CN107390218A - Two-dimensional phase unwrapping method based on minimum Infinite Norm - Google Patents
Two-dimensional phase unwrapping method based on minimum Infinite Norm Download PDFInfo
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- G—PHYSICS
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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- G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
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- G01S13/9023—SAR image post-processing techniques combined with interferometric techniques
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- G—PHYSICS
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- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
- G01S13/88—Radar or analogous systems specially adapted for specific applications
- G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
- G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
- G01S13/9004—SAR image acquisition techniques
- G01S13/9005—SAR image acquisition techniques with optical processing of the SAR signals
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Abstract
The invention belongs to radar signal processing field, discloses a kind of two-dimensional phase unwrapping method based on minimum Infinite Norm, including:Interferometric phase image is obtained, so as to obtain the winding phasing matrix of interferometric phase image;The horizontal wrap phase gradient matrix of interferometric phase image and the vertical wrap phase gradient matrix of interferometric phase image is calculated;Calculate the horizontal absolute phase gradient estimation value matrix and vertical absolute phase gradient estimation value matrix of interferometric phase image;It is calculated the absolute phase matrix of interferometric phase image, the absolute phase matrix of interferometric phase image is interferometric phase image unwrapping as a result, it is possible to be efficiently modified the solving precision of conventional two-dimensional phase unwrapping winding method.
Description
Technical field
The invention belongs to Radar Signal Processing Technology field, more particularly to a kind of two-dimensional phase based on minimum Infinite Norm
Unwrapping method, suitable for interference synthetic aperture radar (InSAR) system phase unwrapping around problem.
Background technology
As conventional synthesis aperture radar (SAR) development, InSAR systems can the work of round-the-clock, round-the-clock, this skill
Art has application in mapping, Ground Deformation monitoring and all many-sides such as natural calamity detection, therefore, the hair of InSAR technologies
Exhibition has been constantly subjected to pay much attention to, and phase unwrapping is critical process step therein around (Phase Unwrapping, PU).
Based on Lp- norm PU methods are most representational a kind of methods, under traditional view, it is believed that p value it is more big more
It is unfavorable for phase unwrapping around because p value is bigger, Optimized model more tends to allow high quality region to share from low quality region
The discontinuous phase potential gradient error of (i.e. residual close quarters), the PU result relative smooths so obtained, but low-quality can be caused
Measuring error caused by region, to high quality regional diffusion, causes the decline of solving precision.
In order to ensure the solving precision in high quality region, traditional PU viewpoints intended to ensure solving result and input striped one
Cause, however, although this way ensure that the solving precision in high quality region, but low quality region be present when inputting in striped
When, these regions there's almost no effective information, now require PU results with input striped it is consistent be irrational.
The content of the invention
In view of the above-mentioned problems, it is an object of the invention to provide a kind of two-dimensional phase unwrapping based on minimum Infinite Norm
Method (is referred to as MIN methods) in the embodiment of the present invention, have adaptive-filtering function, energy during carrying out phase unwrapping
Enough it is efficiently modified the solving precision of conventional two-dimensional phase unwrapping winding method.
In actual applications, it is necessary to which a kind of method, can not only ensure the solving precision in high quality region (i.e. in high quality
Region ensures striped uniformity), also low quality region should be able to be carried out rationally to handle (limitation for relaxing striped uniformity).
To reach above-mentioned purpose, the present invention, which adopts the following technical scheme that, to be achieved.
A kind of two-dimensional phase unwrapping method based on minimum Infinite Norm, methods described include:
Step 1, interferometric phase image is obtained, the size of the interferometric phase image is m × n, wherein, m, n are respectively to be more than zero
Positive integer;The pixel value at position (i, j) place is designated as the winding phase at position (i, j) place in interferometric phase image in figure
So as to obtain the winding phasing matrix of interferometric phase image;Wherein, i=1,2 ..., m, j=1,2 ..., n;
Step 2, according to the winding phasing matrix of the interferometric phase image, the level that interferometric phase image is calculated respectively twines
Around phase gradient matrix and the vertical wrap phase gradient matrix of interferometric phase image;
Step 3, according to the horizontal wrap phase gradient matrix of interferometric phase image, the horizontal absolute phase of interferometric phase image is calculated
Potential gradient estimates value matrix;
According to the vertical wrap phase gradient matrix of interferometric phase image, the vertical absolute phase gradient of interferometric phase image is calculated
Estimate value matrix;
Step 4, value matrix, the interferometric phase image are estimated according to the horizontal absolute phase gradient of the interferometric phase image
Vertical absolute phase gradient estimation value matrix, the absolute phase matrix of interferometric phase image is calculated, the interferometric phase image
Absolute phase matrix is the result of interferometric phase image unwrapping.
