CN113204869B - Phase unwrapping method based on rank information filtering - Google Patents

Phase unwrapping method based on rank information filtering Download PDF

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CN113204869B
CN113204869B CN202110465645.2A CN202110465645A CN113204869B CN 113204869 B CN113204869 B CN 113204869B CN 202110465645 A CN202110465645 A CN 202110465645A CN 113204869 B CN113204869 B CN 113204869B
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谢先明
刘媛媛
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Guilin University of Electronic Technology
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Abstract

The invention discloses a phase unwrapping method based on rank information filtering, which combines an AMPM-based local phase gradient estimation technology with a rank information filter, establishes a phase unwrapping program based on rank information filtering, and converts an interferogram phase unwrapping problem into a state estimation problem under a rank information filtering frame; an H-infinity operator is introduced to optimize the state variable information matrix, so that the state variable estimation precision is improved; and a fast path tracking strategy based on heap ordering is utilized to guide a phase unwrapping path, so that a phase unwrapping program based on rank information filtering is ensured to unwrap an interferogram along a path from a high-quality pixel to a low-quality pixel. Simulation data and measured data experimental results show that the effectiveness of the algorithm can obtain a more robust result from the noise winding interference diagram.

Description

Phase unwrapping method based on rank information filtering
Technical Field
The invention relates to the field of phase unwrapping, in particular to a phase unwrapping method based on rank information filtering.
Background
Phase unwrapping is one of the important steps in data processing such as interferometric synthetic aperture radar measurement (InSAR), optical interferometry, synthetic aperture sonar (InSAS), and magnetic resonance imaging. Because of the periodicity of the trigonometric function, the interference phase of the characterization target parameter obtained from interferometry is limited to the phase main value (-pi, pi) interval, commonly known as the winding phase, and the true interference phase of the reaction target parameter is recovered from the winding phase, namely the so-called phase unwrapping.
Traditional phase unwrapping methods, such as branch-cut method, least square method, quality guiding method, etc., have good unwrapping effect under the condition of less noise and less residual points, and have large unwrapping result error once the noise is large and the residual points are densely distributed. Subsequently, a class of unwrapping algorithms based on nonlinear filtering and state estimation is proposed successively, including extended kalman filter phase unwrapping algorithm (EKFPU), unscented kalman filter phase unwrapping algorithm (kfpu), volumetric kalman filter phase unwrapping algorithm (CKFPU), unscented information filter phase unwrapping algorithm (uipu), etc. These algorithms compensate to some extent for the deficiencies of conventional phase unwrapping algorithms, but efficient and accurate unwrapping of noise interferograms remains a very challenging problem.
Disclosure of Invention
The present invention addresses the shortcomings of the prior art described above by providing a method for phase unwrapping based on Rank Information Filtering (RIF) that can obtain more robust results from noise-wrapped interferograms.
The technical scheme for realizing the aim of the invention is as follows:
a phase unwrapping method based on rank information filtering comprises the following steps:
1) According to the existing nonlinear filtering phase unwrapping model, combining a local phase gradient estimation technology based on a correction matrix beam model (AMPM) with a rank information filter, establishing a phase unwrapping model based on rank information filtering, and converting an interferogram phase unwrapping problem into a state estimation problem under a rank information filtering frame;
2) According to the rank information filtering phase unwrapping model obtained in the step 1), a one-dimensional rank information filtering phase unwrapping algorithm is established;
3) And (3) according to the one-dimensional rank information filtering phase unwrapping algorithm obtained in the step (2), replacing the one-dimensional coordinates with the two-dimensional coordinates, and establishing the two-dimensional rank information filtering phase unwrapping algorithm.
