Sensor network sound field reconstruction method based on graph signal and distributed optimization
By constructing an undirected weighted graph and a global joint optimization objective function, combined with a graph Laplace consistency regularization term and an alternating direction multiplier method, the robustness and continuity issues in sound field reconstruction of sensor networks are solved, achieving efficient and accurate sound field reconstruction, which is applicable to large-scale distributed acoustic sensor networks.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- HANGZHOU EBOYLAMP ELECTRONICS CO LTD
- Filing Date
- 2025-12-04
- Publication Date
- 2026-04-28
AI Technical Summary
Traditional sensor network sound field reconstruction methods suffer from poor robustness, centralization bottlenecks, noise sensitivity and spatial discontinuity, and failure to effectively utilize sound field physical priors, resulting in poor reconstruction accuracy and continuity.
A graph-based signal and distributed optimization approach is adopted to construct an undirected weighted graph. By globally jointly optimizing the objective function, auxiliary and dual variables are introduced. The outer layer is iteratively updated using the alternating direction multiplier method, and combined with the graph Laplace consistency regularization term, the sound field reconstruction of the sensor network is realized.
It significantly improves the accuracy and continuity of reconstruction results, enhances robustness in complex noise environments, reduces communication overhead and computational latency, and avoids the bottleneck effect of the central node.
Smart Images
Figure CN121935593A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of sensor network signal processing technology, specifically relating to a sensor network sound field reconstruction method based on graph signals and distributed optimization. Background Technology
[0002] With the development of the Internet of Things and distributed sensing systems, the demand for monitoring and reconstructing physical fields (such as sound fields) through sensor networks is increasing. Sound field reconstruction is a method that uses technical means to simulate or restore the sound propagation characteristics in a real sound field environment, aiming to provide listeners with an immersive auditory experience. Its core objective is to capture and reproduce the sound wave information in the original sound field, enabling listeners to obtain an auditory experience similar to the original sound field in the reconstructed environment.
[0003] Traditional centralized processing methods require all data to be aggregated at a central node, facing problems such as high communication bandwidth pressure, high system latency, and the risk of single points of failure. Furthermore, in existing technologies, sensor nodes often perform local reconstruction in an isolated manner, making it difficult to explicitly utilize network spatial correlations; centralized methods suffer from communication bottlenecks and single points of failure; and existing distributed methods lack an effective balance between noise, measurement sparsity, and spatial smoothness. Particularly in sound field reconstruction, due to environmental noise interference and measurement incompleteness, sparse reconstructions performed by isolated nodes often have limited accuracy, and the results may contain spatially discontinuous abrupt changes, making it difficult to truly reflect the continuous and smooth characteristics of the physical field.
[0004] Therefore, existing sensor networks (such as acoustic sensor networks) face several key technical challenges when performing sound field reconstruction or signal reconstruction:
[0005] 1) Poor robustness: Traditional methods usually process the data of each node independently, which makes them highly sensitive to local noise and measurement errors, resulting in poor reconstruction accuracy and spatial continuity.
[0006] 2) Centralization bottleneck: Traditional sound field reconstruction methods rely on transmitting all sensor data to the central processor, which has problems such as high communication bandwidth pressure, high risk of single point of failure, and poor scalability. It is not suitable for large-scale, distributed acoustic sensor networks.
[0007] 3) Noise sensitivity and spatial discontinuity: In complex noise environments, the reconstructed sound field based on independent node processing or simple interpolation methods is prone to spatial non-physical fluctuations and discontinuities, making it difficult to reflect the true sound wave propagation law.
[0008] 4) Failure to effectively utilize the physical priors of the sound field: The sound field has an inherent smooth propagation characteristic in space (which can be described by the sound wave governing equations such as the Helmholtz equation), and it exhibits sparsity in certain transform domains (such as the wavenumber domain). Many existing distributed methods have failed to organically integrate this physical prior with the network topology. Summary of the Invention
[0009] The purpose of this invention is to address the problems raised in the background art by proposing a sensor network sound field reconstruction method based on graph signals and distributed optimization.
