided by quantizing factor.

(3) white space is carried out to image mending, method is as follows:

(a) making t is the circulation moment, Ω _tfor t white space constantly, δ Ω _tfor t white space border constantly.Initialization t=1.

(b) determine t white space border δ Ω constantly _t;

(c) for border δ Ω _ton institute a little, calculate relative importance value P (p);

(d) for border δ Ω _ton institute a little, find the maximum point of relative importance value P (p)

that is:

$\hat{p}={\arg \max }_{p\&Element;{\mathrm{\&delta;\&Omega;}}_t}P\left(p\right)$

Central point

after drawing, region to be filled up

determine immediately.

(e) in source region I-Ω, find and

immediate patch piece

for the central point of patch piece, that is:

${\mathrm{\&psi;}}_{\hat{q}}={\arg \min }_{{\mathrm{\&psi;}}_q\&Element;(1-\mathrm{\&Omega;})}d({\mathrm{\&psi;}}_{\hat{p}},{\mathrm{\&psi;}}_q)$

Operational symbol wherein represent

middle non-NULL pixel value and _qthe quadratic sum of the difference of respective pixel, for:

(f) for

will copy to that is,, by the blank in region to be filled up, with patch piece, directly fill.

(g) upgrade confidence level C (p),

also, upgrade the confidence level of being filled up region.Carry out t=t+1.

(h) if now white space filled complete,

stop iteration.If do not meet, return to step (b), continue to calculate.

(4) to all white space executable operations (3), until X piece white space all fills up complete.

(5) so far, all isolated fuzzy and region is fuzzy all removes, obtain finally removing the image S2 that azimuth ambiguity disturbs.Embodiment

For validity of the present invention is described, use this method to process actual measurement TerraSAR-X image.Required processing parameter is as shown in table 1.

Table 1 embodiment parameter

Fig. 3 has provided result.

Fig. 3 (a) is original image, can significantly find that the strong scattering target of picture centre forms azimuth ambiguity in upper and lower two parts, and wherein top is fuzzy due on sea thereby more obvious.In addition, the upper left white box of image is amplified and processed, can find wherein to exist speckle noise.

Fig. 3 (b) is the result after step 1 is processed, and what wherein white was decorated with grid is the definite fuzzy region of this method, can find that the azimuth ambiguity piece on image has all been distinguished and marked out, and classification situation is very desirable.

Fig. 3 (c) is traditional band-pass filtering method result, and removal is unclean can to find azimuth ambiguity, on the sea of image top, still can find that there is blurred signal remnants.In addition, from top, little figure can find, it is stronger that speckle noise becomes.

Fig. 3 (d) is result of the present invention, does not find that obvious azimuth ambiguity is remaining, and meanwhile, intensity of speckle noise does not change.

Therefore, the satellite-borne synthetic aperture radar band pattern azimuth ambiguity inhibition method that the present invention proposes can suppress azimuth ambiguity effectively, improves resolution and the recognition capability of target.

Claims (5)

1. a satellite-borne synthetic aperture radar band pattern azimuth ambiguity inhibition method, comprises following step:

Step 1: determine position the classification of fuzzy region in SAR image;

Be specially:

(1) by haplopia complex pattern, obtain local average image, establishing former haplopia complex pattern is S, and the local average image obtaining is S _μ:

$S_{\mathrm{\&mu;}}(a,r)=\frac{1}{m_a{n}_r}\underset{(x,y)\&Element;L}{\mathrm{\&Sigma;}}S(a,r)$

Wherein, S and S _μbe the complex matrix of m * n, m be orientation to always counting, n is for distance is to always counting, a be orientation to variable, r be apart to variable; L is the rectangle local average window centered by impact point, and the size of window is m _a* n _r, m _afor counting to window in orientation, n _rfor distance is counted to window;

(2) obtain fuzzy orientation to distance to skew:

$\mathrm{\&Delta;a}=\frac{f_p}{f_r}{V}_g$

$\mathrm{\&Delta;r}=\frac{\mathrm{\&lambda;}}{2}(f_D+\frac{f_p}{2})\frac{f_p}{f_r}$

Wherein, Δ a be blurred signal orientation to skew, Δ r be blurred signal distance to skew, f _ddoppler centroid, f _rdoppler frequency rate, V _gsatellite ground speed, f _pbe pulse repetition rate, λ is SAR operation wavelength;

(3) obtain fuzzy ratio:

$G\left(f_d\right)=\sin c\left(\frac{V_g\&CenterDot;(f_d-f_D)\&CenterDot;L_a}{f_r\&CenterDot;R_{\mathrm{ref}}\&CenterDot;\mathrm{\&lambda;}}\right)$

$\mathrm{\&xi;}=\frac{{\&Integral;}_{-\frac{f_p}{2}}^{\frac{f_p}{2}}{\left|G\left(f_d\right)\right|}^{4}d{f}_d}{{\&Integral;}_{\frac{f_p}{2}}^{\frac{{3f}_p}{2}}{\left|G\left(f_d\right)\right|}^{4}d{f}_d}$

Wherein, G (f _d) be antenna radiation pattern, f _dinstantaneous Doppler frequency, L _abe orientation to antenna length, R _refbe center constantly with reference to oblique distance, ξ is fuzzy ratio;

(4) obtain fuzzy judgment matrix B ₁(a, r):

Wherein, Δ a be orientation to side-play amount, Δ r be distance to side-play amount, " 1 " representative exist fuzzy, " 0 " representative be not fuzzy;

(5) obtain fuzzy judgment matrix B ₂(a, r):

Wherein, " 1 " representative exists fuzzy, and " 0 " representative is not fuzzy;

(6) obtain fuzzy judgment matrix B (a, r):

B(a,r)＝B ₁(a,r)∪B ₂(a,r)

B (a, r) is B ₁(a, r) and B ₂the union of (a, r); " 1 " representative exists fuzzy, and " 0 " representative is not fuzzy; Fuzzy judgment matrix B (a, r) and former haplopia complex pattern S, local average image S _μon location of pixels, be one to one, obtain all lituras in image;

(7) according to fuzzy judgment matrix, carry out blurred picture classification; If have 49 fuzzy elements of surpassing adjacent, judge that these fuzzy elements belong to region fuzzy, and these fuzzy elements are all set to 2; At this moment " 0 " indicates without fuzzy, and " 1 " represents isolated fuzzy, and " 2 " represent that region is fuzzy;

Step 2: use compression sensing method to remove isolated fuzzy;

Adopt compression sensing method to remove isolated fuzzy, obtain removing isolated fuzzy image S ₁;

Step 3: adopt the image mending method based on masterplate, removal region is fuzzy;

Based on image S ₁, adopt the image mending method removal region based on masterplate fuzzy, obtain removing the isolated fuzzy and fuzzy image S in region ₂.

2. a kind of satellite-borne synthetic aperture radar band pattern azimuth ambiguity inhibition method according to claim 1, described m _a=40, n _r=15.

3. a kind of satellite-borne synthetic aperture radar band pattern azimuth ambiguity inhibition method according to claim 1, described step 2 is specially:

(1) former haplopia complex pattern S is N=m * n mono-dimensional vector S' by row generate length:

S'＝S(a,1)∪S(a,2)∪…∪S(a,n)

Wherein, a is that orientation is to variable;

(2) to S', sampling obtains the dimensional vector y that length is M _s:

y _s＝ΦS'

Wherein, Φ is sampling matrix, only contains " 0 " and " 1 "; Every row only has 1 " 1 ", altogether M " 1 "; Obviously the column number of " 1 " has determined the position of sampled point in original image; If column number is y, sample coordinate position is

noting, do not sample isolated ambiguous location, is the element position of " 1 " in fuzzy judgment matrix B (a, r);

(3) build sparse property

Order:

S'＝Γ ^-1Ψ ^TS _w

:

y _s＝ΦΓ ^-1Ψ ^TS _w＝ΘS _w

Θ＝ΦΓ ^-1Ψ ^T

Wherein, Γ is Gauss's sharpening matrix (diagonal matrix, diagonal entry meets Gaussian distribution), and Ψ is wavelet transformation base; Θ can be obtained fom the above equation, Θ is called sensing matrix, S _wfor treating restructuring matrix;

(4) solve l ₁norm minimum problem:

${\hat{S}}_w=\arg \min {\left|\right|S_w\left|\right|}_{1}s.t{y}_s=\mathrm{\&Theta;}{S}_w$

Also, meeting y _s=Θ S _wprerequisite under, reconstruct l ₁the S of Norm minimum _w;