Further, in step 1), using the relationship between the unwrapping phases of adjacent pixels of the interferogram, the interferogram phase unwrapping system equation can be expressed as follows:
Figure BDA0003043259350000021
Figure BDA0003043259350000022
wherein x is k Representing the unwrapping phase of the k pixels of the interferogram as a state variable to be evaluated; mu (mu) k-1 Representing the true phase gradient of the k-1 pixel of the interferogram, the estimated value can be obtained by using the local gradient estimation technology based on AMPM
Figure BDA0003043259350000023
w k-1 Representing phase gradient estimation errors; zeta type toy k Observation noise vector, ζ, for interference image k-element state variable 1,k And xi 2,k Measurement noise added to the imaginary and real parts of the complex interference signal, h x k ]Noiseless observation vectors which are the state variables of k pixels of the interference image; z k Is the observation vector of the state variable of the k pixel of the interference image.
Further, in step 2), the interference pattern k-1 pixel state estimation value and the estimation error variance are respectively set as
Figure BDA0003043259350000024
And->
Figure BDA0003043259350000025
The phase unwrapping based on the rank information filtering comprises the steps of:
2-1) generating rank information sampling points according to a rank sampling principle;
2-2) carrying out state prediction on the interference image k pixels to obtain one-step prediction values and one-step prediction error variances of the state variables of the interference image k pixels;
2-3) converting the state space of the interference image k pixels into the information space to obtain an information matrix Y of one-step prediction of the state variables of the interference image k pixels k Sum information vector
Figure BDA0003043259350000026
2-4) carrying out state update on the interference image k pixels to obtain the unwrapped phase of the interference image k pixels and the variance of the phase estimation error.
Further, in step 2-1), the method includes the steps of generating rank information sampling points according to the rank sampling principle:
Figure BDA0003043259350000027
Figure BDA0003043259350000028
in the method, in the process of the invention,
Figure BDA0003043259350000029
for the initial estimation of the state variable of the k pixels of the interference image, χ i,k Represents a rank information sample point generated according to the rank sampling principle, n represents the dimension of the state vector, n=1, u 1 And u 2 Represents a standard state offset, where u 1 ＝0.2,u 2 =0.5; i represents the number of sampling points; />
Figure BDA00030432593500000210
Representing an interference pattern k-1 pixel state estimation value; />
Figure BDA00030432593500000211
Representing an estimation error variance; />
Figure BDA00030432593500000212
Representing the value of the state variable of the k-1 picture element.
Further, in step 2-2), the one-step predicted value of the interferogram k pel state variable:
Figure BDA0003043259350000031
one-step prediction error variance of interferogram k pel state variables:
Figure BDA0003043259350000032
in the method, in the process of the invention,
Figure BDA0003043259350000033
as the weight coefficient, Q k Process error variance caused by the local gradient estimation technology based on AMPM; />
Figure BDA0003043259350000034
Representing one-step predicted values of state variables of k pixels of the interference image; />
Figure BDA0003043259350000035
Representing one-step prediction error variance of the state variable of the k pixels of the interference image; t represents a transpose operation.
Further, in step 2-3), the information matrix Y of one-step prediction of the interferogram k-pel state variables k Sum information vector
Figure BDA0003043259350000036
Figure BDA0003043259350000037
Figure BDA0003043259350000038
Information matrix Y using H-infinity operator k When the optimization is performed, the information matrix in the formula (5) becomes:
Figure BDA0003043259350000039
wherein, gamma s As the attenuation factor, 0.8.ltoreq.gamma.is usually taken s Less than or equal to 2, I is the same as
Figure BDA00030432593500000310
Identity matrix of the same dimension.