The characteristics of technical solution of the present invention and further it is improved to:
(1) step 2 specifically includes:
The horizontal wrap phase gradient note at position (i, j) place in the horizontal wrap phase gradient matrix of (2a) interferometric phase image
ForWherein, i=1,2 ..., m, j=1,2 ..., n-1;
And:
Wherein,The winding phase at position (i, j+1) place in interferometric phase image is represented,Represent interference phase
The winding phase at position (i, j) place in bitmap;
The vertical wrap phase gradient note at position (i, j) place in the vertical wrap phase gradient matrix of (2b) interferometric phase image
ForWherein, i=1,2 ..., m-1, j=1,2 ..., n;
And:
Wherein,Represent the winding phase at position (i+1, j) place in interferometric phase image.
(2) step 3 specifically includes:
The horizontal absolute phase at position (i, j) place in the horizontal absolute phase gradient estimation value matrix of (3a) interferometric phase image
Gradient estimate is designated asWherein, i=1,2 ..., m, j=1,2 ..., n-1;
And:
Wherein,Represent that the level at position (i, j) place in the horizontal wrap phase gradient matrix of interferometric phase image twines
Around phase gradient;
The vertical absolute phase at position (i, j) place in the vertical absolute phase gradient estimation value matrix of (3b) interferometric phase image
Gradient estimate is designated asWherein, i=1,2 ..., m-1, j=1,2 ..., n;
And:
Wherein,Represent that the vertical of position (i, j) place twines in the vertical wrap phase gradient matrix of interferometric phase image
Around phase gradient.
(3) step 4 specifically includes:
By the horizontal absolute phase ladder at position (i, j) place in the horizontal absolute phase gradient estimation value matrix of interferometric phase image
Spend estimateVertical absolute phase gradient estimateAnd the horizontal absolute phase at position (i+1, j) place
Potential gradient estimateThe vertical absolute phase gradient estimate at position (i, j+1) placeBring into as
Lower Optimized model:
Wherein, t (i, j) is free variable, and w (i, j) is t (i, j) weights, set S=(i, j) | i=1,2..., m-
1, j=1,2 ..., n-1) }, ψ (i, j), ψ (i, j+1), ψ (i+1, j) and ψ (i+1, j+1) represent the exhausted of interferometric phase image respectively
It is this to absolute phase of the phasing matrix at position (i, j), position (i, j+1), position (i+1, j) and position (i+1, j+1) place
The Optimized model variable to be solved.
The present invention is a kind of phase unwrapping winding method with adaptive-filtering function, is carrying out phase unwrapping around solution
When, high quality region and low quality region that can be in the interferometric phase image of automatic identification input, ensureing high quality region
On the premise of striped uniformity, moreover it is possible to the noise in low quality region is filtered, improve phase unwrapping around precision.
Brief description of the drawings
In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing
There is the required accompanying drawing used in technology description to be briefly described, it should be apparent that, drawings in the following description are only this
Some embodiments of invention, for those of ordinary skill in the art, on the premise of not paying creative work, can be with
Other accompanying drawings are obtained according to these accompanying drawings.