[0010] To achieve the above objectives, the technical solution adopted by the present invention is as follows:
[0011] This invention proposes a sensor network sound field reconstruction method based on graph signals and distributed optimization, comprising:
[0012] The sensor network of the target area is constructed as an undirected weighted graph, which includes a set of all sensors in the target area, a set of edges of sensors with communication connections, and a set of edge weights consisting of the weights of each edge in the edge set, with each sensor being treated as a node.
[0013] A global joint optimization objective function is constructed, which includes the raw sound field observation data collected by each node, the measurement matrix of each node, the sparse coefficient vector of the sound field at each node, and the edge weights, in order to realize the sound field reconstruction of the sensor network.
[0014] The objective function is solved by introducing auxiliary variables to reconstruct it and setting constraints. Dual variables are introduced to constrain the reconstructed objective function, and an augmented Lagrangian function is constructed. The alternating direction multiplier method is used to iteratively update the sparse coefficient vector of the sound field at each node, the auxiliary variables, and the dual variables until the outer iteration termination condition is met. Then, the sparse coefficient vector of the sound field at each node corresponding to the last outer iteration is taken as the final sparse coefficient vector of the sound field at each node, and the final sparse coefficient vector of the sound field at each node is applied to the sensor network to realize the sound field reconstruction of the sensor network.
[0015] Preferably, the undirected weighted graph is represented as follows: ,in This represents the set of all sensors within the target area, and The number of sensors within the target area. Let be the set of edges formed between the sensors within the target area. Let be the set of edge weights.
[0016] Preferably, the objective function includes a local sparse reconstruction term and a graph Laplacian consistency regularization term, and the objective function is expressed as follows:
[0017] ;
[0018] in, For the first The sparse coefficient vector of the sound field at each node For signal dimension, For the first The raw sound field observation data collected by each node, and is in the time domain or frequency domain. For the first The measurement dimensions of the raw sound field observation data collected by each node. For the first The measurement matrix of each node, and , For the first The node and the first Edges between nodes The weights are the set of edge weights. subset of For the first The node and the first Edges between nodes The weights are the set of edge weights. subset of ,in For nodes With nodes European distance, For distance scale parameters, The sparse regularization coefficients control the sparse coefficient vector of the sound field. The sparsity, These are the global Laplace smoothing weights. For the first The set of neighboring nodes of a node.
[0019] Preferably, when solving the objective function, the objective function is first reconstructed by introducing auxiliary variables, and constraints are set:
[0020] For each edge Introduce a pair of auxiliary variables and Set constraints as , ,and For the first Each node wants its neighboring nodes to... The status I saw regarding myself, and it was the [number]th [item / section]. Auxiliary variables for each node, For the first Each node wants its neighboring nodes to... The status I see about myself, and the first Auxiliary variables for each node; wherein, the auxiliary variables and The initial value is based on the node. and Local observation data and The weighted average construction, i.e. and initial value Alternatively, the initial values of auxiliary variables can be estimated based on the graph topology.
[0021] The reconstructed objective function is expressed as follows:
[0022] ;
[0023] ;
[0024] .
[0025] Preferably, the constraint on the reconstructed objective function introduces dual variables and constructs an augmented Lagrangian function, including:
[0026] Constraints Introducing dual variables ,and For the first The node to the first The augmented Lagrangian function, representing the dual variables of directed edges at n nodes, is as follows:
[0027] ;
[0028] in, Represent the Lagrange function, This is the penalty parameter.
[0029] Preferably, the step of using the alternating direction multiplier method to iteratively update the sparse coefficient vector, auxiliary variable, and dual variable of the sound field at each node until the outer iteration termination condition is met includes:
[0030] First, initialize the sparse coefficient vector of the sound field, auxiliary variables, and dual variables at each node to 0;
[0031] The outer iteration updates of all nodes are executed in parallel, and during each outer iteration update of each node, the sparse coefficient vector of the sound field, the auxiliary variables, and the dual variables are updated sequentially.