Further, the method comprises the steps of,in step 2-4), the cross covariance
Figure BDA00030432593500000311
Measurement prediction value +.>
Figure BDA00030432593500000312
The method comprises the following steps:
z i,k ＝h[χ i,k ] (8)
Figure BDA00030432593500000313
Figure BDA00030432593500000314
information status distribution i k And corresponding information matrix distribution I k The method comprises the following steps:
Figure BDA00030432593500000315
Figure BDA00030432593500000316
Figure BDA00030432593500000317
wherein eta is k Observing vector residual error for interference image k pixel state variable, R k Observing noise variance for the interferogram k pel state variable,
updated information matrix Y k And information vector y k The method comprises the following steps of:
Figure BDA0003043259350000041
Figure BDA0003043259350000042
the updated state estimation values and the state estimation error variances are respectively as follows:
Figure BDA0003043259350000043
Figure BDA0003043259350000044
wherein,,
Figure BDA0003043259350000045
representing the state estimation of the k pixels of the interference image, namely the unwrapping phase of the k pixels of the interference image; />
Figure BDA0003043259350000046
Representing the phase estimation error variance of the k pixels of the interference image; the one-dimensional RIF unwrapping algorithm can unwrap the interferogram wrapping phases in a row-by-row or column-by-column manner until all wrapping phases in the interferogram are unwrapped.
Further, in step 3), two-dimensional coordinates (m, n) are used to replace one-dimensional k, and if the interference image element (m, n) is the pixel to be unwound, the initial state predicted value of the pixel is obtained
Figure BDA0003043259350000047
And its prediction error variance->
Figure BDA0003043259350000048
The calculation can be as follows:
Figure BDA0003043259350000049
Figure BDA00030432593500000410
Figure BDA00030432593500000411
wherein the pixels of the interference pattern (a, s) are unwrapped pixels in 8 pixels adjacent to the pixel to be unwrapped,
Figure BDA00030432593500000412
and->
Figure BDA00030432593500000413
Representing state estimates of the pixels of the interferograms (a, s) and their estimated error variances; />
Figure BDA00030432593500000414
Phase gradient estimation values representing interference pixels (m, n) and (a, s) can be obtained by using an AMPM-based local gradient estimation technique; d, d (a,s) Weights representing the state estimates of the pixels of the interferograms (a, s);
rank information sampling point χ of interferogram (m, n) pixel i,(m,n) The calculation can be as follows:
Figure BDA00030432593500000415
one-step predicted value of state variable
Figure BDA00030432593500000416
Figure BDA0003043259350000051
State variable one-step prediction error variance
Figure BDA0003043259350000052
Figure BDA0003043259350000053
Wherein Q is [(m,n)|(a,s)] For the variance of process errors caused by the local gradient estimation technology based on AMPM, a fast path tracking strategy based on heap ordering is utilized to guide a phase unwrapping path, and a RIF phase unwrapping program is guided to complete recursion estimation of interferogram wrapping pixels along a path from high-quality pixels to low-quality pixels.
The method applies a high-efficiency and steady rank information filter to interferogram phase unwrapping, and combines an AMPM-based local phase gradient estimation technology with a fast path tracking strategy based on heap ordering, so as to provide a phase unwrapping algorithm based on rank information filtering. The method comprises the steps of establishing a phase unwrapping program based on rank information filtering, and acquiring phase gradient information of the phase unwrapping program based on rank information filtering by using a local phase gradient estimation technology based on AMPM; and a fast path tracking strategy based on heap ordering is utilized to guide a phase unwrapping path, so that a phase unwrapping program based on rank information filtering is ensured to unwrap an interferogram along a path from a high-quality pixel to a low-quality pixel. The simulation data and the actual measurement data experimental results show that the effectiveness of the algorithm can obtain a more robust result from the noise winding interference diagram.