Fig. 1 is a kind of flow of the two-dimensional phase unwrapping method based on minimum Infinite Norm provided in an embodiment of the present invention
Schematic diagram;
Fig. 2 is for emulating interferometric phase image, respectively show the result of the inventive method and conventional method, own
The abscissa of figure corresponds to corresponding matrix column, and the ordinate of all figures corresponds to the row of corresponding matrix.In Fig. 2, Fig. 2 (a) is reference
Unwrapping phase diagram;Fig. 2 (b) is with reference to interferometric phase image;Fig. 2 (c) is the interferometric phase image of emulation;Fig. 2 (d) is coefficient correlation
Figure;Fig. 2 (e) is L∞The PU result figures of-norm methods;Fig. 2 (f) is L2The PU result figures of-norm (2 norm) method;Fig. 2 (g)
For L1The PU result figures of-norm methods;Fig. 2 (h) is the PU result figures of SNAPHU methods;Fig. 2 (i) is the PU results of PUMA methods
Figure;Fig. 2 (j) is the PU result figures of MIN methods;Difference result figures of the Fig. 2 (k) between Fig. 2 (a) and 2 (e);Fig. 2 (l) is Fig. 2
(a) the difference structure chart between 2 (f);Difference result figures of the Fig. 2 (m) between Fig. 2 (a) and 2 (g);Fig. 2 (n) is Fig. 2 (a)
Difference result figure between 2 (h);Difference result figures of the Fig. 2 (o) between Fig. 2 (a) and 2 (i);Fig. 2 (p) is Fig. 2 (a) and 2
(j) the difference result figure between;Fig. 2 (q) is L∞- norm method PU results wind phase diagram again;Fig. 2 (r) is L2- norm sides
Method PU results wind phase diagram again;Fig. 2 (s) winds phase diagram again for MIN method PU results;
Fig. 3 is for surveying interferometric phase image, respectively show the result of the inventive method and conventional method, own
The abscissa of figure corresponds to corresponding matrix column, and the ordinate of all figures corresponds to the row of corresponding matrix.In Fig. 3, Fig. 3 (a) is actual measurement
Interferometric phase image;Fig. 3 (b) is L∞The PU result figures of-norm methods;Fig. 3 (c) is L2The PU result figures of-norm methods;Fig. 3
(d) it is L1The PU result figures of-norm methods;Fig. 3 (e) is the PU result figures of SNAPHU methods;Fig. 3 (f) is the PU of PUMA methods
Result figure;Fig. 3 (g) is the PU result figures of MIN methods;Fig. 3 (h) is L∞- norm method PU results wind phase diagram again;Fig. 3
(i) it is L2- norm method PU results wind phase diagram again;Fig. 3 (j) winds phase diagram again for MIN method PU results;Fig. 3
(k) the filter result figure for being Fig. 3 (a);Fig. 3 (l) is Fig. 3 (j) filter result figure.
Embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Site preparation describes, it is clear that described embodiment is only part of the embodiment of the present invention, rather than whole embodiments.It is based on
Embodiment in the present invention, those of ordinary skill in the art are obtained every other under the premise of creative work is not made
Embodiment, belong to the scope of protection of the invention.
The embodiment of the present invention provides a kind of two-dimensional phase unwrapping method based on minimum Infinite Norm, as shown in figure 1, institute
The method of stating includes:
Step 1, interferometric phase image is obtained, the size of the interferometric phase image is m × n, position (i, j) in interferometric phase image
The pixel value at place is designated as the winding phase at position (i, j) place in interferometric phase imageSo as to obtain twining for interferometric phase image
Around phasing matrix;Wherein, i=1,2 ..., m, j=1,2 ..., n.
Step 2, according to the winding phasing matrix of the interferometric phase image, the level that interferometric phase image is calculated respectively twines
Around phase gradient matrix and the vertical wrap phase gradient matrix of interferometric phase image.
Step 2 specifically includes:
The horizontal wrap phase gradient note at position (i, j) place in the horizontal wrap phase gradient matrix of (2a) interferometric phase image
ForWherein, i=1,2 ..., m, j=1,2 ..., n-1;
And:
Wherein,The winding phase at position (i, j+1) place in interferometric phase image is represented,Represent interference phase
The winding phase at position (i, j) place in bitmap;
The vertical wrap phase gradient note at position (i, j) place in the vertical wrap phase gradient matrix of (2b) interferometric phase image
ForWherein, i=1,2 ..., m-1, j=1,2 ..., n;
And:
Wherein,Represent the winding phase at position (i+1, j) place in interferometric phase image.
