CN107390218A - Two-dimensional phase unwrapping method based on minimum Infinite Norm - Google Patents

Two-dimensional phase unwrapping method based on minimum Infinite Norm Download PDF

Info

Publication number
CN107390218A
CN107390218A CN201710749117.3A CN201710749117A CN107390218A CN 107390218 A CN107390218 A CN 107390218A CN 201710749117 A CN201710749117 A CN 201710749117A CN 107390218 A CN107390218 A CN 107390218A
Authority
CN
China
Prior art keywords
phase
interferometric
matrix
phase image
gradient
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN201710749117.3A
Other languages
Chinese (zh)
Other versions
CN107390218B (en
Inventor
邢孟道
蓝洋
于瀚雯
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Xidian University
Original Assignee
Xidian University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Xidian University filed Critical Xidian University
Priority to CN201710749117.3A priority Critical patent/CN107390218B/en
Publication of CN107390218A publication Critical patent/CN107390218A/en
Application granted granted Critical
Publication of CN107390218B publication Critical patent/CN107390218B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • 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
    • G01S13/9021—SAR image post-processing techniques
    • G01S13/9023—SAR image post-processing techniques combined with interferometric techniques
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • 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

Landscapes

  • Engineering & Computer Science (AREA)
  • Remote Sensing (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • General Physics & Mathematics (AREA)
  • Signal Processing (AREA)
  • Image Processing (AREA)

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

Two-dimensional phase unwrapping method based on minimum Infinite Norm
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)

  1. 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.
  2. 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.
  3. 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.
  4. 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>&amp;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>&amp;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>&amp;le;</mo> <mi>&amp;psi;</mi> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>-</mo> <mi>&amp;psi;</mi> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> <mo>-</mo> <msubsup> <mi>&amp;Delta;</mi> <mi>&amp;psi;</mi> <mi>x</mi> </msubsup> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> <mo>&amp;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>&amp;le;</mo> <mi>&amp;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>&amp;psi;</mi> <mo>(</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>)</mo> <mo>-</mo> <msubsup> <mi>&amp;Delta;</mi> <mi>&amp;psi;</mi> <mi>x</mi> </msubsup> <mo>(</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>)</mo> <mo>&amp;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>&amp;le;</mo> <mi>&amp;psi;</mi> <mo>(</mo> <mi>i</mi> <mo>+</mo> <mn>1</mn> <mo>,</mo> <mi>j</mi> <mo>)</mo> <mo>-</mo> <mi>&amp;psi;</mi> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> <mo>-</mo> <msubsup> <mi>&amp;Delta;</mi> <mi>&amp;psi;</mi> <mi>y</mi> </msubsup> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> <mo>&amp;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>&amp;le;</mo> <mi>&amp;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>&amp;psi;</mi> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>-</mo> <msubsup> <mi>&amp;Delta;</mi> <mi>&amp;psi;</mi> <mi>y</mi> </msubsup> <mo>(</mo> <mi>i</mi> <mo>,</mo> <mi>j</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> <mo>&amp;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>&amp;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.
CN201710749117.3A 2017-08-28 2017-08-28 Two-dimensional phase unwrapping method based on minimum infinite norm Active CN107390218B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201710749117.3A CN107390218B (en) 2017-08-28 2017-08-28 Two-dimensional phase unwrapping method based on minimum infinite norm

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201710749117.3A CN107390218B (en) 2017-08-28 2017-08-28 Two-dimensional phase unwrapping method based on minimum infinite norm

Publications (2)

Publication Number Publication Date
CN107390218A true CN107390218A (en) 2017-11-24
CN107390218B CN107390218B (en) 2020-06-05

Family

ID=60345427

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201710749117.3A Active CN107390218B (en) 2017-08-28 2017-08-28 Two-dimensional phase unwrapping method based on minimum infinite norm

Country Status (1)

Country Link
CN (1) CN107390218B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112596036A (en) * 2020-09-25 2021-04-02 南京信息工程大学 Diagnosis method of MIMO radar array under impulsive noise