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FIGS. 1 a-1 f are simulated interferometry, wherein FIGS. 1 a-1 c are true unwrapping phases of three interferometry, FIG. 1d is a noise wrapping phase diagram of the true interferometry phase of FIG. 1a, FIG. 1e is a noise wrapping phase diagram of the true interferometry phase of FIG. 1b, and FIG. 1f is a noise wrapping phase diagram of the true interferometry phase of FIG. 1 c;
FIGS. 2 a-2 c are the results of unwrapping FIG. 1d with the method of the present invention, where FIG. 2a shows unwrapped phases, FIG. 2b shows phase unwrapped errors, and FIG. 2c shows phase unwrapped error histograms;
FIGS. 3 a-3 c are the results of unwrapping FIG. 1e with the method of the present invention, where FIG. 3a shows unwrapped phases, FIG. 3b shows phase unwrapped errors, and FIG. 3c shows phase unwrapped error histograms;
FIGS. 4 a-4 c are the results of unwrapping FIG. 1f with the method of the present invention, where FIG. 4a shows unwrapped phases, FIG. 4b shows phase unwrapped errors, and FIG. 4c shows phase unwrapped error histograms;
fig. 5 a-5 c show the results of unwrapping measured data using the method of the present invention, wherein fig. 5a shows a partial Etna volcanic interference pattern, fig. 5b shows unwrapping phase, and fig. 5c shows unwrapping phase re-wrapping results.
Detailed Description
The following description of the technical solutions according to the embodiments of the present invention will be provided fully with reference to the accompanying drawings in which it is apparent that the described embodiments are only some embodiments, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Examples:
a phase unwrapping method based on rank information filtering comprises the following steps:
1) According to the existing nonlinear filtering phase unwrapping model, combining an AMPM-based local phase gradient estimation technology with a rank information filter, establishing a phase unwrapping model based on rank information filtering, and converting an interferogram phase unwrapping problem into a state estimation problem under a rank information filtering framework;
using the relationship between the unwrapped phases of adjacent pixels of the interferogram, the interferogram phase unwrapping system equation can be expressed as follows:
Figure BDA0003043259350000061
Figure BDA0003043259350000062
wherein x is k Representing the unwrapping phase of the k pixels of the interferogram as a state variable to be evaluated; mu (mu) k-1 Representing the true phase gradient of the k-1 pixel of the interferogram, the estimated value can be obtained by using the local gradient estimation technology based on AMPM
Figure BDA0003043259350000063
w k-1 Representing phase gradient estimation errors; zeta type toy k Observation noise vector, ζ, for interference image k-element state variable 1,k And xi 2,k Measurement noise added to the imaginary and real parts of the complex interference signal, h x k ]Noiseless observation vectors which are the state variables of k pixels of the interference image; z k An observation vector which is an interference image k pixel state variable;
2) According to the rank information filtering phase unwrapping model obtained in the step 1), a one-dimensional rank information filtering phase unwrapping algorithm is established;
let the state estimation value of the interference pattern k-1 pixel and the estimation error variance respectively be
Figure BDA0003043259350000064
And->
Figure BDA0003043259350000065
The phase unwrapping based on the rank information filtering comprises the steps of:
2-1) rank information sampling points generated according to the rank sampling principle:
Figure BDA0003043259350000066
Figure BDA0003043259350000067
in the method, in the process of the invention,
Figure BDA0003043259350000068
for the initial estimation of the state variable of the k pixels of the interference image, χ i,k Represents a rank information sample point generated according to the rank sampling principle, n represents the dimension of the state vector, n=1, u 1 And u 2 Represents a standard state offset, where u 1 ＝0.2,u 2 =0.5; i represents the number of sampling points; />
Figure BDA0003043259350000069
And->
Figure BDA00030432593500000610
Respectively representing the state estimation value and the estimation error variance of the interference image k-1 pixel;
Figure BDA00030432593500000611
representing a k-1 pel state variable value;
2-2) carrying out state prediction on the interference image k pixels to obtain one-step prediction values and one-step prediction error variances of the state variables of the interference image k pixels;
one-step predicted value of state variable of k pixels of an interferogram:
Figure BDA0003043259350000071
one-step prediction error variance of interferogram k pel state variables:
Figure BDA0003043259350000072
in the method, in the process of the invention,