[0032] Preferably, the formula for updating the sparse coefficient vector of the sound field during one outer layer iteration is as follows:
[0033] (1);
[0034] in, Indicates the first During the next outer iteration process, the first The update results of the sparse coefficient vector of the sound field at each node. Indicates the first During the next outer iteration process, the first Auxiliary variables for each node, Indicates the first During the next outer iteration process, the first The node to the first The dual variables of the directed edges of each node;
[0035] Combining the linear and quadratic terms of formula (1) and completing the square coordination, formula (1) is equivalent to:
[0036] (2);
[0037] Formula (2) is solved using a fast iterative threshold shrinkage algorithm:
[0038] Perform sparse coefficient vector of sound field The process involves one iteration, and this iteration is called the inner iteration:
[0039] In one inner iteration, the update of the sparse coefficient vector of the sound field is as follows:
[0040] ;
[0041] in,
[0042] ;
[0043] ;
[0044] ;
[0045] ;
[0046] ;
[0047] in, For the first The first step in the inner layer iteration process The update results of the sparse coefficient vector of the sound field at each node. For the first Momentum point during the inner iteration process. For function gradient, For the first Smoothing terms in the inner iteration process. The momentum coefficient, For the first Momentum parameters during the inner-layer iteration process. For the first The inner iteration step size of each node, For the first The intermediate parameters of each node, It is a matrix spectral norm, For the gradient descent step, For the first The number of neighboring nodes of a node. This is a component-wise soft thresholding operator;
[0048] The inner iteration employs an accelerated gradient strategy, where the momentum parameter... Dynamically adjust based on local gradient changes: when Reset when the value exceeds the preset threshold. To avoid oscillation, otherwise press Update; Inner iteration step size A backtracking search mechanism is used: the initial step size is In each inner iteration, if Then shrink the inner iteration step size , until the Armijo condition is met;
[0049] Adaptive adjustment is achieved through backtracking search, with an initial step size of [value missing]. However, in each inner iteration, the function dynamically shrinks or expands based on the effect of local gradient descent to ensure that the objective function decreases monotonically.
[0050] When the number of inner iterations reaches the maximum When the time comes, terminate the inner iteration and output the result. For the last inner iteration That is, the first During the next outer iteration process, the first The update result of the sparse coefficient vector of the sound field at each node is the result of the last inner iteration in the current inner iteration. ,in , All are preset values.
[0051] Preferably, during one outer iteration, the update obtained during the current outer iteration is... It is sent to all neighboring nodes and used to update auxiliary variables, and the update formula for the auxiliary variables is as follows:
[0052] (3);
[0053] Formula (3) is about , The convex problem has a unique closed-form solution. By setting the gradient of equation (3) to zero, we obtain a system of linear equations, as follows:
[0054] right Find the partial derivative and set it to zero:
[0055] ;
[0056] get:
[0057] (4);
[0058] right Find the partial derivative and set it to zero:
[0059] ;
[0060] get:
[0061] (5);
[0062] Combining formulas (4) and (5), we obtain a system of linear equations:
[0063] ;
[0064] Solving for:
[0065] ;
[0066] ;
[0067] in, For the first During the next outer iteration process, the first Auxiliary variables for each node, For the first During the next outer iteration process, the first Auxiliary variables for each node, It is the identity matrix;
[0068] when and hour, ,at this time:
[0069] .
[0070] Preferably, during one outer iteration, the update obtained during the current outer iteration is... and To update the dual variable, the update formula for the dual variable is as follows:
[0071] ;
[0072] in, For the first During the next outer iteration process, the first The node to the first The dual variables of the directed edges of each node.
[0073] Preferably, when the outer iteration termination condition is met, the sparse coefficient vector of the sound field at each node corresponding to the last outer iteration is taken as the final sparse coefficient vector of the sound field at each node. and through Reconstruct the sound field at each node;
[0074] The outer iteration termination condition is: when the constraint residual is less than the first threshold. And the dual residual is less than the second threshold. ,Right now: ,and If the outer iteration terminates, then the outer iteration terminates.
[0075] Alternatively, the outer iteration will terminate when the number of outer iterations reaches the preset maximum number.
[0076] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0077] This sensor network sound field reconstruction method based on graph signals and distributed optimization combines the physical topology of the sensor network with the spatial smoothness prior of the sound field by introducing a graph Laplace consistency regularization term. It utilizes the overall spatial correlation of the sensor network to suppress estimation abrupt changes caused by local noise and measurement errors, which significantly improves the accuracy, continuity and robustness of the reconstruction results in complex noise environments.
