Signal processing method based on branch cutting method and extended Kalman filtering phase unwrapping fusion

Abstract

The invention relates to the technical field of signal processing, in particular to a signal processing method based on phase unwrapping fusion of a branch cutting method and extended Kalman filtering, and the method comprises the following steps: detecting a residual point and generating a branch cutting line; based on connected region segmentation, a basis is provided for subsequent steps; performing branch cutting method path expansion based on the segmented region; carrying out extended Kalman filtering (EKF) local estimation based on the segmented region; integrating results, and constructing an adaptive fusion mechanism; and final phase output is performed on a comprehensive result. The stability of the algorithm under different noise levels is remarkably improved through a fusion mechanism, the stability is tested, the global topological advantage of the branch cutting method and the local precision of the EKF are utilized, it is ensured that the unwrapping result keeps continuity in the whole phase field, compared with a traditional branch cutting method, the phase root mean square error is lower, and compared with a pure EKF method, the method has the advantages that the method is simple and convenient to implement. And the accuracy in the boundary region is higher.

Description

Technical Field

[0001] The present invention relates to the field of signal processing technology, and in particular to a signal processing method based on the fusion of branch cutting method and extended Kalman filter phase unwrapping. Background Art

[0002] Existing phase unwrapping technologies mainly face challenges such as phase jumps, noise interference and discontinuous area processing. Traditional methods such as path dependence method and least squares method often perform poorly in complex scenarios, especially when the measurement area contains multiple discontinuous areas.

[0003] Currently, branch cutting and extended Kalman filtering are widely used in the field of phase unwrapping, but each has its limitations. While the traditional branch cutting method can ensure global topological correctness, it is sensitive to noise and has limited local accuracy. The extended Kalman filtering method has good noise immunity but has difficulty handling phase discontinuities and large phase jumps. Noise interference is common in industrial detection environments, and phase discontinuities at the boundaries of the measured object are difficult for traditional single methods to simultaneously address. When the phase field is divided into multiple discontinuous regions by invalid regions, how to ensure the consistency of the unwrapping results in each region? Existing methods lack effective statistical constraints when merging between domains.

[0004] Based on this, the present invention provides a signal processing method based on the fusion of branch cutting method and extended Kalman filter phase unwrapping to solve the technical problems raised above. Summary of the Invention

[0005] The purpose of the present invention is to provide a signal processing method based on the fusion of branch cutting method and extended Kalman filter phase unwrapping to solve the problems mentioned in the above background technology.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] The present invention proposes a signal processing method based on the fusion of branch cutting method and extended Kalman filter phase unwrapping, comprising the following steps:

[0008] S1. Residual point detection and branch tangent generation;

[0009] S2. Segment the connected regions based on step S1 to provide a basis for subsequent steps;

[0010] S3. Branch cutting method path expansion based on step S2 segmentation area;

[0011] S4. Perform extended Kalman filter EKF local estimation within the segmented area based on step S2 and in parallel with step S3;

[0012] S5. Integrate the results of step S3 and step S4 to build an adaptive fusion mechanism;

[0013] S6. Integrate the results of steps S1 to S5 to output the final phase.

[0014] Preferably, the implementation steps of step S1 are:

[0015] S11. Residual point identification: By analyzing the gradient change of the wrapped phase, the singular points in the phase field are located, providing target points for subsequent branch tangent generation;

[0016] S12. Adaptive threshold adjustment: Dynamically adjust the residual point determination threshold based on local phase quality, including phase smoothness and noise level, to improve residual point detection accuracy;

[0017] S13. Branch tangent optimization: Generate the shortest path branch tangent based on the residual point position and the principle of physical continuity to avoid the integral path passing through discontinuous areas and provide topological constraints for the segmentation of connected areas.

[0018] Preferably, the implementation steps of step S2 are: dividing the phase field into multiple independent connected areas, the connected areas are defined by the branch cuts or invalid areas generated by step S1, and each area serves as a local operation unit to provide a spatially isolated underlying structure for branch cut path expansion and EKF local estimation.

[0019] Preferably, the implementation steps of step S3 are:

[0020] S31. Flood fill algorithm: Starting from the high phase quality area, gradually expand the phase according to the phase gradient and distance decay priority, bypassing the branch tangent area generated in step S1;

[0021] S32. Global topology constraint: Ensure that the unfolding results within each connected region segmented in step S2 meet the global requirement of phase continuity, which complements the EKF estimation in step S4.