Figure BDA0003043259350000073
as the weight coefficient, Q k Process error variance caused by the local gradient estimation technology based on AMPM; />
Figure BDA0003043259350000074
Representing one-step predicted values of state variables of k pixels of the interference image; />
Figure BDA0003043259350000075
Representing one-step prediction error variance of the state variable of the k pixels of the interference image; t represents a transpose operation;
2-3) converting the state space of the interference image k pixels into the information space to obtain an information matrix Y of one-step prediction of the state variables of the interference image k pixels k Sum information vector
Figure BDA0003043259350000076
Information matrix Y for one-step prediction of interference image k pixel state variable k And information vector->
Figure BDA0003043259350000077
Figure BDA0003043259350000078
Figure BDA0003043259350000079
Information matrix Y using H-infinity operator k When the optimization is performed, the information matrix in the formula (5) becomes:
Figure BDA00030432593500000710
wherein, gamma s As the attenuation factor, 0.8.ltoreq.gamma.is usually taken s Less than or equal to 2, I is the same as
Figure BDA00030432593500000711
A co-dimensional identity matrix;
2-4) carrying out state update on the interference image k pixels to obtain unwrapped phases of the interference image k pixels and a variance of phase estimation errors; cross covariance
Figure BDA00030432593500000712
Measurement prediction value +.>
Figure BDA00030432593500000713
The method comprises the following steps:
z i,k ＝h[χ i,k ] (8)
Figure BDA00030432593500000714
Figure BDA0003043259350000081
information status distribution i k And corresponding information matrix distribution I k The method comprises the following steps:
Figure BDA0003043259350000082
Figure BDA0003043259350000083
Figure BDA0003043259350000084
wherein eta is k Observing vector residual error for interference image k pixel state variable, R k Observing noise variance for the interferogram k pel state variable,
updated information matrix Y k And information vector y k The method comprises the following steps of:
Figure BDA0003043259350000085
Figure BDA0003043259350000086
the updated state estimation values and the state estimation error variances are respectively as follows:
Figure BDA0003043259350000087
Figure BDA0003043259350000088
wherein,,
Figure BDA0003043259350000089
representing the state estimation of the k pixels of the interference image, namely the unwrapping phase of the k pixels of the interference image; />
Figure BDA00030432593500000810
Representing the phase estimation error variance of the k pixels of the interference image; the one-dimensional RIF unwrapping algorithm can unwrap the interferogram wrapping phases in a row-by-row or column-by-column manner until all wrapping phases in the interferogram are unwrapped;
3) And (3) according to the one-dimensional rank information filtering phase unwrapping algorithm obtained in the step (2), replacing the one-dimensional coordinates with the two-dimensional coordinates, and establishing the two-dimensional rank information filtering phase unwrapping algorithm.
Using two-dimensional coordinates (m, n) to replace one-dimensional k, and setting an interference image element (m, n) as an element to be unwound, and predicting the initial state of the element
Figure BDA00030432593500000811
And its prediction error variance->
Figure BDA00030432593500000812
The calculation can be as follows:
Figure BDA00030432593500000813
Figure BDA00030432593500000814
Figure BDA00030432593500000815
wherein the pixels of the interference pattern (a, s) are unwrapped pixels in 8 pixels adjacent to the pixel to be unwrapped,
Figure BDA00030432593500000816
and->
Figure BDA00030432593500000817
Representing state estimates of the pixels of the interferograms (a, s) and their estimated error variances; />
Figure BDA0003043259350000091
Representing phase gradient estimates between interference pixels (m, n) and (a, s) can be obtained using AMPM-based local gradient estimation techniques [13 ]]；d (a,s) Weights representing the state estimates of the pixels of the interferograms (a, s);
rank information sampling point χ of interferogram (m, n) pixel i,(m,n) The calculation can be as follows:
Figure BDA0003043259350000092
one-step predicted value of state variable
Figure BDA0003043259350000093
Figure BDA0003043259350000094
State variable one-step prediction error variance
Figure BDA0003043259350000095
Figure BDA0003043259350000096
Wherein Q is [(m,n)|(a,s)] For the variance of process errors caused by the local gradient estimation technology based on AMPM, a fast path tracking strategy based on heap ordering is utilized to guide a phase unwrapping path, and a RIF phase unwrapping program is guided to complete recursion estimation of interferogram wrapping pixels along a path from high-quality pixels to low-quality pixels.