[0078] This method uses the alternating direction multiplier method to iteratively update the sparse coefficient vector of the sound field, auxiliary variables, and dual variables at each node, decomposing the complex global optimization problem into local subproblems that can be processed in parallel at each node. Each node only needs to communicate with its direct neighbors, avoiding the bottleneck effect of the central node and significantly reducing the system's communication overhead and computational latency. Attached Figure Description
[0079] Figure 1 This is a flowchart illustrating the sensor network sound field reconstruction method based on graph signals and distributed optimization according to the present invention.
[0080] Figure 2 This is the execution algorithm for the sensor network sound field reconstruction method based on graph signals and distributed optimization in this invention. Detailed Implementation
[0081] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0082] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to limit the invention.
[0083] like Figures 1-2 As shown, a sensor network sound field reconstruction method based on graph signals and distributed optimization is presented. The application scenarios of this sound field reconstruction method include: 1. Sound field reconstruction of large indoor auditoriums / concert halls: A distributed microphone array is arranged between the audience seating and the stage. This method recovers a high-resolution spatial sound pressure field for acoustic optimization and auditory analysis. (Figure copyright) The parameters can be determined by the Euclidean distance between sensors, the correlation coefficient of the received signal, or through offline / online similarity learning methods; in strong reverberation environments, learned priors can be introduced into the dictionary or observation front end to compensate for model mismatch caused by reverberation; 2. Industrial plant noise mapping and equipment fault detection: Under complex noise background and reverberation conditions, graph-based spatial smoothing helps to suppress local abnormal measurements, improve the robustness of environmental noise distribution maps, and support the location of noise sources and abnormal equipment; 3. Urban traffic noise monitoring and noise source tracking: Long-term monitoring of roads or intersections is carried out through multi-point distributed sensor networks, and online tracking and temporal reconstruction of sound source activities are achieved by using time-varying graphs and sliding window mechanisms; 4. Emergency rescue and trapped person awakening: In temporary sensor networks rapidly deployed in collapsed buildings or disaster areas, asynchronous update and compressed communication strategies are used to achieve voice / sound source detection and localization in low-bandwidth and energy-constrained environments, assisting in rescue decision-making.
[0084] A sensor network sound field reconstruction method based on graph signals and distributed optimization includes:
[0085] Step 1: Construct the sensor network of the target area into an undirected weighted graph. The undirected weighted graph includes a set of all sensors in the target area, a set of edges between the sensors, and a set of edge weights consisting of the weights of each edge in the edge set. Each sensor is treated as a node.
[0086] The undirected weighted graph is represented as follows: ,in This represents the set of all sensors within the target area, and The number of sensors in the target area (e.g., 64). It is the set of edges formed between the sensors in the target area (representing the communication connection relationship between nodes). Let be the set of edge weights, where the elements in the set of edge weights are... , representing a node and The strength of the acoustic correlation between them If and only if ;or , Used to quantize nodes With nodes The spatial correlation strength between acoustic physical fields; ,in For nodes With nodes European distance, This is a distance scale parameter used to control the rate at which the weights decay with distance (typical values are as follows). ( (average node spacing) , );when When the weight is small, A value close to 1 indicates a high correlation between the sound field information of the two nodes; however, as the distance increases, the weights decay rapidly according to a Gaussian function, which weakens the influence of distant nodes on the local graph smoothing term.
[0087] Step 2: Construct a global joint optimization objective function that includes the original sound field observation data collected by each node, the measurement matrix of each node, the sparse coefficient vector of the sound field at each node, and the edge weights, in order to realize the sound field reconstruction of the sensor network.
[0088] The objective function includes a local sparse reconstruction term and a graph Laplacian consistency regularization term, and the formula for the objective function is as follows:
[0089] ;
[0090] in, For the first The sparse coefficient vector of the sound field at each node The signal dimension (e.g., 128). For the first The raw sound field observation data collected by each node, and is in the time domain or frequency domain. For the first The measurement dimensions of the raw sound field observation data collected by each node. For the first The measurement matrix (or dictionary matrix) of each node, and , For the first The node and the first Edges between nodes The weights are the set of edge weights. subset of ,in For nodes With nodes European distance, For distance scale parameters, For sparse regularization coefficients, such as Controlling the sparse coefficient vector of the sound field The sparsity, The global Laplace smoothing weights are, for example... , For the first The set of neighboring nodes of a node. Let be the set of sparse coefficient vectors of the sound field at all nodes within the target region. Let L1 be the L1 norm of the vector, which is the sum of its absolute values. Let be the Euclidean norm of the vector. The square of the Euclidean norm;
[0091] Among them, in the objective function For local sparse reconstruction terms, ensure that the estimation result of each node (i.e., the first) The sparse coefficient vector of the sound field at each node ) and its local observation data (i.e., the first Raw sound field observation data collected by each node It matches, and at the same time passes Norm Promotion The sparsity of the sound field is consistent with the sparse prior of the physical sound field in a specific transform domain.