[0022] Preferably, the implementation steps of step S4 are:

[0023] S41. State Modeling: Using the true phase and its gradient as state variables, a dynamic model is constructed to provide a mathematical framework for local phase estimation.

[0024] S42. Noise Adaptation: Dynamically adjust the system noise and observation noise covariance matrix based on the local phase variance to improve noise immunity.

[0025] S43. Prediction and update: Based on the previous step estimation, the local phase estimate is gradually optimized through state prediction and observation update based on the wrapped phase data, providing local refined results for step S5 fusion.

[0026] Preferably, the implementation steps of step S5 are:

[0027] S51. Weight calculation: Dynamically assign weights to the results of steps S3 and S4 based on the complexity of the local structure, balancing global correctness and local accuracy;

[0028] S52. Cross-scale consistency constraint: The fusion results are globally corrected using the coarse-scale phase results to avoid phase jumps between regions and ensure the overall continuity of the output phase.

[0029] S53. Error feedback optimization: Combine the local error estimates from steps S3 and S4, iteratively adjust the fusion parameters to improve the overall accuracy and provide an optimized fusion result for the output of the final phase.

[0030] Preferably, the implementation steps of step S6 are: integrating the global topological correctness of the branch cutting method in step S3 and the local noise resistance of the EKF in step S4, outputting a high-precision, high-robustness unfolded phase, which is suitable for complex scenes with high noise and multiple discontinuous areas to provide reliable input for subsequent three-dimensional reconstruction and deformation measurement applications.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] The present invention significantly improves the stability of the algorithm under different noise levels through a fusion mechanism. After testing, it maintains an unfolding accuracy of more than 90% when the signal-to-noise ratio drops by 20%. It utilizes the global topological advantages of the branch cutting method and the local accuracy of the EKF to ensure that the unfolding result maintains continuity throughout the phase field, effectively processing complex scenes containing discontinuous areas, and has strong adaptability to object shapes, surface characteristics, and imaging conditions. It demonstrates excellent general performance in a variety of test scenarios. Compared with the traditional branch cutting method, the present invention has a lower phase root mean square error and higher accuracy in boundary areas than the simple EKF method. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 An overview of the system operation architecture of the present invention is shown;

[0034] Figure 2 shows a fusion algorithm flow chart of the present invention;

[0035] Figure 3 shows an identification diagram of the residual points of the present invention;

[0036] Figure 4 Shown is a placement branch tangent diagram of the present invention;

[0037] Figure 5 A schematic diagram of flood filling according to the present invention is shown;

[0038] Figure 6 Shown is a connected domain segmentation and processing diagram of the present invention;

[0039] Figure 7 shows a state space representation diagram of the present invention;

[0040] Figure 8 Shown is a schematic diagram of Sigma point sampling of the present invention;

[0041] Figure 9 It shows how the branch cutting method of the present invention and EKF are deeply integrated at the algorithm level;

[0042] Figure 10 A one-dimensional data display prediction diagram of the present invention is shown;

[0043] Figure 11 The effect diagram of the two-dimensional cross-region segmentation phase unwrapping of the present invention is shown. DETAILED DESCRIPTION

[0044] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0045] Example 1, please refer to Figures 1 to 11 The present invention proposes a signal processing method based on the fusion of branch cutting method and extended Kalman filter phase unwrapping, comprising the following steps:

[0046] S1. Residual point detection and branch tangent generation;

[0047] In this embodiment, it should be noted that the implementation steps of step S1 are:

[0048] S11. Residual point identification: By analyzing the gradient change of the wrapped phase, the singular points in the phase field are located, providing target points for subsequent branch tangent generation;

[0049] S12. Adaptive threshold adjustment: Dynamically adjust the residual point determination threshold based on local phase quality, including phase smoothness and noise level, to improve residual point detection accuracy;

[0050] S13. Branch tangent optimization: Generate the shortest path branch tangent based on the residual point location and the principle of physical continuity, avoiding the integral path passing through discontinuous areas and providing topological constraints for the segmentation of connected regions.