Step 3, according to the horizontal wrap phase gradient matrix of interferometric phase image, the horizontal absolute phase of interferometric phase image is calculated
Potential gradient estimates value matrix;
According to the vertical wrap phase gradient matrix of interferometric phase image, the vertical absolute phase gradient of interferometric phase image is calculated
Estimate value matrix.
Step 3 specifically includes:
The horizontal absolute phase at position (i, j) place in the horizontal absolute phase gradient estimation value matrix of (3a) interferometric phase image
Gradient estimate is designated asWherein, i=1,2 ..., m, j=1,2 ..., n-1;
And:
Wherein,Represent that the level at position (i, j) place in the horizontal wrap phase gradient matrix of interferometric phase image twines
Around phase gradient;
The vertical absolute phase at position (i, j) place in the vertical absolute phase gradient estimation value matrix of (3b) interferometric phase image
Gradient estimate is designated asWherein, i=1,2 ..., m-1, j=1,2 ..., n;
And:
Wherein,Represent that the vertical of position (i, j) place twines in the vertical wrap phase gradient matrix of interferometric phase image
Around phase gradient.
Step 4, value matrix, the interferometric phase image are estimated according to the horizontal absolute phase gradient of the interferometric phase image
Vertical absolute phase gradient estimation value matrix, the absolute phase matrix of interferometric phase image is calculated, the interferometric phase image
Absolute phase matrix is the result of interferometric phase image unwrapping.
Step 4 specifically includes:
By the horizontal absolute phase ladder at position (i, j) place in the horizontal absolute phase gradient estimation value matrix of interferometric phase image
Spend estimateVertical absolute phase gradient estimateAnd the horizontal absolute phase at position (i+1, j) place
Potential gradient estimateThe vertical absolute phase gradient estimate at position (i, j+1) placeBring into as
Lower Optimized model:
Wherein, t (i, j) is free variable, and w (i, j) is t (i, j) weights, set S=(i, j) | i=1,2..., m-
1, j=1,2 ..., n-1) }, ψ (i, j), ψ (i, j+1), ψ (i+1, j) and ψ (i+1, j+1) represent the exhausted of interferometric phase image respectively
It is this to absolute phase of the phasing matrix at position (i, j), position (i, j+1), position (i+1, j) and position (i+1, j+1) place
The Optimized model variable to be solved.
Generally, w (i, j) can by interferometric phase image Quality Map obtain, when need not weight, make w (i, j)=
1.Above-mentioned Optimized model is a linear programming model, and unwrapping result can be obtained by solving the model.
It should be noted that the Optimized model is in L1On the basis of-norm (1 norm), to each four adjacent pictures
Absolute phase (i.e. ψ (i, j), ψ (i, j+1), ψ (i+1, j) and ψ (i+1, j+1)) on element uses L∞- norm's (Infinite Norm)
Enter row constraint, thus, L∞Filter function is introduced in L possessed by-norm1In-norm Optimized models, so, the optimization mould
Type can either pass through L1- norm keeps striped uniformity (i.e. without filtering) in the high quality region of interferometric phase image, simultaneously
Also L can be utilized∞The filtering that-norm plays a part of in the low quality region of interferometric phase image, due to not needing any nondominant hand
Section helps L∞- norm identifies low quality region to complete filter function, it may be said that phase unwrapping proposed by the invention is around side
Method has adaptive-filtering function.
Effectiveness of the invention can be described further by following experiment.
(1) InSAR emulates the experiment of data
1st, data explanation
Emulate data using County, Hebei Province, China Shangyi mountain area digital elevation model, emulation generate interferometric phase image
When, in order to increase phase unwrapping around difficulty, add noise, added in high quality region coefficient correlation be 0.8 noise,
The noise that coefficient correlation is 0 is added in low quality region.
2nd, emulation content and interpretation of result
In order to show the validity of the inventive method, emulation experiment is by the inventive method and L∞-norm、L2-norm、L1-
The conventional methods such as norm, SNAPHU, PUMA have carried out contrast experiment.