[0092] In the objective function The graph Laplace consistency regularization term is physically a numerical approximation of the continuity constraint on the smoothness of the sound field on a discrete sensor network. A smoothness prior constraint based on the graph topology is introduced, utilizing weights... Penalize neighboring nodes estimated value and Between Norm difference. Weights Larger (indicating node) With nodes The stronger the correlation in physics / acoustics, the stronger the penalty, thus forcing the reconstruction results to converge in the sparse domain. This guides the reconstruction process to achieve a smooth transition in the sparse domain, effectively suppressing abrupt changes in estimates caused by local noise or measurement errors, and leveraging the overall spatial correlation of the network to improve the robustness and accuracy of the reconstruction algorithm.
[0093] Step 3: Solve the objective function, reconstructing it by introducing auxiliary variables and setting constraints. Introduce dual variables to the constraints of the reconstructed objective function and construct an augmented Lagrangian function. Use the alternating direction multiplier method to iteratively update the sparse coefficient vector of the sound field at each node, the auxiliary variables, and the dual variables until the outer iteration termination condition is met. Then, use the sparse coefficient vector of the sound field at each node corresponding to the last outer iteration as the final sparse coefficient vector of the sound field at each node, and apply the final sparse coefficient vector of the sound field at each node to the sensor network to realize the sound field reconstruction of the sensor network, including:
[0094] Step 3.1: When solving the objective function, first reconstruct the objective function by introducing auxiliary variables and setting constraints:
[0095] For each edge Introduce a pair of auxiliary variables and Set constraints as , ,and For the first Each node wants its neighboring nodes to... The status I saw regarding myself, and it was the [number]th [item / section]. Auxiliary variables for each node, For the first Each node wants its neighboring nodes to... The status I see about myself, and the first Auxiliary variables for each node; where the auxiliary variables and The initial value is based on the node. and Local observation data and The weighted average construction, i.e. and initial value Alternatively, the initial values of auxiliary variables can be estimated based on the graph topology (this construction method can utilize the local correlation of the graph topology to accelerate the convergence of the outer iteration of ADMM and improve the spatial smoothness of the reconstructed sound field), and the formula for estimating the initial values of auxiliary variables based on the graph topology is as follows:
[0096] First, perform signal smoothing preprocessing on the graph:
[0097] Each node First, calculate the local initial estimate:
[0098] ;
[0099] Perform TFig_init (3-5) graph diffusion iterations, and between two adjacent graph diffusion iterations, each node... The relationship of the local initial estimates is as follows:
[0100] ;
[0101] in, The diffusion coefficient (usually taken as 0.5-0.8) is used, and a good initial estimate can generally be obtained by setting TFig_init=3;
[0102] Then, the initial values of the auxiliary variables are constructed based on the diffusion results:
[0103] ;
[0104] in, For small perturbations based on Graph Laplace smoothing:
[0105] .
[0106] The reconstructed objective function is expressed as follows:
[0107] ;
[0108] ;
[0109] ;
[0110] By rewriting the globally coupled graph Laplacian consistency regularization term as the L2 norm difference of variables on the edges, the coupling is localized to each edge, while the variables... Only with The relevant edge variables are constrained, which facilitates parallel computation of nodes.
[0111] Step 3.2: Introduce dual variables to the constraints of the reconstructed objective function and construct the augmented Lagrangian function, including:
[0112] Constraints Introducing dual variables (Lagrange multipliers), and For the first The node to the first The augmented Lagrangian function, representing the dual variables of directed edges at n nodes, is as follows:
[0113] ;
[0114] in, Represent the Lagrange function, The penalty parameter has an empirical value range of [ , ],like ;
[0115] Dual variables Update in subsequent iterations to reduce constraint violations, augmentation term Used for numerical stabilization and accelerating convergence.