[0051] S2. Segment the connected regions based on step S1 to provide a basis for subsequent steps;

[0052] In this embodiment, it should be noted that the implementation steps of step S2 are: dividing the phase field into multiple independent connected regions, where the connected regions are defined by the branch cuts or invalid regions generated in step S1, and each region serves as a local operation unit to provide a spatially isolated underlying structure for branch cut path expansion and EKF local estimation;

[0053] S3. Branch cutting method path expansion based on step S2 segmentation area;

[0054] In this embodiment, it should be noted that the implementation steps of step S3 are:

[0055] S31. Flood fill algorithm: Starting from the high phase quality area, gradually expand the phase according to the phase gradient and distance decay priority, bypassing the branch tangent area generated in step S1;

[0056] S32. Global topology constraint: ensures that the unfolding results within each connected region segmented in step S2 meet the global requirement of phase continuity, which complements the EKF estimation in step S4;

[0057] S4. Perform extended Kalman filter EKF local estimation within the segmented area based on step S2 and in parallel with step S3;

[0058] In this embodiment, it should be noted that the implementation steps of step S4 are:

[0059] S41. State Modeling: Using the true phase and its gradient as state variables, a dynamic model is constructed to provide a mathematical framework for local phase estimation.

[0060] S42. Noise Adaptation: Dynamically adjust the system noise and observation noise covariance matrix based on the local phase variance to improve noise immunity.

[0061] S43. Prediction and Update: Based on the previous estimation, the local phase estimate is gradually optimized through state prediction and observation update based on the wrapped phase data, providing a local refined result for fusion in step S5.

[0062] S5. Integrate the results of step S3 and step S4 to build an adaptive fusion mechanism;

[0063] In this embodiment, it should be noted that the implementation steps of step S5 are:

[0064] S51. Weight calculation: Dynamically assign weights to the results of steps S3 and S4 based on the complexity of the local structure, balancing global correctness and local accuracy;

[0065] S52. Cross-scale consistency constraint: The fusion results are globally corrected using the coarse-scale phase results to avoid phase jumps between regions and ensure the overall continuity of the output phase.

[0066] S53. Error feedback optimization: Combining the local error estimates from steps S3 and S4, iteratively adjust the fusion parameters to improve overall accuracy and provide an optimized fusion result for the final phase output;

[0067] S6. The results of steps S1 to S5 are combined to produce the final phase output;

[0068] In this embodiment, it should also be noted that the implementation steps of step S6 are: integrating the global topological correctness of the branch cutting method in step S3 and the local noise resistance of the EKF in step S4, outputting a high-precision, high-robustness unfolded phase, which is suitable for complex scenes with high noise and multiple discontinuous areas to provide reliable input for subsequent three-dimensional reconstruction and deformation measurement applications.

[0069] In practical applications, the phase unwrapping and fusion method combining the branch cutting method with the extended Kalman filter of the present invention addresses the shortcomings of traditional phase unwrapping technology in complex scenarios and proposes a dual-path parallel processing architecture. Specifically, the method includes the following steps:

[0070] See also Figures 1 to 11 ,This method first introduces an improved branch cutting framework based on ,residual point detection;

[0071] Phase residual detection uses a high-precision four-point differential model:

[0072]

[0073] in and The phase differences in the x and y directions are calculated respectively. After the calculated R(i,j) is modulo 2π, the residual point is defined as: rp(i,j)=1 if|R(i,j)|>π, otherwise rp(i,j)=0;

[0074] In order to improve the accuracy of residual point detection, this method introduces a quality-guided adaptive threshold:

[0075] Thr(i,j)=π·[1-α·Q(i,j)];

[0076] Where Q(i,j) is the local phase quality evaluation function:

[0077]

[0078] is the local phase variance, is the wrapped phase gradient, α, β, and γ are adjustment parameters;

[0079] After detecting the residual points, this method innovatively proposes a residual link optimization strategy to construct the minimum total length tangent according to the principle of physical continuity;

[0080] Introducing distance-weighted residual connection cost function:

[0081] C(i,j,m,n)=d(i,j,m,n)·[1+ρ·|Q(i,j)-Q(m,n)|];

[0082] Where d(i,j,m,n) is the Euclidean distance and ρ is the quality difference penalty factor;

[0083] The optimization goal is to minimize the total tangent length:

[0084] min∑(p,q)∈BCC(p,q);

[0085] BC represents the set of all branch tangents;

[0086] To avoid excessively long tangents, segment cutting constraints are introduced:

[0087] L(BC k )≤Lmax;

[0088] Among them BC k is the kth tangent line, Lmax is the maximum allowed length, usually set to 10-15% of the image diagonal length;

