Underdetermined blind source separation method and system based on dictionary learning and sparse reconstruction
By transforming the underdetermined blind source separation problem into a sparse coding problem, and utilizing dictionary learning and sparse reconstruction methods, the difficulty of solving underdetermined blind source separation is solved, achieving efficient and robust source signal separation.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- GUANGZHOU UNIVERSITY
- Filing Date
- 2023-05-15
- Publication Date
- 2026-06-19
AI Technical Summary
The underdetermined blind source separation problem is difficult to solve due to the lack of sufficient observation information. Traditional methods are inefficient in dictionary updates and sparse approximation processes, making it difficult to obtain strongly sparsity solutions.
The underdetermined mixed blind source separation problem is transformed into a sparse source signal reconstruction problem by using a compressed sensing model. The dictionary learning method is used to update the dictionary and sparse coefficients simultaneously, and the source signals are separated by a sparse reconstruction method.
It improves blind source separation performance, enhances adaptability and robustness, and can effectively separate source signals in noisy environments.
Smart Images
Figure CN116738189B_ABST
Abstract
Description
Technical Field
[0001] This document relates to the field of signal processing technology, and in particular to an underdetermined blind source separation method and system based on dictionary learning and sparse reconstruction. Background Technology
[0002] Underdetermined blind source separation technology has been widely applied in various fields, such as biomedical signal processing, audio source signal separation, and self-noise reduction for auditory micro-aircraft. However, due to the lack of sufficient observational information, underdetermined multichannel blind source separation is an NP-hard problem, and its solution faces significant technical challenges. To address this issue, traditional methods utilize sparse component analysis (SCI), assuming that the source signal satisfies a certain sparsity and can be decomposed into a combination of a small number of components, thereby reconstructing the source signal. However, since the sparse decomposition of the signal depends on the fit between the dictionary and the signal, the problem of dictionary learning needs to be considered. Most dictionary learning algorithms involve iterative dictionary updates and sparse approximation; to find a suitable dictionary, iterative updates of the dictionary and its coefficients are required. However, how to obtain a strongly sparsity-enhanced solution while avoiding the triviality of dictionary analysis remains an unsolved problem. Summary of the Invention
[0003] This invention provides an underdetermined blind source separation method and system based on dictionary learning and sparse reconstruction, aiming to solve the above-mentioned problems.
[0004] This invention provides an underdetermined blind source separation method based on dictionary learning and sparse reconstruction, comprising:
[0005] S1. Model the mixed signal to obtain an underdetermined mixed blind source separation model;
[0006] S2. Use the compressed sensing model to transform the underdetermined mixed blind source separation model into a sparse source signal reconstruction problem;
[0007] S3. Use dictionary learning methods to simultaneously update the dictionary and the sparse coefficients in the sparse source signal reconstruction problem.
[0008] S4. Solve the sparse source signal reconstruction problem by using the sparse reconstruction method based on the sparse coefficients, thereby separating the source signal.
[0009] This invention provides an underdetermined blind source separation system based on dictionary learning and sparse reconstruction, comprising:
[0010] The modeling module is used to model mixed signals and obtain an underdetermined mixed blind source separation model;
[0011] The signal reconstruction module is used to transform the underdetermined mixed blind source separation model into a sparse source signal reconstruction problem using a compressed sensing model.
[0012] The dictionary learning module is used to simultaneously update the dictionary and the sparse coefficients in the sparse source signal reconstruction problem using dictionary learning methods.
[0013] The source signal separation module is used to solve the problem of sparse source signal reconstruction based on sparse coefficients using sparse reconstruction methods, thereby separating the source signal.
[0014] By employing the embodiments of the present invention, the underdetermined multi-channel blind source separation problem is transformed into a sparse coding problem. The source signals are separated by dictionary learning and sparse reconstruction, overcoming the limitation of the difficulty in solving the underdetermined mixed blind source separation problem. The method of the present invention has the characteristics of high separation performance, strong adaptability, and good robustness. Attached Figure Description
[0015] To more clearly illustrate the technical solutions in one or more embodiments of this specification or in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0016] Figure 1 This is a flowchart of an embodiment of the underdetermined blind source separation method based on dictionary learning and sparse reconstruction of the present invention;
[0017] Figure 2 This is a diagram of the speech source signal according to an embodiment of the present invention;
[0018] Figure 3 This is a diagram of the mixed speech signal according to an embodiment of the present invention;
[0019] Figure 4 This is a schematic diagram of a speech source signal separated by the underdetermined blind source separation method based on dictionary learning and sparse reconstruction according to an embodiment of the present invention.