[0116] Step 3.3: Use the Alternating Direction Multiplier Method (ADMM) to iteratively update the sparse coefficient vector, auxiliary variables, and dual variables of the acoustic field at each node in the outer layer (each outer layer iteration updates the local sparse coefficient vector in sequence, i). (A fast iterative threshold shrinkage algorithm / FISTA can be used for inner layer solving, and a warm-start, backtracking search, and dynamic inner layer accuracy strategy can be adopted.) (ii) Auxiliary variables on edges (iii) Dual variables Each outer iteration only needs to exchange auxiliary variables or their compressed representations with neighboring nodes, thus achieving a fully distributed solution. Outer iterations can employ synchronous or asynchronous update strategies (supporting time-varying graph topology and asynchronous updates (ensuring approximate convergence even when nodes are offline or experience large delays)), including:
[0117] First, initialize the sparse coefficient vector of the sound field, auxiliary variables, and dual variables at each node to 0;
[0118] The outer iteration updates of all nodes are executed in parallel, and during each outer iteration update of each node, the sparse coefficient vector of the sound field, the auxiliary variables, and the dual variables are updated sequentially.
[0119] Step 3.3.1: During one outer iteration, the formula for updating the sparse coefficient vector of the sound field is obtained based on the augmented Lagrangian function as follows:
[0120] (1);
[0121] in, Indicates the first During the next outer iteration process, the first The update results of the sparse coefficient vector of the sound field at each node. Indicates the first During the next outer iteration process, the first Auxiliary variables for each node, Indicates the first During the next outer iteration process, the first The node to the first The dual variables of the directed edges of each node;
[0122] Combining the linear and quadratic terms of formula (1) and completing the square coordination, formula (1) is equivalent to:
[0123] (2);
[0124] Formula (2) is solved using a fast iterative threshold shrinkage algorithm:
[0125] Perform sparse coefficient vector of sound field Step iteration ( Take 20–100, such as This iteration is called the inner iteration.
[0126] In one inner iteration, the update of the sparse coefficient vector of the sound field is as follows:
[0127] ;
[0128] in,
[0129] ;
[0130] ;
[0131] ;
[0132] ;
[0133] ;
[0134] in, For the first The first step in the inner layer iteration process The update results of the sparse coefficient vector of the sound field at each node. For the first Momentum point during the inner iteration process. For function gradient, For the first Smoothing terms in the inner iteration process. The momentum coefficient, For the first The momentum parameter during the inner iteration process (e.g., 2). For the first The inner iteration step size of each node, For the first The intermediate parameters of each node, It is a matrix spectral norm, For the gradient descent step, For the first The number of neighboring nodes of a node. This is a component-wise soft thresholding operator;
[0135] To further improve the convergence speed of the inner layer, an accelerated gradient strategy is adopted for the inner layer iteration, where the momentum parameter... Dynamically adjust based on local gradient changes: when Greater than a preset threshold (e.g.) When resetting, To eliminate oscillations caused by momentum accumulation, otherwise continue pressing... Update; Inner iteration step size A backtracking search mechanism is used: the initial step size is In each inner iteration, if Then shrink the inner iteration step size , This process continues until the Armijo condition is met; this adaptive strategy ensures the stability and fast convergence of the inner layer iterations, and is particularly suitable for non-uniform noise environments in sound field reconstruction.
[0136] When the number of inner iterations reaches the maximum When the time comes, terminate the inner iteration and output the result. For the last inner iteration That is, the first During the next outer iteration process, the first The update result of the sparse coefficient vector of the sound field at each node is the result of the last inner iteration in the current inner iteration. ,in , All are preset values ( Pick to ).