[0089] After the tangent lines are generated, this method uses an improved flood-fill algorithm to perform path tracing expansion;

[0090] Define the path integral function for the branch-cut constraint:

[0091]

[0092] Where C is the path that bypasses all tangents, from the starting point s to the target point t;

[0093] The implementation uses a priority queue to manage extension points, and the extension priority is determined by the quality function:

[0094] pri(i,j)=Q(i,j)·exp(-λ·dist(i,j,s));

[0095] Where dist(i,j,s) is the distance from point (i,j) to the starting point s, and λ is the distance attenuation parameter;

[0096] In parallel, the present invention introduces an extended Kalman filter framework to handle phase unwrapping;

[0097] Model the phase field as a state-space representation:

[0098] x(k+1)=f(x(k))+w(k);

[0099] z(k)=h(x(k))+v(k);

[0100] in is the state vector, which contains the true phase and the phase derivatives in two directions, is the observed quantity, i.e., the wrapped phase;

[0101] The state transfer function f and observation function h are defined as:

[0102] f(x(k))=[x 1 (k)+x 2 (k)·dx+x 3 (k)·dy,x 2 (k),x 3 (k)]T;

[0103] h(x(k))=W(x1(k));

[0104] Where W is the wrapping operator, dx and dy are the intervals between adjacent pixels;

[0105] The covariance matrix of system noise w(k) and observation noise v(k) is adaptively designed based on the local phase quality:

[0106]

[0107] R(k)=σz 2 (k);

[0108] in are phase and gradient variance estimates, respectively, obtained through local window statistics:

[0109]

[0110] η1, η2, and η3 are scaling factors, usually in the range [0.5, 2.0];

[0111] The state prediction and update of the extended Kalman filter adopts the classic EKF framework, but introduces an innovative adaptive gain adjustment mechanism;

[0112] Prediction steps:

[0113]

[0114] P(k|k-1)=F(k)·P(k-1|k-1)·F(k)T+Q(k);

[0115] in is the state transfer Jacobian matrix;

[0116] Observation update steps:

[0117] K(k)=P(k|k-1)·H(k)T·[H(k)·P(k|k-1)·H(k)T+R(k)] -1 ;

[0118]

[0119] P(k|k)=[IK(k)·H(k)]·P(k|k-1);

[0120] in is the observed Jacobian matrix, H(k) = [1, 0, 0] within the phase wrapping interval and [0, 0, 0] at the phase jump;

[0121] This invention innovatively introduces a dynamic trust mechanism for observation:

[0122] K′(k)=K(k)·trust(k);

[0123]

[0124] in is the observed predicted value, μ is the trust adjustment parameter;

[0125] The core innovation of this invention lies in the adaptive fusion mechanism of the branch-cutting method and the EKF results;

[0126] The fusion process is defined as:

[0127]

[0128] in The result of branch cutting method, is the extended Kalman filter result, ω is the position adaptive weight;

[0129] The weight calculation uses an innovative phase consistency evaluation:

[0130]

[0131] Where S(i,j) is the structural complexity measure,

[0132]

[0133] Ts is the structural complexity threshold, and κ controls the transition steepness;

[0134] CBC and CEKF are confidence assessments of two methods respectively:

[0135] CBC(i,j)=exp(-δBC·EBC(i,j));

[0136] CEKF(i,j)=exp(-δEKF·EEKF(i,j));

[0137] Where EBC and EEKF are their respective local expansion error estimates, and δBC and δEKF are scaling parameters;

[0138] To improve fusion accuracy, this method also introduces cross-scale consistency constraints:

[0139]

[0140] in is the unwrapped phase pre-calculated at the coarse-scale layer, and s is the scale factor;

[0141] This constraint is transformed into an energy minimization problem:

[0142]

[0143] Where τ is the balance parameter, and the final fusion result is obtained by solving the variational method;

[0144] The fusion method of the present invention realizes the complementary advantages of the two algorithms. The final unwrapped phase has both global consistency and local accuracy, and the noise resistance performance is greatly improved.

[0145] It is particularly suitable for phase field unfolding with a variety of complex scenes and high noise mixtures, such as high dynamic range interferometry, medical imaging with discontinuous boundaries, and SAR interferometry in complex terrain.