In order to verify the performance of each method, different algorithms comprise an iterative least squares method (ILS), a quality guide method (QGPU) and the method, the simulation and the actual measurement interferograms are unwrapped under the same MATLAB software environment (Intel i5-8265U@1.60G CPU+8GB RAM), and the unwrapped results of each algorithm are compared and analyzed.
Fig. 1 shows three different simulated interferograms of 256×256 pixels, wherein fig. 1 a-1 c show the real interference phases, fig. 1 d-1 f show the noisy winding phase diagrams, respectively, with signal to noise ratios of 7.44dB, 2.18dB, 0.73dB, and the three interferograms are unwrapped using a Rank Information Filter Phase Unwrapping (RIFPU) algorithm.
FIGS. 2 a-2 c are the results of unwrapping FIG. 1d with the method of the present invention, where FIG. 2a shows unwrapped phases, FIG. 2b shows phase unwrapped errors, and FIG. 2c shows phase unwrapped error histograms;
FIGS. 3 a-3 c are the results of unwrapping FIG. 1e with the method of the present invention, where FIG. 3a shows unwrapped phases, FIG. 3b shows phase unwrapped errors, and FIG. 3c shows phase unwrapped error histograms;
FIGS. 4 a-4 c are the results of unwrapping FIG. 1f with the method of the present invention, where FIG. 4a shows unwrapped phases, FIG. 4b shows phase unwrapped errors, and FIG. 4c shows phase unwrapped error histograms;
fig. 5 a-5 c show the results of unwrapping measured data using the method of the present invention, wherein fig. 5a shows a partial Etna volcanic interference pattern, fig. 5b shows unwrapping phase, and fig. 5c shows unwrapping phase re-wrapping results.
The result of unwrapping the noise-wrapped phase diagrams shown in fig. 1 d-1 f by the method is shown in fig. 2 a-4 c, and it can be seen that the unwrapping phase obtained by the method has better consistency with the real interference diagram, and the phase unwrapping error is smaller. The first list lists the root mean square error of Iterative Least Squares (ILS), quality guided methods (QGPU) and the method unwrapping different signal-to-noise interference patterns, it can be seen that the root mean square error of the method is much smaller than the QGPU and ILS methods.
Table one phase unwrapping error for each algorithm
Figure BDA0003043259350000101
In the experimental data, fig. 5a is a partial Etna volcanic interference diagram, the unwrapping phase of the method is shown in fig. 5b, and the unwrapping phase is shown in fig. 5 c. The unwrapping phase obtained by the method is continuous and consistent, and the rewinding phase diagram stripes are consistent with the original interference diagram stripes, which shows that the method obtains more effective unwrapping results.
The preferred embodiments of the invention disclosed above are merely to aid in the description of the invention and are not intended to limit the invention to the specific embodiments described. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best understand and utilize the invention.