[0137] Step 3.3.2: During one outer iteration, update the data obtained during the current outer iteration. It is sent to all neighboring nodes (where quantization, differential, or random projection compression is used during transmission to reduce communication overhead) and used to update auxiliary variables, and the update formula for the auxiliary variables is as follows:
[0138] (3);
[0139] Formula (3) is about , The convex problem has a unique closed-form solution. By setting the gradient of equation (3) to zero, we obtain a system of linear equations, as follows:
[0140] right Find the partial derivative and set it to zero:
[0141] ;
[0142] get:
[0143] (4);
[0144] right Find the partial derivative and set it to zero:
[0145] ;
[0146] get:
[0147] (5);
[0148] Combining formulas (4) and (5), we obtain a system of linear equations:
[0149] ;
[0150] Solving for:
[0151] ;
[0152] ;
[0153] in, For the first During the next outer iteration process, the first Auxiliary variables for each node, For the first During the next outer iteration process, the first Auxiliary variables for each node, It is the identity matrix;
[0154] when and hour, ,at this time:
[0155] .
[0156] Step 3.3.3: During one outer iteration, update the data obtained during the current outer iteration. and To update the dual variable, the update formula for the dual variable is as follows:
[0157] ;
[0158] in, For the first During the next outer iteration process, the first The node to the first The dual variables of the directed edges of each node.
[0159] Step 3.4: Determine whether the outer iteration termination condition has been met. If it has, use the sparse coefficient vector of the sound field at each node corresponding to the last outer iteration as the final sparse coefficient vector of the sound field at each node, and apply the final sparse coefficient vector of the sound field at each node to the sensor network to realize the sound field reconstruction of the sensor network. If it has not been met, return to step 3.3.
[0160] When the outer iteration termination condition is met, the sparse coefficient vector of the sound field at each node corresponding to the last outer iteration is taken as the final sparse coefficient vector of the sound field at each node. and through Reconstruct the sound field at each node, thereby realizing the sound field reconstruction of the sensor network;
[0161] The outer iteration termination condition is: when the constraint residual is less than the first threshold. (If it is) And the dual residual is less than the second threshold. (If it is) ),Right now: ,and If the outer iteration terminates, then the outer iteration terminates.
[0162] Alternatively, the outer iteration will terminate when the number of iterations reaches a preset maximum (e.g., 200).
[0163] This sensor network sound field reconstruction method based on graph signals and distributed optimization combines the physical topology of the sensor network with the spatial smoothness prior of the sound field by introducing a graph Laplace consistency regularization term. It utilizes the overall spatial correlation of the sensor network to suppress estimation abrupt changes caused by local noise and measurement errors, significantly improving the accuracy, continuity, and robustness of the reconstruction results in complex noise environments. The method uses an alternating direction multiplier method to iteratively update the sparse coefficient vector, auxiliary variables, and dual variables of the sound field at each node, decomposing the complex global optimization problem into local subproblems that can be processed in parallel at each node. Each node only needs to communicate with its direct neighbors, avoiding the bottleneck effect of the central node and significantly reducing the system's communication overhead and computational latency.
[0164] By explicitly enforcing spatial smoothness through the graph Laplacian consistency regularization term, the reconstructed sound pressure level distribution and sound source localization results more closely match the actual propagation characteristics of sound waves, effectively avoiding non-physical artifacts resembling a checkerboard pattern. By combining sparse constraints and graph smoothness constraints, the prior knowledge of the signal and spatial correlation can be utilized to jointly suppress observation noise and outlier interference, maintaining high reconstruction accuracy even under strong background noise. This scheme adopts a fully distributed solution architecture, eliminating the need for an expensive central computing unit. Sensor nodes are plug-and-play, and the system can quickly adapt to changes in network topology, making it ideal for applications such as large-scale urban noise monitoring and distributed acoustic fault diagnosis of industrial equipment.
[0165] This sensor network sound field reconstruction method based on graph signals and distributed optimization combines the physical topology of the sensor network with the spatial smoothness prior of the sound field by introducing a graph Laplace consistency regularization term. It utilizes the overall spatial correlation of the sensor network to suppress estimation abrupt changes caused by local noise and measurement errors, which significantly improves the accuracy, continuity and robustness of the reconstruction results in complex noise environments.
[0166] This method uses the alternating direction multiplier method to iteratively update the sparse coefficient vector of the sound field, auxiliary variables, and dual variables at each node, decomposing the complex global optimization problem into local subproblems that can be processed in parallel at each node. Each node only needs to communicate with its direct neighbors, avoiding the bottleneck effect of the central node and significantly reducing the system's communication overhead and computational latency.