[0020] Figure 5 This is a schematic diagram of an underdetermined blind source separation system based on dictionary learning and sparse reconstruction, according to an embodiment of the present invention. Detailed Implementation
[0021] To enable those skilled in the art to better understand the technical solutions in one or more embodiments of this specification, the technical solutions in one or more embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this specification, and not all of the embodiments. Based on one or more embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of this document.
[0022] Method Implementation Examples
[0023] This invention provides an underdetermined blind source separation method based on dictionary learning and sparse reconstruction. Figure 1 This is a flowchart of an underdetermined blind source separation method based on dictionary learning and sparse reconstruction, according to an embodiment of the present invention. Figure 1 As shown, the underdetermined blind source separation method based on dictionary learning and sparse reconstruction in this embodiment of the invention specifically includes:
[0024] Step S1: Model the mixed signal to obtain an underdetermined mixed blind source separation model. Step S1 specifically includes:
[0025] The mathematical model for underdetermined mixed signals in noisy environments is as follows:
[0026] X(t)=A·S(t)+N(t), (1)
[0027] Where the number of source signals N is greater than the number of sensors M, i.e., N>M, in the underdetermined mixed case, X(t)=[x1(t),x2(t),...,x M (t)] T ∈R M×T It is a mixed signal matrix, [·] T Denotes the transpose of a matrix, A∈R M×N It is an unknown mixture matrix, S(t)=[s1(t),s2(t),...,s N (t)] T ∈R N×T The source signal matrix is unknown, and N(t) is the system disturbance.
[0028] Step S2: Transform the underdetermined mixed blind source separation model into a sparse source signal reconstruction problem using a compressed sensing model. Step S2 specifically includes:
[0029] The mixed signal matrix X(t) in step 1 is vectorized by superimposing the column vectors of matrix X(t) into a single vector, as shown in equation (1).
[0030]
[0031] Among them, Λ ij ∈R T×T It is a diagonal matrix, and its diagonal elements are a. ij Let x = vec(X) T ), s = vec(S T Then, equation (2) can be written as:
[0032] x=M·s (3)
[0033] Where M is the observation matrix and s is a sparse vector, represented using sparse representation:
[0034] s=D·c (4)
[0035] Where D is the dictionary matrix, and c is the sparse representation of s, combining equations (3) and (4), we get
[0036] x=M·D·c (5)
[0037] The above model transformation can transform the underdetermined blind source separation problem into a sparse source signal reconstruction problem based on dictionary learning.
[0038] Step S3: Simultaneously update the dictionary and the sparse coefficients in the sparse source signal reconstruction problem using a dictionary learning method. Step S3 specifically includes:
[0039] Dictionary learning is the process of finding the optimal dictionary representation for the training signal. Using mixed signals to train the dictionary involves solving the following optimization problem:
[0040]
[0041] Here, Y is the sparse representation of the mixed signal, and μ is an appropriate hyperparameter that treats the sparse coefficients as a function of the dictionary, updating the corresponding sparse coefficients while updating the dictionary.
[0042] make
[0043]
[0044] Then, the dictionary is updated using the gradient descent linear search method. The gradient of the objective function is calculated as follows:
[0045]
[0046] To update the dictionary, let
[0047]
[0048] definition
[0049]
[0050] Where, p j and D :,j These are the j-th columns of P and D, respectively, and q j It is the direction of line search, q j D :,j =0, new dictionary D :,j+1 It can be done in q j Move in the direction of D :,j get:
[0051]
[0052] Here, α is the step size, determined using the golden section search method. Therefore, the dictionary update rule is as follows:
[0053]
[0054] Complete the dictionary learning.
[0055] Step S4: Based on the sparse coefficients, use the sparse reconstruction method to solve the sparse source signal reconstruction problem, thereby separating the source signal. Step S4 specifically includes:
[0056] To obtain a sparse solution, solve the following optimization problem:
[0057]
[0058] Define the Lagrange function:
[0059] L(c,λ)=J(c)+λ T (x-MDc) (14)
[0060] make
[0061]
[0062] in,
[0063]
[0064]
[0065] therefore,
[0066] Π(c)·c-(MD) T λ=0 (18)
[0067] achievable
[0068] c = Π -1 (c)·(MD) T λ (19)
[0069] Substituting equation (19) into equation (15), we get
[0070] x = MD·Π -1 (c)·(MD) T λ (20)
[0071] thereby,
[0072] λ=[MD·Π -1 (c)·(MD) T ] -1 ·x (21)
[0073] Substituting equation (21) into equation (19), we get
[0074] c = Π -1 (c)·(MD) T ·[MD·Π -1 (c)·(MD) T ] -1 ·x (22)
[0075] Complete sparse reconstruction.
[0076] To improve computational efficiency, x is divided into multiple sub-blocks based on block operations. The sources separated from each sub-block are concatenated to reconstruct the complete source signal, thus achieving source signal separation.
[0077] The following specific examples demonstrate the feasibility and superiority of the proposed method in solving the problem of blind source separation in underdetermined mixed signals.
[0078] In this embodiment, two microphones are used to receive three speech source signals, forming a 2-channel, 3-source underdetermined mixed signal. Two blind source separation performance evaluation criteria are selected: source-to-distortion ratio (SDR) and source-to-interference ratio (SIR), with higher values indicating better separation results. To visualize the separation results, the speech source signals are used for comparison, and the visualization results are as follows: Figures 2-4 As shown, where Figure 2 This is a diagram of the speech source signal according to an embodiment of the present invention; Figure 3 This is a diagram of the mixed speech signal according to an embodiment of the present invention; Figure 4 This is a schematic diagram of a speech source signal separated by the underdetermined blind source separation method based on dictionary learning and sparse reconstruction according to an embodiment of the present invention; (Comparison) Figure 2 and Figure 4It can be observed that the separated speech source signals are very close to the original source signals before mixing. Furthermore, to demonstrate the superiority of the proposed method in terms of evaluation criteria, several internationally popular dictionary-based blind source separation algorithms are selected for comparison: K-means singular value decomposition (K-SVD) is an iterative algorithm that alternates between sparse coding and dictionary atomic update processes to adapt to sparse signals; the greedy adaptive dictionary (GAD) is a computationally fast dictionary learning algorithm that uses a minimum sparsity index to represent the sparsity of speech signals; and the simultaneous codeword optimization (SimCO) algorithm treats the codewords of any subset and their corresponding sparse coefficients as functions of the dictionary, thereby simultaneously updating these sparse coefficients. To demonstrate its robustness to noise, a signal-to-noise ratio (SNR) of 10 dB to 50 dB was selected. The experimental results are shown in Table 1. The comparison shows that the present invention has good adaptability to noise. Compared with other algorithms, the SDR and SIR results obtained by the method of the present invention are better, which verifies the superiority of the method of the present invention.
[0079] Table 1 Comparison of Blind Source Separation Performance for Underdetermined Mixed Signals
[0080]
[0081] This invention proposes an underdetermined blind source separation method based on dictionary learning and sparse reconstruction. First, the mixed signal undergoes model preprocessing, and the underdetermined mixed blind source separation model is transformed into a sparse source signal reconstruction problem using a compressed sensing model. Then, a dictionary learning method is used to simultaneously update the dictionary and the corresponding sparse coefficients, and a sparse reconstruction method is used to separate the source signals. Finally, the effectiveness of the proposed method for separating underdetermined mixed speech signals is verified through examples, and the superiority of the proposed method is illustrated by comparing it with several dictionary learning-based blind source separation algorithms.
[0082] The embodiments of the present invention have the following beneficial effects:
[0083] This invention establishes a compressed sensing model, transforming the underdetermined multi-channel blind source separation problem into a sparse coding problem. It separates source signals through dictionary learning and sparse reconstruction, overcoming the limitation of the difficulty in solving the underdetermined mixed blind source separation problem. The method of this invention has the characteristics of high separation performance, strong adaptability, and good robustness.
[0084] System Implementation Examples
[0085] This invention provides an underdetermined blind source separation system based on dictionary learning and sparse reconstruction. Figure 5 This is a schematic diagram of an underdetermined blind source separation system based on dictionary learning and sparse reconstruction according to an embodiment of the present invention. Figure 5 As shown, the underdetermined blind source separation system based on dictionary learning and sparse reconstruction in this embodiment of the invention specifically includes:
[0086] Modeling module 50 is used to model mixed signals and obtain an underdetermined mixed blind source separation model; specifically, modeling module 50 is used for:
[0087] The mathematical model for underdetermined mixed signals in noisy environments is as follows:
[0088] X(t)=A·S(t)+N(t), (1)
[0089] Where the number of source signals N is greater than the number of sensors M, i.e., N>M, in the underdetermined mixed case, X(t)=[x1(t),x2(t),...,x M (t)] T ∈R M×T It is a mixed signal matrix, [·] T Denotes the transpose of a matrix, A∈R M×N It is an unknown mixture matrix, S(t)=[s1(t),s2(t),...,s N (t)] T ∈R N×T The source signal matrix is unknown, and N(t) is the system disturbance.