(5) adopt orthogonal matching pursuit algorithm to be reconstructed, concrete grammar is as follows:

(a) known vector of samples y _s, sensing matrix Θ; Making t is the circulation moment, r _t, Λ _t, Β _t, S _wtbe respectively t residual error constantly, indexed set, rebuilds atom set, treats restructuring matrix; Initialization r ₀=y _s,

order circulation is t=1 constantly;

(b) find out residual error r _t-1respectively be listed as θ with sensing matrix Θ _jinner product the maximum, record the corresponding footmark λ of maximum column _t, that is:

λ _t＝j _max＝argmax _j＝1…N|<r _t-1,θ _j>|

(c) upgrade indexed set Λ _t=Λ _t-1∪ { λ _t, the reconstruction atom set in the sensing matrix that record finds

(d) by least square method, obtain immediate S _wt,

(e) upgrade residual error $r_t=y_s-B_t{\hat{S}}_{\mathrm{wt}},t=t+1;$

(f) if || r _t|| ₂< δ, stops iteration, and wherein δ, for stopping thresholding, exports end product if do not meet, return to step (b), continue iterative computation;

(g) by S'=Γ ^-1Ψ ^ts _wsolve S';

(6) the isolated fuzzy pixel in former haplopia complex pattern S is substituted with corresponding element in S'; So far, obtain removing isolated fuzzy image S ₁.

4. a kind of satellite-borne synthetic aperture radar band pattern azimuth ambiguity inhibition method according to claim 3, described δ=0.1 * || y _s|| ₂.

5. a kind of satellite-borne synthetic aperture radar band pattern azimuth ambiguity inhibition method according to claim 1, described step 3 is specially:

(1) by S ₁middle region vague image vegetarian refreshments all sets to 0, and obtains X piece white space;

(2) establish the confidence level that in C (p) token image, p is ordered; Initialization C (p), order

and $C\left(p\right)=1,\&ForAll;p\&Element;I-\mathrm{\&Omega;};$ Make confidence level $C\left(p\right)=\frac{{\mathrm{\&Sigma;}}_{{q\&Element;\mathrm{\&psi;}}_p\&cap;(1-\mathrm{\&Omega;})}C\left(q\right)}{\left|{\mathrm{\&psi;}}_p\right|},\&ForAll;p\&Element;\mathrm{\&delta;\&Omega;},$ Wherein, Ψ _pfor next step rectangular area centered by p point that is about to fill up, | Ψ _p| be region Ψ _parea;

Make weighted direction

wherein,

for linear trend vector, be Ψ _pthe interior image gradient maximal value direction of ∩ (I-Ω), n _pfor the normal vector of p Dian Chu border δ Ω, α is quantizing factor;

Make relative importance value

(3) white space is carried out to image mending, method is as follows:

(a) making t is the circulation moment, Ω _tfor t white space constantly, δ Ω _tfor the white space border of t white space constantly, initialization t=1;

(b) determine t white space border δ Ω constantly _t;

(c) for border δ Ω _ton institute a little, calculate relative importance value P (p);

(d) for border δ Ω _ton institute a little, find the maximum point of relative importance value P (p) that is:

$\hat{p}={\arg \max }_{p\&Element;{\mathrm{\&delta;\&Omega;}}_t}P\left(p\right)$

Central point

after drawing, region to be filled up

determine immediately;

(e) in source region I-Ω, find and

immediate patch piece

for the central point of patch piece, that is:

${\mathrm{\&psi;}}_{\hat{q}}={\arg \min }_{{\mathrm{\&psi;}}_q\&Element;(1-\mathrm{\&Omega;})}d({\mathrm{\&psi;}}_{\hat{p}},{\mathrm{\&psi;}}_q)$

Operational symbol wherein

represent

middle non-NULL pixel value and Ψ _qthe quadratic sum of the difference of respective pixel, for:

(f) for

will copy to

that is,, by the blank in region to be filled up, with patch piece, directly fill;

(g) upgrade confidence level

also, upgrade the confidence level of being filled up region, carry out t=t+1;

(h) if now white space filled complete,

stop iteration; If do not meet, return to step (b);

(4) to all white space executable operations (3), until X piece white space all fills up complete;

(5) obtain finally removing the image S that azimuth ambiguity disturbs ₂.

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