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102621549A (en) * 2011-10-14 2012-08-01 中国人民解放军国防科学技术大学 Multi-baseline/multi-frequency-band interference phase unwrapping frequency domain quick algorithm
WO2014074631A1 (en) * 2012-11-07 2014-05-15 Neva Ridge Technologies Sar point cloud generation system
CN104808203A (en) * 2015-03-03 2015-07-29 电子科技大学 Multi-baseline InSAR phase unwrapping method by iterating maximum likelihood estimation

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102621549A (en) * 2011-10-14 2012-08-01 中国人民解放军国防科学技术大学 Multi-baseline/multi-frequency-band interference phase unwrapping frequency domain quick algorithm
WO2014074631A1 (en) * 2012-11-07 2014-05-15 Neva Ridge Technologies Sar point cloud generation system
CN104808203A (en) * 2015-03-03 2015-07-29 电子科技大学 Multi-baseline InSAR phase unwrapping method by iterating maximum likelihood estimation

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
于瀚雯等: "利用L1范数的多基线InSAR相位解缠绕技术", 《西安电子科技大学学报》 *
刘会涛等: "A Novel Mixed-Norm Multibaseline Phase-Unwrapping Algorithm Based", 《IEEE GEOSCIENCE AND REMOTE SENSING LETTERS》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN112596036A (en) * 2020-09-25 2021-04-02 南京信息工程大学 Diagnosis method of MIMO radar array under impulsive noise
CN112596036B (en) * 2020-09-25 2023-09-22 南京信息工程大学 Diagnosis method of MIMO radar array under impact noise

Also Published As

Publication number Publication date
CN107390218B (en) 2020-06-05

Similar Documents

Publication Publication Date Title
US10229533B2 (en) Methods and systems for fast resampling method and apparatus for point cloud data
Ma Three-dimensional irregular seismic data reconstruction via low-rank matrix completion
Radice et al. High-order fully general-relativistic hydrodynamics: new approaches and tests
Gneiting et al. Estimators of fractal dimension: Assessing the roughness of time series and spatial data
Métivier et al. A graph space optimal transport distance as a generalization of Lp distances: application to a seismic imaging inverse problem
Schneiders et al. Dense velocity reconstruction from tomographic PTV with material derivatives
Bonettini et al. On the convergence of a linesearch based proximal-gradient method for nonconvex optimization
CN102854533B (en) A kind of denoising method improving seismic data signal to noise ratio (S/N ratio) based on wave field separation principle
Chambolle et al. An upwind finite-difference method for total variation–based image smoothing
Alho et al. Dynamic AdS/QCD and the spectrum of walking gauge theories
Belhadj Terrain modeling: a constrained fractal model
KR100915574B1 (en) Remeshing apparatus and method to restore sharp features of surface mesh smoothed enough
CN109146797B (en) A kind of impulsive noise ancient book image inpainting method sparse based on Lp pseudonorm and overlapping group
CN108153984B (en) High-precision Galois gold artificial viscous shock wave capturing method based on flow field density step
CN102831588B (en) De-noising processing method for three-dimensional seismic images
CN105607122B (en) A kind of earthquake texture blending and Enhancement Method based on full variation geological data decomposition model
JP2022001861A (en) Full-wave form inversion method, device and electronic facility
CN107798156A (en) A kind of frequency domain 2.5 ties up viscoelastic wave method for numerical simulation and device
CN103325141A (en) 3D model construction method based on non-isocentre C-shaped arm 2D projected image
Zhang et al. A high-order well-balanced positivity-preserving moving mesh DG method for the shallow water equations with non-flat bottom topography
CN107390218A (en) Two-dimensional phase unwrapping method based on minimum Infinite Norm
CN105405100A (en) Sparse drive SAR image reconstruction regularization parameter automatic selection method
CN102737378B (en) Method and system for partitioning image by using geodesic active contour
CN103871035A (en) Image denoising method and device
WO2022067790A1 (en) Point cloud layering method, decoder, encoder, and storage medium

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant