CN115047454A - Based on L 1 Norm regularized SAR phase unwrapping method - Google Patents

Based on L 1 Norm regularized SAR phase unwrapping method Download PDF

Info

Publication number
CN115047454A
CN115047454A CN202210338788.1A CN202210338788A CN115047454A CN 115047454 A CN115047454 A CN 115047454A CN 202210338788 A CN202210338788 A CN 202210338788A CN 115047454 A CN115047454 A CN 115047454A
Authority
CN
China
Prior art keywords
sar
phase
norm
interference
unwrapping
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.)
Pending
Application number
CN202210338788.1A
Other languages
Chinese (zh)
Inventor
毕辉
魏昭琦
张晶晶
李勇
宋宇凡
王丽平
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.)
Shenzhen Research Institute Of Nanjing University Of Aeronautics And Astronautics
Nanjing University of Aeronautics and Astronautics
Original Assignee
Shenzhen Research Institute Of Nanjing University Of Aeronautics And Astronautics
Nanjing University of Aeronautics and Astronautics
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 Shenzhen Research Institute Of Nanjing University Of Aeronautics And Astronautics, Nanjing University of Aeronautics and Astronautics filed Critical Shenzhen Research Institute Of Nanjing University Of Aeronautics And Astronautics
Priority to CN202210338788.1A priority Critical patent/CN115047454A/en
Publication of CN115047454A publication Critical patent/CN115047454A/en
Pending legal-status Critical Current

Links

Images

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
    • G01S13/9021—SAR image post-processing techniques
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations

Landscapes

  • Engineering & Computer Science (AREA)
  • Remote Sensing (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Theoretical Computer Science (AREA)
  • Mathematical Physics (AREA)
  • Data Mining & Analysis (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Computational Mathematics (AREA)
  • Pure & Applied Mathematics (AREA)
  • Databases & Information Systems (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Algebra (AREA)
  • Radar Systems Or Details Thereof (AREA)
  • Image Processing (AREA)

Abstract

The invention discloses a method based on L 1 A norm regularized SAR phase unwrapping method includes the steps that firstly, SAR main images and SAR sub images of the same target scene are obtained through an SAR, and phases of the SAR main images and the SAR sub images are obtained respectively; secondly, carrying out interference processing on the phases of the SAR main image and the SAR auxiliary image to obtain interference phases; then, based on the obtained interference phase, L-based is established 1 A norm regularized SAR phase unwrapped model; finally, solving L by adopting a basis pursuit algorithm 1 And (5) normalizing the norm to obtain the unwrapped phase. The method can perform phase unwrapping based on the interference image to obtain real phase information, and the unwrapped phase is closer to a real value; the obtained unwrapped phase has higher quality.

Description

Based on L 1 Norm regularized SAR phase unwrapping method
Technical Field
The invention belongs to the technical field of interferometric synthetic aperture radar imaging and sparse signal processing, and particularly relates to a method based on L 1 Provided is a norm regularized SAR phase unwrapping method.
Background
An interferometric Synthetic Aperture Radar (SAR) imaging technology is popular in research of scholars at home and abroad in recent years, breaks through the two-dimensional limitation of the traditional SAR imaging, and obtains height information of a target area by utilizing a phase difference of two SAR images, so that the SAR imaging technology is widely applied to the fields of terrain exploration, terrain mapping and the like. The conventional InSAR technology comprises image registration, interference phase generation, phase flattening, phase unwrapping and generation of a Digital Elevation Model (DEM). The phase unwrapping is an important step, and can recover interference phases wrapped in an interval of [ -pi, pi ] under the periodic influence of a trigonometric function, so as to obtain real phase information. The existing phase unwrapping method has the disadvantages of low calculation speed, more singular points after phase unwrapping and poor quality of the generated DEM, thereby greatly restricting the application of the interference SAR technology.
Disclosure of Invention
The purpose of the invention is as follows: in order to solve the problems of the prior art, the invention provides a method based on L 1 The SAR phase unwrapping method with normalized norm has higher quality of unwrapping phase.
The technical scheme is as follows: the invention relates to a method based on L 1 A norm regularized SAR phase unwrapping method includes the following steps:
(1) acquiring SAR main and auxiliary images of the same target scene through an SAR, and respectively acquiring phases of the SAR main and auxiliary images;
(2) carrying out interference processing on the phases of the SAR main image and the SAR auxiliary image to obtain an interference phase;
(3) establishing a phase based on L based on the interference phase obtained in the step (2) 1 A norm regularized SAR phase unwrapping model;
(4) solving for L using basis pursuit algorithm 1 And (5) carrying out norm regularization to obtain the phase after unwrapping.
Further, the step (1) is realized as follows:
the SAR main and auxiliary images of the target scene acquired by the SAR platform are respectively s 1 And s 2 According to the InSAR imaging geometric relationship, the main image and the auxiliary image are respectively expressed as follows:
Figure BDA0003577831920000021
Figure BDA0003577831920000022
wherein, | a 1 I and A 2 L represents the amplitude of the two complex images, λ, respectively c Denotes the wavelength, r 1 And r 2 Indicates the slant distance phi obj1 And phi obj2 Representing the scatter phase of the two images separately, usually by | a 1 |＝|a 2 |，φ obj1 ＝φ obj2 。
Further, the step (2) is realized as follows:
according to an interference SAR theory, conjugate multiplication is carried out on main and auxiliary images, and the obtained result is an interference phase which is expressed as:
Figure BDA0003577831920000023
wherein arg (. circle.) represents the angle.
Further, the step (3) is realized as follows:
in the actual unwrapping process, since the interfering phase gradient and the unwrapping phase gradient are not always equal, there will be an ambiguity number k 1 (i, j) and k 2 (i, j), the blur number is expressed as:
Figure BDA0003577831920000024
Figure BDA0003577831920000025
construction based on L 1 Norm regularized SAR phase unwrapping model with interference phase image size of M × N for k 1 (i, j) and k 2 The solution of (i, j) can be translated into solving the following linear programming problem:
Figure BDA0003577831920000026
the constraint conditions are as follows:
Figure BDA0003577831920000031
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003577831920000032
Figure BDA0003577831920000033
wherein, c 1 (i, j) and represent c 2 (i, j) weight size, x 1 (i, j) and x 2 (i, j) are all positive integers; if c (i, j), x (i, j), Ψ (i, j) are expressed as vector forms c, x, Ψ, respectively, then equation (13) and equation (14) are expressed as:
min c T x and Ax ═ b, x ≧ 0 (17)
Wherein the content of the first and second substances,
Figure BDA0003577831920000034
in the formula (18), the first and second groups,
Figure BDA0003577831920000035
expressed as:
Figure BDA0003577831920000036
wherein the content of the first and second substances,
Figure BDA0003577831920000037
Figure BDA0003577831920000038
Figure BDA0003577831920000039
Figure BDA0003577831920000041
Figure BDA0003577831920000042
let x ═ Dy, where D is represented by:
Figure BDA0003577831920000043
thus, equation (17) can be written as:
min||y|| 1 and Cy ═ b, y ≥ 0 (26)
Wherein, C ═ AD; by solving for L 1 The regularization problem to obtain a solution of equation (26), i.e.:
Figure BDA0003577831920000044
wherein the content of the first and second substances,
Figure BDA0003577831920000045
for the reconstructed ambiguity, argmin {. cndot } represents taking the minimum value, μ represents the regularization parameter.
Further, the step (4) is realized as follows:
(41) setting initial value y of fuzzy number (0) 0; regularization parameter initial value μ (0) 0; the maximum iteration number k is 100;
(42) and (3) calculating a residual error estimated value in the k iterative calculation:
P＝E-C T (C -1 (CC T )) (28)
q＝C T (b -1 (CC T )) (29)
x (k) ＝P(y (k) -μ (k) )+q (30)
wherein E represents an identity matrix, y (k) Representing the fuzzy number in the k iteration calculation; mu.s (k) Representing a regularization parameter in the k-th iterative computation;
(43) updating the fuzzy number in the (k + 1) th iterative computation:
y (k+1) ＝max(0，x (k) +μ (k) -1)-max(0，-x (k) -μ (k) -1) (31)
y (k+1) representing the fuzzy number in the k +1 th iteration calculation after updating;
(44) updating the regularization parameter μ at the k +1 th iteration (k+1) ：
μ (k+1) ＝μ (k) +x (k) *-y (k-1) (32)
μ (k+1) Representing the regularization parameter during the updated (k + 1) th iterative computation;
(45) calculating an iteration error Resi:
Resi＝||y (k) -y (k+1) || 2 (33)
(46) calculating a threshold value epsilon:
Figure BDA0003577831920000051
(47) if Resi ∈ and the iteration number k is smaller than or equal to the preset maximum iteration number, the iteration number k +1 is carried out, and a step (42) is carried out; otherwise, stopping calculation;
(48) output y (k) ，
Figure BDA0003577831920000052
Has the advantages that: compared with the prior art, the invention has the beneficial effects that: the method can perform phase unwrapping based on the interference image to obtain real phase information, and the unwrapped phase is closer to a real value; the unwrapping phase obtained by the method has higher quality.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of interferometric SAR phase unwrapping;
FIG. 3 is a graph of simulation results of phase unwrapping; wherein, (a1) is a simulation result diagram for phase unwrapping by adopting a basis tracking algorithm; (a2) subtracting the true value from the BP algorithm result to obtain a difference; (b1) a simulation result diagram of phase unwrapping is obtained by adopting a linear programming method; (b2) the difference obtained by subtracting the real value from the LP method result; (c1) the simulation result diagram is a simulation result diagram for phase unwrapping by adopting an integer linear programming method; (c2) the difference is the result of the ILP method subtracted from the true value.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The invention provides a method based on L 1 A norm regularized SAR phase unwrapping method, as shown in fig. 1 and 2, specifically includes the following steps:
step S1: and acquiring SAR main images and SAR auxiliary images of the same target scene through the SAR, and respectively acquiring the phases of the SAR main images and the SAR auxiliary images.
The SAR main and auxiliary images of the target scene acquired by the SAR platform are respectively s 1 And s 2 According to the imaging geometry of InSAR (interferometric SAR, InSAR for short), the primary and secondary images can be respectively expressed as
Figure BDA0003577831920000061
Figure BDA0003577831920000062
Wherein, | a 1 I and A 2 L represents the amplitude of the two complex images, λ, respectively c Denotes the wavelength, r 1 And r 2 Indicates the slant distance phi obj1 And phi obj2 Representing the scatter phase of the two images separately, usually by | a 1 |＝|a 2 |，φ obj1 ＝φ obj2 。
Step S2: according to the interference SAR theory, conjugate multiplication is carried out on the main image and the auxiliary image, and the obtained result is an interference phase which can be expressed as:
Figure BDA0003577831920000063
wherein arg (. circle.) represents the angle.
Due to the periodicity of the trigonometric function, the result φ E [ - π, π ] obtained by equation (3) cannot reflect the true phase information, and therefore we need to perform unwrapping operation on the interference phase.
Let the interference phase image size be M × N, each pixel point be represented as (i, j), phi (i, j) represents the wrapping phase of each pixel point, and psi (i, j) represents the unwrapping phase, i.e., the true phase, of each pixel point. The relationship between winding phase and true phase can be expressed as:
Figure BDA0003577831920000064
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003577831920000065
represents the winding operator, i.e. the operator that restores the winding phase to the true phase. Order toThe derivatives of Ψ (i, j) in the range and azimuth directions are Ψ 1 (i, j) and Ψ 2 (i, j), then can be expressed as:
Ψ 1 (i，j)＝Ψ(i+1，j)-Ψ(i，j) (5)
Ψ 2 (i，j)＝Ψ(i，j+1)-Ψ(i，j) (6)
similarly, the derivatives φ (i, j) in the distance and azimuth directions 1 (i, j) and phi 2 (i, j) may be represented as:
φ 1 (i，j)＝φ 1 (i+1，j)-φ(i，j) (7)
φ 2 (i，j)＝φ(i，j+1)-φ(i，j) (8)
when phi is 1 (i，j)∈[-π，π]And phi is 2 (i，j)∈[-π，π]Then, one can obtain:
Ψ 1 (i，j)＝φ 1 (i，j) (9)
Ψ 2 (i，j)＝φ 2 (i, j) (10) in most cases, the equations (9) and (10) hold, but in the actual unwinding process, there is a fuzzy number k 1 (i, j) and k 2 (i, j) so that equation (9) and equation (10) do not hold, the fuzzy number can be expressed as:
Figure BDA0003577831920000071
Figure BDA0003577831920000072
step S3: establishment based on L 1 Norm regularized SAR phase unwrapping model.
To k is paired with 1 (i, j) and k 2 The solution of (i, j) can be translated into solving the following linear programming problem
Figure BDA0003577831920000073
The constraint conditions are as follows:
Figure BDA0003577831920000074
wherein:
Figure BDA0003577831920000075
Figure BDA0003577831920000076
c 1 (i, j) and c 2 (i, j) represents a weight size, x 1 (i, j) and x 2 (i, j) are all positive integers.
By representing c (i, j), x (i, j), Ψ (i, j) as vector forms c, x, Ψ, respectively, then equation (13) and equation (14) can be expressed as:
min c T x and Ax ═ b, x ≧ 0 (17)
Wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003577831920000081
in the formula (18), the first and second groups,
Figure BDA0003577831920000082
can be expressed as:
Figure BDA0003577831920000083
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003577831920000084
Figure BDA0003577831920000085
Figure BDA0003577831920000086
Figure BDA0003577831920000087
Figure BDA0003577831920000088
let x be Dy, where D is represented by:
Figure BDA0003577831920000091
thus, equation (17) can be written as
min||y|| 1 And Cy ≧ b, y ≧ 0 (26)
Wherein, C ═ AD. Can be realized by solving L 1 Regularization problem to obtain a solution of equation (26):
Figure BDA0003577831920000092
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA0003577831920000093
for the reconstructed ambiguity, argmin {. cndot } represents taking the minimum value, μ represents the regularization parameter.
Step S4: solving for L using basis pursuit algorithm 1 And (5) carrying out norm regularization to obtain the phase after unwrapping.
1) Setting initial value y of fuzzy number (0) 0; regularization parameter initial value mu (0) 0; the maximum number of iterations k is 100.
2) And (3) calculating a residual error estimated value in the k iterative calculation:
P＝E-C T (C -1 (CC T )) (28)
q＝C T (b -1 (CC T )) (29)
x (k) ＝P(y (k) -μ (k) )+q (30)
wherein E represents an identity matrix, y (k) Representing the fuzzy number in the k iteration calculation; mu.s (k) The regularization parameter at the time of the kth iterative computation is represented.
3) And updating the fuzzy number in the k +1 th iteration calculation:
y (k+1) ＝max(0，x (k) +μ(k)-1)-max(0，-x (k) -μ (k) -1) (31)
wherein, y (k+1) And (4) representing the fuzzy number of the updated (k + 1) th iteration calculation.
4) Updating the regularization parameter μ at the k +1 th iteration (k+1) ：
μ (k+1 )＝μ (k) +x (k) -y (k+1 ) (32)
Wherein, mu (k+1) And (3) representing the regularization parameter in the k +1 th iteration calculation after updating.
5) Calculating an iteration error Resi:
Resi＝||y (k) -y (k+1) || 2 (33)
6) calculating a threshold value epsilon:
Figure BDA0003577831920000101
7) if Resi ∈ and the iteration number k is smaller than or equal to the preset maximum iteration number, the iteration number k +1 is carried out, and the step 2) is carried out; otherwise, stopping the calculation.
8) Output y (k) ，
Figure BDA0003577831920000102
The invention is provided by experimentsFor verification by the method, FIG. 3(a1) is based on L 1 The norm is normalized to obtain an unwrapping phase; (a2) is based on L 1 The norm regularization processing is carried out to obtain a result of the difference between the unwrapping phase and the true value; fig. 3 (b1) shows the unwrapped phase obtained by the LP algorithm; (b2) performing a difference result between the unwrapping phase and a true value obtained based on the LP algorithm processing; fig. 3 (c1) shows the unwrapped phase processed based on the ILP algorithm; (c2) the difference between the unwrapped phase and the true value obtained based on the ILP algorithm processing is obtained. Comparing the SAR phase quality obtained by the three methods, it is not difficult to see that the method based on L provided by the invention 1 The norm regularized phase unwrapping method can better perform phase unwrapping, obtain unwrapped phases with better quality, and obtain results closer to true values.
It should be noted that the various features described in the above embodiments may be combined in any suitable manner without departing from the scope of the invention. The invention is not described in detail in order to avoid unnecessary repetition.

Claims (5)

1. Based on L 1 The norm regularized SAR phase unwrapping method is characterized by comprising the following steps of:
(1) acquiring SAR main and auxiliary images of the same target scene through an SAR, and respectively acquiring phases of the SAR main and auxiliary images;
(2) carrying out interference processing on the phases of the SAR main image and the SAR auxiliary image to obtain interference phases;
(3) establishing a phase based on L based on the interference phase obtained in the step (2) 1 A norm regularized SAR phase unwrapping model;
(4) solving for L using basis pursuit algorithm 1 And (5) normalizing the norm to obtain the unwrapped phase.
2. The L-based of claim 1 1 The norm regularized SAR phase unwrapping method is characterized in that the step (1) is realized by the following process:
respectively acquiring SAR main and auxiliary images of target scene by SAR platformIs s is 1 And s 2 According to the InSAR imaging geometric relationship, the main image and the auxiliary image are respectively expressed as follows:
Figure FDA0003577831910000011
Figure FDA0003577831910000012
wherein, | a 1 | and | a 2 L represents the amplitude of the two complex images, λ, respectively c Denotes the wavelength, r 1 And r 2 Indicates the slant distance phi obj1 And phi obj2 Representing the scatter phase of the two images separately, usually by a 1 |＝|a 2 |，φ obj1 ＝φ pbj2 。
3. The L-based of claim 1 1 The SAR phase unwrapping method with norm regularization is characterized in that the step (2) is realized by the following steps:
according to an interference SAR theory, conjugate multiplication is carried out on main and auxiliary images, and the obtained result is an interference phase which is expressed as:
φ＝arg(s 1 s 2 * ) (3)
wherein arg (. circle.) represents the angle.
4. The L-based of claim 1 1 The SAR phase unwrapping method with norm regularization is characterized in that the step (3) is realized as follows:
in the actual unwrapping process, since the interfering phase gradient and the unwrapping phase gradient are not always equal, there will be an ambiguity number k 1 (i, j) and k 2 (i, j), the blur number is expressed as:
Figure FDA0003577831910000021
Figure FDA0003577831910000022
construction based on L 1 Norm regularized SAR phase unwrapping model with interference phase image size of M × N for k 1 (i, j) and k 2 The solution of (i, j) can be translated into solving the following linear programming problem:
Figure FDA0003577831910000023
the constraint conditions are as follows:
Figure FDA0003577831910000024
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003577831910000025
Figure FDA0003577831910000026
wherein, c 1 (i, j) and represent c 2 (i, j) weight size, x 1 (i, j) and x 2 (i, j) are all positive integers; if c (i, j), x (i, j), Ψ (i, j) are expressed as vector forms c, x, Ψ, respectively, then equation (13) and equation (14) are expressed as:
min c T x and Ax ═ b, x ≧ 0 (17)
Wherein the content of the first and second substances,
Figure FDA0003577831910000027
in the case of the formula (18),
Figure FDA0003577831910000031
expressed as:
Figure FDA0003577831910000032
wherein the content of the first and second substances,
Figure FDA0003577831910000033
Figure FDA0003577831910000034
Figure FDA0003577831910000035
Figure FDA0003577831910000036
Figure FDA0003577831910000037
let x be Dy, where D is represented by:
Figure FDA0003577831910000038
thus, equation (17) can be written as:
min||y|| 1 and Cy ═ b, y ≥ 0 (26)
Wherein, C ═ AD; by solving for L 1 The regularization problem to obtain a solution of equation (26), i.e.:
Figure FDA0003577831910000039
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA00035778319100000310
for the reconstructed ambiguity, argmin {. cndot } represents taking the minimum value, μ represents the regularization parameter.
5. The range-based L of claim 1 1 The SAR phase unwrapping method with number regularization is characterized in that the step (4) is realized by the following steps:
(41) setting initial value y of fuzzy number (0) 0; regularization parameter initial value μ (0) 0; the maximum iteration number k is 100;
(42) and (3) calculating a residual error estimated value in the k iterative calculation:
P＝E-C T (C -1 (CC T )) (28)
q＝C T (b -1 (CC T )) (29)
x (k) ＝P(y (k) -μ (k) )+q (30)
wherein E represents an identity matrix, y (k) Representing the fuzzy number in the k iteration calculation; mu.s (k) Representing a regularization parameter in the k-th iterative computation;
(43) and updating the fuzzy number in the k +1 th iteration calculation:
y (k+1) ＝max(0，x (k) +μ (k) -1)-max(0，-x (k) -μ (k) -1) (31)
y (k+1) representing the fuzzy number in the k +1 th iteration calculation after updating;
(44) updating the regularization parameter mu in the (k + 1) th iterative computation (k+1) ：
μ (k+1) ＝μ (k) +x (k) -y (k+1) (32)
μ (k+1) Represents the updated (k + 1) th iterationThe regularization parameter of (a);
(45) calculating an iteration error Resi:
Resi＝||y (k) -y (k+1 || 2 (33)
(46) calculating a threshold value s:
Figure FDA0003577831910000041
(47) if Resi > ∈ and the iteration number k is smaller than or equal to the preset maximum iteration number, the iteration number k +1 is carried out, and the step (42) is carried out; otherwise, stopping calculation;
(48) output y (k) ，
Figure FDA0003577831910000042
CN202210338788.1A 2022-04-01 2022-04-01 Based on L 1 Norm regularized SAR phase unwrapping method Pending CN115047454A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202210338788.1A CN115047454A (en) 2022-04-01 2022-04-01 Based on L 1 Norm regularized SAR phase unwrapping method

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202210338788.1A CN115047454A (en) 2022-04-01 2022-04-01 Based on L 1 Norm regularized SAR phase unwrapping method

Publications (1)

Publication Number Publication Date
CN115047454A true CN115047454A (en) 2022-09-13

Family

ID=83157735

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202210338788.1A Pending CN115047454A (en) 2022-04-01 2022-04-01 Based on L 1 Norm regularized SAR phase unwrapping method

Country Status (1)

Country Link
CN (1) CN115047454A (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117269960A (en) * 2023-09-12 2023-12-22 中国矿业大学 Rapid norm phase unwrapping method based on gradient optimization

Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2021227423A1 (en) * 2020-05-13 2021-11-18 深圳大学 Insar digital elevation model construction method and system based on dynamic baseline
CN114019507A (en) * 2021-10-27 2022-02-08 南京航空航天大学 Based on L1/2Norm regularized SAR interferogram generation method

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2021227423A1 (en) * 2020-05-13 2021-11-18 深圳大学 Insar digital elevation model construction method and system based on dynamic baseline
CN114019507A (en) * 2021-10-27 2022-02-08 南京航空航天大学 Based on L1/2Norm regularized SAR interferogram generation method

Non-Patent Citations (5)

* Cited by examiner, † Cited by third party
Title
HUI BI等: "L2, 1-norm Regularization Based Sparse SAR Imaging From Periodic Block Sampling Data: Initial Result", 《 2020 21ST INTERNATIONAL RADAR SYMPOSIUM (IRS)》, 13 November 2020 (2020-11-13) *
VAN DER SANDEN等: "InSAR coherence for automated lake ice extent mapping: TanDEM-X bistatic and pursuit monostatic results", 《INTERNATIONAL JOURNAL OF APPLIED EARTH OBSERVATION AND GEOINFORMATION》, 15 October 2018 (2018-10-15) *
亓宁轩;: "InSAR相位解缠算法的比较", 测绘与空间地理信息, no. 03, 25 March 2016 (2016-03-25) *
孙希龙: "SAR层析与差分层析成像技术研究", 《中国优秀硕士学位论文全文库 信息科技辑》, 15 October 2014 (2014-10-15), pages 31 - 102 *
陈强;杨莹辉;刘国祥;程海琴;刘伟堂;: "基于边界探测的InSAR最小二乘整周相位解缠方法", 测绘学报, no. 03, 15 June 2012 (2012-06-15) *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117269960A (en) * 2023-09-12 2023-12-22 中国矿业大学 Rapid norm phase unwrapping method based on gradient optimization
CN117269960B (en) * 2023-09-12 2024-04-26 中国矿业大学 Rapid norm phase unwrapping method based on gradient optimization

Similar Documents

Publication Publication Date Title
CN108594222B (en) Elevation reconstruction method and device for dual-frequency interference synthetic aperture radar
CN108765476B (en) Polarized image registration method
CN115047454A (en) Based on L 1 Norm regularized SAR phase unwrapping method
CN108132468B (en) Multi-baseline polarization interference SAR building height extraction method
CN101206763A (en) Multi-frame self-adaptive optical image high-resolution restoration method by using wavefront data
CN113223066B (en) Multi-source remote sensing image matching method and device based on characteristic point fine tuning
CN111402395A (en) Passive polarization three-dimensional reconstruction method based on CNN correction
CN108761458B (en) Morphological refinement-based interference SAR water body digital elevation model correction method
CN114371477A (en) InSAR multi-baseline phase unwrapping method
CN115272683A (en) Central differential information filtering phase unwrapping method based on deep learning
CN114019507A (en) Based on L1/2Norm regularized SAR interferogram generation method
Kuglin et al. Map-matching techniques for terminal guidance using Fourier phase information
CN112665529B (en) Object three-dimensional shape measuring method based on stripe density area segmentation and correction
Soğanlui et al. Dictionary learning for sparsity-driven SAR image reconstruction
CN114693755B (en) Non-rigid registration method and system for multimode image maximum moment and space consistency
CN116681844A (en) Building white film construction method based on sub-meter stereopair satellite images
CN114895305B (en) L-based 1 Norm regularized sparse SAR self-focusing imaging method and device
CN113066023B (en) SAR image speckle removing method based on self-calibration convolutional neural network
CN111739158B (en) Three-dimensional scene image recovery method
CN116203560A (en) Space-borne large strabismus high-resolution sliding SAR frequency domain imaging method
CN106934783B (en) Time domain reconstruction method for high-frequency time-series remote sensing data
CN106485677B (en) Fast and efficient interference phase filtering method
CN113066015B (en) Multi-mode remote sensing image rotation difference correction method based on neural network
Quidu et al. Subpixel image registration for coherent change detection between two high resolution sonar passes
CN110223250B (en) SAR geometric correction method based on homography transformation

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