Fig. 2 (a) show the reference absolute phase obtained by digital complex demodulation.Fig. 2 (b) is to be obtained by Fig. 2 (a)
Preferable interferometric phase image.Fig. 2 (c) show the interferometric phase image of emulation, and Fig. 2 (d) is in emulation generation Fig. 2 (c) when institute
Using coefficient correlation, in order to increase PU difficulty, processing is not filtered in Fig. 2 (c).In addition, can from Fig. 2 (d)
See, emulation when to Fig. 2 (c) add several noise ranges (coefficient correlation of high quality simulation of domain be 0.8, make an uproar
0) coefficient correlation that sound simulation of domain uses is.Fig. 2 (e), Fig. 2 (f) and Fig. 2 (g) are respectively L∞- norm methods, L2- norm sides
Method and L1The PU results of-norm methods.Fig. 2 (h) is the PU results of SNAPHU methods, and it counts cost pattern and is arranged to TOPO.
Fig. 2 (i) is the PU results of PUMA methods, and the clique potential exponent parameters of PUMA methods are arranged to 0.5.Fig. 2
(j) be the inventive method PU results.All methods carry out PU solutions in the case of no weighting.Fig. 2 (k)-Fig. 2
(p) be respectively Fig. 2 (e)-Fig. 2 (j) and Fig. 2 (a) difference, Fig. 2 (k)-Fig. 2 (p) statistical information sieve is listed in Table 1.
The statistical information of table 1.PU results
From fig. 2 it can be seen that L∞- norm and L2- norm PU methods can obtain very smooth PU results, still
Their PU precision is very low.L1- norm, PUMA, SNAPHU and MIN method can ensure PU precision in high quality region,
So their performances generally are better than L∞- norm and L2- norm methods.However, because MIN methods have to low quality region
Adaptive-filtering function, the noise region in MIN method PU results shown in Fig. 2 (j) is more smooth relative to Fig. 2 (g)-(i),
That is, in low quality region, the PU precision of MIN methods is higher than L1- norm, PUMA and SNAPHU method.By foregoing right
Than, it can be deduced that conclusion, the filter function of MIN methods can reduce PU errors.Fig. 2 (q), Fig. 2 (r) and Fig. 2 (s) illustrate figure
2 (e), Fig. 2 (f) wind phase diagram again with Fig. 2's (j), because L1- norm, PUMA and SNAPHU method being capable of strict guarantee bars
Line uniformity, so Fig. 2 (g), Fig. 2 (h) and Fig. 2's (i) winds bar graph and Fig. 2 (c) equally again.By by Fig. 2 (c) with figure
2 (q), Fig. 2 (r), Fig. 2 (s) are contrasted, it can be seen that L∞- norm and L2- norm PU methods are to input interferometric phase image production
Destructive filtering has been given birth to, but MIN methods can ensure striped uniformity in high quality region, and carried out to noise region
Adaptive-filtering.In addition, pass through comparison diagram 2 (b) and Fig. 2 (s), it can be seen that, the noise range that is recovered by MIN methods
Phase fringes, be the preferable striped relatively shown in Fig. 2 (b).
(2) measured data is tested
Fig. 3 (a) is actual measurement interferometric phase image." good " region and " bad " region can be clearly visible that wherein.Fig. 3 (b),
Fig. 3 (c) and Fig. 3 (d) is for L respectively∞- norm methods, L2- norm methods and L1The PU results of-norm methods.Fig. 3 (e) is
The PU results of SNAPHU methods, it counts cost pattern and is arranged to TOPO.Fig. 3 (f) be PUMA methods PU results, PUMA methods
Clique potential exponent parameters be arranged to 0.5.Fig. 3 (g) is the PU results of the inventive method.All sides
Method carries out PU solutions in the case of no weighting.Fig. 3 (h), Fig. 3 (i), Fig. 3 (j) are Fig. 3 (b), Fig. 3 (c), Fig. 3 respectively
(g) wind phase diagram again, due to Fig. 3 (d), Fig. 3 (e) Fig. 3 (f) to wind striped again identical with Fig. 3 (a), therefore herein no longer
Displaying.It can be seen that the PU results of Fig. 3 (b), Fig. 3 (c), Fig. 3 (g) noise range than Fig. 3 (d), Fig. 3 (e), Fig. 3 (f) noise
Area is smooth.However, by by Fig. 3 (a) compared with Fig. 3 (h), Fig. 3 (i), it is evident that L2- norm methods, L∞- norm methods pair
Input interferometric phase image has carried out undue filtering, i.e. the input phase striped in high quality region is totally disrupted.At this
In the case of kind, the precision of the PU solving results in high quality region is greatly diminished.L1- norm methods, SNAPHU methods, PUMA
Method strict guarantee striped uniformity, therefore the PU precision in high quality region is believable.If comparison diagram 3 (a) and Fig. 3
(j), it can be seen that the filter function of MIN methods is acted on only for noise region.Therefore, MIN methods not only ensure
Good region almost with L1- norm methods, SNAPHU methods are as PUMA methods, and to the input phase striped of error area
Filtered.In order to further show the filter effect of MIN methods, employ simple filtering method (i.e. 3 × 3 windows
Mean filter) Fig. 3 (a) and Fig. 3 (j) striped is filtered again, shown in result such as Fig. 3 (k) and Fig. 3 (l) of filtering.Cause
To filter the logical step in not InSAR processing again to Fig. 3 (a) and Fig. 3 (g), so Fig. 3 (k) and Fig. 3 (l) phase
Striped is excessively smooth.It can be seen that Fig. 3 (a) low quality region is still noise in Fig. 3 (k).However, in Fig. 3 (l),
To Fig. 3 (a) noise regions, some rational new stripeds are generated.In other words, Fig. 3 (l) discloses the filter effect of MIN methods
Trend.
To sum up, we have been respectively adopted emulation data and have demonstrated effectiveness of the invention with measured data.
The foregoing is only a specific embodiment of the invention, but protection scope of the present invention is not limited thereto, any
Those familiar with the art the invention discloses technical scope in, change or replacement can be readily occurred in, should all be contained
Cover within protection scope of the present invention.Therefore, protection scope of the present invention should be based on the protection scope of the described claims.
Claims (4)
- A kind of 1. two-dimensional phase unwrapping method based on minimum Infinite Norm, it is characterised in that methods described includes:Step 1, interferometric phase image is obtained, the size of the interferometric phase image is m × n, position (i, j) place in interferometric phase image Pixel value is designated as the winding phase at position (i, j) place in interferometric phase imageSo as to obtain the winding phase of interferometric phase image Bit matrix;Wherein, i=1,2 ..., m, j=1,2 ..., n;Step 2, according to the winding phasing matrix of the interferometric phase image, the horizontal wrap phase of interferometric phase image is calculated respectively The vertical wrap phase gradient matrix of potential gradient matrix and interferometric phase image;Step 3, according to the horizontal wrap phase gradient matrix of interferometric phase image, the horizontal absolute phase for calculating interferometric phase image is terraced Degree estimation value matrix;According to the vertical wrap phase gradient matrix of interferometric phase image, the vertical absolute phase gradient estimation of interferometric phase image is calculated Value matrix;Step 4, according to the horizontal absolute phase gradient of the interferometric phase image estimate value matrix, the interferometric phase image it is vertical Absolute phase gradient estimates value matrix, is calculated the absolute phase matrix of interferometric phase image, the interferometric phase image it is absolute Phasing matrix is the result of interferometric phase image unwrapping.
- A kind of 2. two-dimensional phase unwrapping method based on minimum Infinite Norm according to claim 1, it is characterised in that Step 2 specifically includes:The horizontal wrap phase gradient at position (i, j) place is designated as in the horizontal wrap phase gradient matrix of (2a) interferometric phase imageWherein, i=1,2 ..., m, j=1,2 ..., n-1;And:Wherein,The winding phase at position (i, j+1) place in interferometric phase image is represented,Represent interferometric phase image The winding phase at middle position (i, j) place;The vertical wrap phase gradient at position (i, j) place is designated as in the vertical wrap phase gradient matrix of (2b) interferometric phase imageWherein, i=1,2 ..., m-1, j=1,2 ..., n;And:Wherein,Represent the winding phase at position (i+1, j) place in interferometric phase image.