[0146] Throughout this specification, references to terms such as "one embodiment," "example," or "specific example" indicate that the specific features, structures, materials, or characteristics described in conjunction with that embodiment or example are included in at least one embodiment or example of the present invention. In this specification, schematic representations of these terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0147] The preferred embodiments of the present invention disclosed above are intended only to help illustrate the present invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the present invention to the specific embodiments described. Obviously, many modifications and variations are possible based on the content of this specification. These embodiments are selected and described in detail in this specification to better explain the principles and practical applications of the present invention, thereby enabling those skilled in the art to better understand and utilize the present invention. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A signal processing method based on branch cutting and extended Kalman filter phase unwrapping fusion, characterized in that: The following steps are involved: S1. Residual point detection and branch tangent generation; S2. Segment the connected regions based on step S1 to provide a basis for subsequent steps; S3. Branch cutting method path expansion based on step S2 segmentation area; S4. Perform extended Kalman filter EKF local estimation within the segmented area based on step S2 and in parallel with step S3; S5. Integrate the results of step S3 and step S4 to build an adaptive fusion mechanism; S6. Integrate the results of steps S1 to S5 to output the final phase.

2. The signal processing method based on branch cutting method and extended Kalman filter phase unwrapping fusion according to claim 1, characterized in that: The implementation steps of step S1 are: S11. Residual point identification: By analyzing the gradient change of the wrapped phase, the singular points in the phase field are located, providing target points for subsequent branch tangent generation; S12. Adaptive threshold adjustment: Dynamically adjust the residual point determination threshold based on local phase quality, including phase smoothness and noise level, to improve residual point detection accuracy; S13. Branch tangent optimization: Generate the shortest path branch tangent based on the residual point position and the principle of physical continuity to avoid the integral path passing through discontinuous areas and provide topological constraints for the segmentation of connected areas.

3. The signal processing method based on branch cutting method and extended Kalman filter phase unwrapping fusion according to claim 2, characterized in that: The implementation steps of step S2 are: dividing the phase field into multiple independent connected regions, where the connected regions are defined by the branch cuts or invalid regions generated in step S1, and each region serves as a local operation unit to provide a spatially isolated underlying structure for branch cut path expansion and EKF local estimation.

4. The signal processing method based on branch cutting and extended Kalman filter phase unwrapping fusion according to claim 3, characterized in that: The implementation steps of step S3 are: S31. Flood fill algorithm: Starting from the high phase quality area, gradually expand the phase according to the phase gradient and distance decay priority, bypassing the branch tangent area generated in step S1; S32. Global topology constraint: Ensure that the unfolding results within each connected region segmented in step S2 meet the global requirement of phase continuity, which complements the EKF estimation in step S4.

5. The signal processing method based on branch cutting method and extended Kalman filter phase unwrapping fusion according to claim 4 is characterized in that: The implementation steps of step S4 are: S41. State Modeling: Using the true phase and its gradient as state variables, a dynamic model is constructed to provide a mathematical framework for local phase estimation. S42. Noise Adaptation: Dynamically adjust the system noise and observation noise covariance matrix based on the local phase variance to improve noise immunity. S43. Prediction and update: Based on the previous step estimation, the local phase estimate is gradually optimized through state prediction and observation update based on the wrapped phase data, providing local refined results for step S5 fusion.

6. The signal processing method based on branch cutting method and extended Kalman filter phase unwrapping fusion according to claim 5, characterized in that: The implementation steps of step S5 are: S51. Weight calculation: Dynamically assign weights to the results of steps S3 and S4 based on the complexity of the local structure, balancing global correctness and local accuracy; S52. Cross-scale consistency constraint: The fusion results are globally corrected using the coarse-scale phase results to avoid phase jumps between regions and ensure the overall continuity of the output phase. S53. Error feedback optimization: Combine the local error estimates from steps S3 and S4, iteratively adjust the fusion parameters to improve the overall accuracy and provide an optimized fusion result for the output of the final phase.

7. The signal processing method based on branch cutting method and extended Kalman filter phase unwrapping fusion according to claim 6, characterized in that: The implementation steps of step S6 are: combining the global topological correctness of the branch cutting method in step S3 and the local noise resistance of the EKF in step S4, outputting a high-precision and high-robustness unfolded phase, which is suitable for complex scenes with high noise and multiple discontinuous areas to provide reliable input for subsequent three-dimensional reconstruction and deformation measurement applications.

Images