Claims (5)

1. The phase unwrapping method based on rank information filtering is characterized by comprising the following steps:
1) According to the existing nonlinear filtering phase unwrapping model, combining an AMPM-based local phase gradient estimation technology with a rank information filter, establishing a phase unwrapping model based on rank information filtering, and converting an interferogram phase unwrapping problem into a state estimation problem under a rank information filtering framework;
2) According to the rank information filtering phase unwrapping model obtained in the step 1), a one-dimensional rank information filtering phase unwrapping algorithm is established;
3) According to the one-dimensional rank information filtering phase unwrapping algorithm obtained in the step 2), replacing the one-dimensional coordinates with the two-dimensional coordinates, and establishing a two-dimensional rank information filtering phase unwrapping algorithm;
in step 1), using the relationship between the unwrapping phases of adjacent pixels of the interferogram, the interferogram phase unwrapping system equation can be expressed as follows:
Figure FDA0004241825440000011
Figure FDA0004241825440000012
wherein x is k Representing the unwrapping phase of the k pixels of the interferogram as a state variable to be evaluated; mu (mu) k-1 Representing the true phase gradient of the k-1 pixel of the interferogram, the estimated value can be obtained by using the local gradient estimation technology based on AMPM
Figure FDA0004241825440000013
w k-1 Representing phase gradient estimation errors; zeta type toy k Observation noise vector, ζ, for interference image k-element state variable 1,k And xi 2,k Measurement noise added to the imaginary and real parts of the complex interference signal, h x k ]Noiseless observation vectors which are the state variables of k pixels of the interference image; z k An observation vector which is an interference image k pixel state variable;
in the step 2), the state estimation value and the estimation error variance of the interference pattern k-1 pixel are respectively set as
Figure FDA0004241825440000014
And->
Figure FDA0004241825440000015
The phase unwrapping based on the rank information filtering comprises the steps of:
2-1) generating rank information sampling points according to a rank sampling principle;
2-2) carrying out state prediction on the interference image k pixels to obtain one-step prediction values and one-step prediction error variances of the state variables of the interference image k pixels;
2-3) converting the state space of the interference image k pixels into the information space to obtain an information matrix Y of one-step prediction of the state variables of the interference image k pixels k Sum information vector
Figure FDA0004241825440000016
2-4) carrying out state update on the interference image k pixels to obtain unwrapped phases of the interference image k pixels and a variance of phase estimation errors;
in step 3), two-dimensional coordinates (m, n) are used for replacing one-dimensional k, and an interference image element is arranged(m, n) is the pixel to be disentangled, then the pixel initial state predicted value
Figure FDA0004241825440000017
And its prediction error variance->
Figure FDA0004241825440000018
The calculation can be as follows:
Figure FDA0004241825440000021
Figure FDA0004241825440000022
Figure FDA0004241825440000023
wherein the pixels of the interference pattern (a, s) are unwrapped pixels in 8 pixels adjacent to the pixel to be unwrapped,
Figure FDA0004241825440000024
and->
Figure FDA0004241825440000025
Representing state estimates of the pixels of the interferograms (a, s) and their estimated error variances; />
Figure FDA0004241825440000026
Phase gradient estimation values representing interference pixels (m, n) and (a, s) can be obtained by using an AMPM-based local gradient estimation technique; d, d (a,s) Weights representing the state estimates of the pixels of the interferograms (a, s);
rank information sampling point χ of interferogram (m, n) pixel i,(m,n) The calculation can be as follows:
Figure FDA0004241825440000027
one-step predicted value of state variable
Figure FDA0004241825440000028
Figure FDA0004241825440000029
State variable one-step prediction error variance
Figure FDA00042418254400000210
Figure FDA00042418254400000211
Wherein w is a weight coefficient; n represents the dimension of the state vector;
Figure FDA00042418254400000212
representing an initial state prediction value of the interference image element (m, n); u (u) 1 And u 2 Representing standard state deviation; />
Figure FDA00042418254400000213
Representing the interference image element (m, n) prediction error variance; q (Q) [(m,n)|(a,s)] For the variance of process errors caused by the local gradient estimation technology based on AMPM, a fast path tracking strategy based on heap ordering is utilized to guide a phase unwrapping path, and a RIF phase unwrapping program is guided to complete recursion estimation of interferogram wrapping pixels along a path from high-quality pixels to low-quality pixels.
2. The phase unwrapping method based on rank information filtering according to claim 1, wherein in step 2-1), the phase unwrapping method includes generating rank information sampling points according to a rank sampling principle:
Figure FDA0004241825440000031
Figure FDA0004241825440000032
in the method, in the process of the invention,
Figure FDA0004241825440000033
for the initial estimation of the state variable of the k pixels of the interference image, χ i,k Represents a rank information sample point generated according to the rank sampling principle, n represents the dimension of the state vector, n=1, u 1 And u 2 Represents a standard state offset, where u 1 ＝0.2,u 2 =0.5; i represents the number of sampling points; />
Figure FDA0004241825440000034
And->
Figure FDA0004241825440000035
Respectively representing the state estimation value and the estimation error variance of the interference image k-1 pixel; />
Figure FDA0004241825440000036
Representing the value of the state variable of the k-1 picture element.
3. The method for phase unwrapping based on rank information filtering according to claim 1, wherein in step 2-2), the interferogram k-pel state variable is predicted in one step:
Figure FDA0004241825440000037
one-step prediction error variance of interferogram k pel state variables:
Figure FDA0004241825440000038
in the method, in the process of the invention,
Figure FDA0004241825440000039
as the weight coefficient, Q k Process error variance caused by the local gradient estimation technology based on AMPM; />
Figure FDA00042418254400000310
Representing one-step predicted values of state variables of k pixels of the interference image; />
Figure FDA00042418254400000311
Representing one-step prediction error variance of the state variable of the k pixels of the interference image; t represents a transpose operation; x-shaped articles i,k Representing rank information sampling points generated according to a rank sampling principle; u (u) 1 And u 2 Representing standard state deviation; n represents the dimension of the state vector.
4. The method for phase unwrapping based on rank information filtering according to claim 1, wherein in step 2-3), the interferogram k-pel state variable is predicted in one step as an information matrix Y k Sum information vector
Figure FDA00042418254400000312
Figure FDA00042418254400000313
Figure FDA00042418254400000314
Information matrix Y using H-infinity operator k When the optimization is performed, the information matrix in the formula (5) becomes:
Figure FDA00042418254400000315
wherein, gamma s Taking gamma as attenuation factor of 0.8 ∈γ s Less than or equal to 2, I is the same as
Figure FDA00042418254400000316
A co-dimensional identity matrix; />
Figure FDA00042418254400000317
Representing one-step predicted values of state variables of k pixels of the interference image; />
Figure FDA0004241825440000041
Representing the one-step prediction error variance of the interferogram k-pel state variable.
5. The method for phase unwrapping based on rank information filtering of claim 1, wherein in step 2-4), the cross covariance
Figure FDA0004241825440000042
Measurement prediction value +.>
Figure FDA0004241825440000043
The method comprises the following steps:
z i,k ＝h[χ i,k ] (8)
Figure FDA0004241825440000044
Figure FDA0004241825440000045
information status distribution i k And corresponding information matrix distribution I k The method comprises the following steps:
Figure FDA0004241825440000046
Figure FDA0004241825440000047
Figure FDA0004241825440000048
wherein eta is k Observing vector residual error for interference image k pixel state variable, R k Observing noise variance for the interferogram k pel state variable,
updated information matrix Y k And information vector y k The method comprises the following steps of:
Figure FDA0004241825440000049
Figure FDA00042418254400000410
the updated state estimation values and the state estimation error variances are respectively as follows:
Figure FDA00042418254400000411
Figure FDA00042418254400000412
wherein,,
Figure FDA00042418254400000413
representing an interferometric k-pel state estimate, i.e., an interferometric k-pel solutionWinding phase; />
Figure FDA00042418254400000414
Representing the phase estimation error variance of the k pixels of the interference image; w is a weight coefficient; z k An observation vector which is an interference image k pixel state variable; />
Figure FDA00042418254400000415
Representing one-step predicted values of state variables of k pixels of the interference image; />
Figure FDA00042418254400000416
Representing the information matrix Y with H-infinity operators k Performing optimized information matrix; n represents the dimension of the state vector; the one-dimensional RIF unwrapping algorithm unwraps the interferogram wrapping phases in a row-by-row or column-by-column manner until all wrapping phases in the interferogram are unwrapped.
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