- A kind of 3. two-dimensional phase unwrapping method based on minimum Infinite Norm according to claim 1, it is characterised in that Step 3 specifically includes:The horizontal absolute phase gradient at position (i, j) place in the horizontal absolute phase gradient estimation value matrix of (3a) interferometric phase image Estimate is designated asWherein, i=1,2 ..., m, j=1,2 ..., n-1;And:Wherein,Represent the horizontal wrap phase at position (i, j) place in the horizontal wrap phase gradient matrix of interferometric phase image Potential gradient;The vertical absolute phase gradient at position (i, j) place in the vertical absolute phase gradient estimation value matrix of (3b) interferometric phase image Estimate is designated asWherein, i=1,2 ..., m-1, j=1,2 ..., n;And:Wherein,Represent the vertical wrap phase at position (i, j) place in the vertical wrap phase gradient matrix of interferometric phase image Potential gradient.
- A kind of 4. two-dimensional phase unwrapping method based on minimum Infinite Norm according to claim 1, it is characterised in that Step 4 specifically includes:The horizontal absolute phase gradient at position (i, j) place in the horizontal absolute phase gradient estimation value matrix of interferometric phase image is estimated EvaluationVertical absolute phase gradient estimateAnd the horizontal absolute phase ladder at position (i+1, j) place Spend estimateThe vertical absolute phase gradient estimate at position (i, j+1) placeBring into following excellent Change model:<mrow> <mi>min</mi> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>m</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mi>w</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mi>t</mi> <mrow> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> </mrow><mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> </mrow> </mtd> <mtd> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mo>-</mo> <mi>t</mi> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> <mo>&le;</mo> <mi>&psi;</mi> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>-</mo> <mi>&psi;</mi> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> <mo>-</mo> <msubsup> <mi>&Delta;</mi> <mi>&psi;</mi> <mi>x</mi> </msubsup> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> <mo>&le;</mo> <mi>t</mi> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mi>t</mi> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> <mo>&le;</mo> <mi>&psi;</mi> <mo>(</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>-</mo> <mi>&psi;</mi> <mo>(</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>)</mo> <mo>-</mo> <msubsup> <mi>&Delta;</mi> <mi>&psi;</mi> <mi>x</mi> </msubsup> <mo>(</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>)</mo> <mo>&le;</mo> <mi>t</mi> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mi>t</mi> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> <mo>&le;</mo> <mi>&psi;</mi> <mo>(</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>)</mo> <mo>-</mo> <mi>&psi;</mi> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> <mo>-</mo> <msubsup> <mi>&Delta;</mi> <mi>&psi;</mi> <mi>y</mi> </msubsup> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> <mo>&le;</mo> <mi>t</mi> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mo>-</mo> <mi>t</mi> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> <mo>&le;</mo> <mi>&psi;</mi> <mo>(</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>-</mo> <mi>&psi;</mi> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>-</mo> <msubsup> <mi>&Delta;</mi> <mi>&psi;</mi> <mi>y</mi> </msubsup> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>&le;</mo> <mi>t</mi> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mtd> </mtr> <mtr> <mtd> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> <mo>&Element;</mo> <mi>S</mi> </mtd> </mtr> </mtable> </mfenced> </mtd> </mtr> </mtable> </mfenced>Wherein, t (i, j) is free variable, and w (i, j) is t (i, j) weights, set S=(i, j) | i=1,2..., m-1, j =1,2 ..., n-1) }, ψ (i, j), ψ (i, j+1), ψ (i+1, j) and ψ (i+1, j+1) represent the absolute of interferometric phase image respectively Phasing matrix is that this is excellent in the absolute phase at position (i, j), position (i, j+1), position (i+1, j) and position (i+1, j+1) place Change the variable of model needs solution.
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