[0090] Signal reconstruction module 52 is used to transform the underdetermined mixed blind source separation model into a sparse source signal reconstruction problem using a compressed sensing model; signal reconstruction module 52 is specifically used for:
[0091] Vectorization is performed on the mixed signal matrix, where the column vectors of matrix X(t) are superimposed onto a single vector, as shown in equation (1).
[0092]
[0093] Among them, Λ ij ∈R T×T It is a diagonal matrix, and its diagonal elements are a. ij Let x = vec(X) T ), s = vec(S T Then, equation (2) can be written as:
[0094] x=M·s (3)
[0095] Where M is the observation matrix and s is a sparse vector, represented using sparse representation:
[0096] s=D·c (4)
[0097] Where D is the dictionary matrix, and c is the sparse representation of s, combining equations (3) and (4), we get
[0098] x=M·D·c (5)
[0099] The above model transformation can transform the underdetermined blind source separation problem into a sparse source signal reconstruction problem based on dictionary learning.
[0100] Dictionary learning module 54 is used to simultaneously update the dictionary and the sparse coefficients in the sparse source signal reconstruction problem using dictionary learning methods; dictionary learning module 54 is specifically used for:
[0101] Dictionary learning is the process of finding the optimal dictionary representation for the training signal. Using mixed signals to train the dictionary involves solving the following optimization problem:
[0102]
[0103] Here, Y is the sparse representation of the mixed signal, and μ is an appropriate hyperparameter that treats the sparse coefficients as a function of the dictionary, updating the corresponding sparse coefficients while updating the dictionary.
[0104] make
[0105]
[0106] Then, the dictionary is updated using the gradient descent linear search method. The gradient of the objective function is calculated as follows:
[0107]
[0108] To update the dictionary, let
[0109]
[0110] definition
[0111]
[0112] Where, p j and D :,j These are the j-th columns of P and D, respectively, and q j It is the direction of line search, q j D :,j =0, new dictionary D :,j+1 It can be done in q j Move in the direction of D :,j get:
[0113]
[0114] Here, α is the step size, determined using the golden section search method. Therefore, the dictionary update rule is as follows:
[0115]
[0116] Complete the dictionary learning.
[0117] The source signal separation module 56 is used to solve the sparse source signal reconstruction problem based on the sparse coefficients using a sparse reconstruction method, thereby separating the source signal. Specifically, the source signal separation module 56 is used for:
[0118] To obtain a sparse solution, solve the following optimization problem:
[0119]
[0120] Define the Lagrange function:
[0121] L(c,λ)=J(c)+λ T (x-MDc) (14)
[0122] make
[0123]
[0124] in,
[0125]
[0126]
[0127] therefore,
[0128] Π(c)·c-(MD) T λ=0 (18)
[0129] achievable
[0130] c = Π -1 (c)·(MD) T λ (19)
[0131] Substituting equation (19) into equation (15), we get
[0132] x = MD·Π -1 (c)·(MD) T λ (20)
[0133] thereby,
[0134] λ=[MD·Π -1 (c)·(MD) T ] -1 ·x (21)
[0135] Substituting equation (21) into equation (19), we get
[0136] c = Π -1 (c)·(MD) T ·[MD·Π -1 (c)·(MD) T ] -1 ·x (22)
[0137] Complete sparse reconstruction.
[0138] To improve computational efficiency, x is divided into multiple sub-blocks based on block operations. The sources separated from each sub-block are concatenated to reconstruct the complete source signal, thus achieving source signal separation.
[0139] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A method for underdetermined blind source separation based on dictionary learning and sparse reconstruction, characterized in that, include: S1. Model the mixed signal to obtain an underdetermined mixed blind source separation model; S2. The underdetermined hybrid blind source separation model is transformed into a sparse source signal reconstruction problem using a compressed sensing model; S3. Simultaneously update the dictionary and the corresponding sparse coefficients in the sparse source signal reconstruction problem using a dictionary learning method; S4. Solve the sparse source signal reconstruction problem using the sparse coefficients, thereby separating the source signal; Step S1 specifically includes: The underdetermined mixed signal in a noisy environment is modeled using Equation 1: Formula 1 ; Among them, the number of source signals N Greater than the number of sensors M ,Right now, N>M Uncertain mixed situation It is a mixed signal matrix. To represent the transpose of a matrix, It is an unknown mixture matrix. It is an unknown source signal matrix. It is a system disturbance; Step S2 specifically includes: Vectorize the mixed signal matrix to convert the matrix... The column vectors are superimposed onto a single vector, and the underdetermined hybrid blind source separation model is expressed as: Formula 2; in, It is a diagonal matrix, and its diagonal elements are... ,make , The underdetermined hybrid blind source separation model is then written as: Official 3; in, It is the observation matrix. It is a sparse vector, Using sparse representation: Formula 4; in, It is a dictionary matrix. yes The sparse representation of the signal is transformed into a sparse source signal reconstruction problem based on dictionary learning by formula 5 according to formulas 3 and 4. Equation 5; Step S3 specifically includes: The dictionary learning algorithm is used to solve the following optimization problem: Equation 6; in, It is a sparse representation of mixed signals. It is an appropriate hyperparameter that treats the sparse coefficients as a function of the dictionary, updating the corresponding sparse coefficients while updating the dictionary; make Equation 7; Then, the dictionary is updated using the gradient descent linear search method, and the gradient of the objective function is calculated as follows: Equation 8; To update the dictionary, let Official 9; definition Official 10; in, and They are and The List, It is the direction of line search. The new dictionary Through move in the direction get: Equation 11; wherein is a step size, determined using a golden section search method, and the dictionary update rule is as follows: Equation 12.
2. The method of claim 1, wherein, Step S4 specifically includes: To obtain a sparse solution, solve the following optimization problem: Formula 13; The sparse solution is obtained using Equation 14, thus completing the sparse reconstruction: Equation 14.
3. An underdetermined blind source separation system based on dictionary learning and sparse reconstruction, characterized in that, include: The modeling module is used to model mixed signals and obtain an underdetermined mixed blind source separation model; The signal reconstruction module is used to transform the underdetermined mixed blind source separation model into a sparse source signal reconstruction problem using a compressed sensing model. The dictionary learning module is used to simultaneously update the dictionary and the corresponding sparse coefficients in the sparse source signal reconstruction problem using a dictionary learning method. The source signal separation module is used to solve the sparse source signal reconstruction problem based on the sparse coefficients using a sparse reconstruction method, thereby separating the source signal; The modeling module is specifically used for: The underdetermined mixed signal in a noisy environment is modeled using Equation 1: Formula 1 ; Among them, the number of source signals N Greater than the number of sensors M ,Right now, N>M Uncertain mixed situation It is a mixed signal matrix. To represent the transpose of a matrix, It is an unknown mixture matrix. It is an unknown source signal matrix. It is a system disturbance; The signal reconstruction module is specifically used for: Vectorize the mixed signal matrix to convert the matrix... The column vectors are superimposed onto a single vector, and the underdetermined hybrid blind source separation model is expressed as: Official 2; in, It is a diagonal matrix, and its diagonal elements are... ,make , The underdetermined hybrid blind source separation model is then written as: Official 3; wherein, is an observation matrix, is a sparse vector, and is represented as sparse. Formula 4; in, It is a dictionary matrix. yes The sparse representation of the signal is transformed into a sparse source signal reconstruction problem based on dictionary learning by formula 5 according to formulas 3 and 4. Formula 5; The dictionary learning module is specifically used for: The dictionary learning algorithm is used to solve the following optimization problem: Official 6; wherein, is a sparse representation of the mixed signal, is an appropriate hyper-parameter that updates the sparse coefficients as a function of the dictionary, updating the corresponding sparse coefficients at the same time as the dictionary is updated; make Official 7; Then, the dictionary is updated using the gradient descent linear search method, and the gradient of the objective function is calculated as follows: Official 8; To update the dictionary, let Official 9; definition Official 10; in, and They are and The List, It is the direction of line search. The new dictionary Through move in the direction get: Official 11; wherein is a step size, determined using a golden section search method, and the dictionary update rule is as follows: Equation 12.
4. The system of claim 3, wherein, The source signal separation module is specifically used for: To obtain a sparse solution, solve the following optimization problem: Official 13; The sparse solution is obtained using Equation 14, thus completing the sparse reconstruction: Equation 14.