[0167] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.
[0168] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0169] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.
Claims
1. A sensor network sound field reconstruction method based on graph signals and distributed optimization, characterized in that: The sensor network sound field reconstruction method based on graph signals and distributed optimization includes: The sensor network of the target area is constructed as an undirected weighted graph, which includes a set of all sensors in the target area, a set of edges of sensors with communication connections, and a set of edge weights consisting of the weights of each edge in the edge set, with each sensor being treated as a node. A global joint optimization objective function is constructed, which includes the raw sound field observation data collected by each node, the measurement matrix of each node, the sparse coefficient vector of the sound field at each node, and the edge weights, in order to realize the sound field reconstruction of the sensor network. The objective function is solved by introducing auxiliary variables to reconstruct it and setting constraints. Dual variables are introduced to constrain the reconstructed objective function, and an augmented Lagrangian function is constructed. The alternating direction multiplier method is used to iteratively update the sparse coefficient vector of the sound field at each node, the auxiliary variables, and the dual variables until the outer iteration termination condition is met. Then, the sparse coefficient vector of the sound field at each node corresponding to the last outer iteration is taken as the final sparse coefficient vector of the sound field at each node, and the final sparse coefficient vector of the sound field at each node is applied to the sensor network to realize the sound field reconstruction of the sensor network.
2. The sensor network sound field reconstruction method based on graph signals and distributed optimization as described in claim 1, characterized in that: The undirected weighted graph is represented as follows: ,in This represents the set of all sensors within the target area, and The number of sensors within the target area. Let be the set of edges formed between the sensors within the target area. Let be the set of edge weights.
3. The sensor network sound field reconstruction method based on graph signals and distributed optimization as described in claim 2, characterized in that: The objective function includes a local sparse reconstruction term and a graph Laplacian consistency regularization term, and the formula for the objective function is as follows: ； in, For the first The sparse coefficient vector of the sound field at each node For signal dimension, For the first The raw sound field observation data collected by each node, and is in the time domain or frequency domain. For the first The measurement dimensions of the raw sound field observation data collected by each node. For the first The measurement matrix of each node, and , For the first The node and the first Edges between nodes The weights are the set of edge weights. subset of For the first The node and the first Edges between nodes The weights are the set of edge weights. subset of ,in For nodes With nodes European distance, For distance scale parameters, The sparse regularization coefficients control the sparse coefficient vector of the sound field. The sparsity, These are the global Laplace smoothing weights. For the first The set of neighboring nodes of a node.
4. The sensor network sound field reconstruction method based on graph signals and distributed optimization as described in claim 3, characterized in that: When solving the objective function, first reconstruct the objective function by introducing auxiliary variables and setting constraints: For each edge Introduce a pair of auxiliary variables and Set constraints as , ,and For the first Each node wants its neighboring nodes to... The status I saw regarding myself, and it was the [number]th [item / section]. Auxiliary variables for each node, For the first Each node wants its neighboring nodes to... The status I see about myself, and the first Auxiliary variables for each node; wherein, the auxiliary variables and The initial value is based on the node. and Local observation data and The weighted average construction, i.e. and initial value Alternatively, the initial values of auxiliary variables can be estimated based on the graph topology. The reconstructed objective function is expressed as follows: ； ； 。 5. The sensor network sound field reconstruction method based on graph signals and distributed optimization as described in claim 4, characterized in that: The constraints on the reconstructed objective function introduce dual variables and construct an augmented Lagrangian function, including: Constraints Introducing dual variables ,and For the first The node to the first The augmented Lagrangian function, representing the dual variables of directed edges at n nodes, is as follows: ； in, Represent the Lagrange function, This is the penalty parameter.
6. The sensor network sound field reconstruction method based on graph signals and distributed optimization as described in claim 5, characterized in that: The method of using alternating direction multipliers to iteratively update the sparse coefficient vector, auxiliary variables, and dual variables of the sound field at each node until the outer iteration termination condition is met includes: First, initialize the sparse coefficient vector of the sound field, auxiliary variables, and dual variables at each node to 0; The outer iteration updates of all nodes are executed in parallel, and during each outer iteration update of each node, the sparse coefficient vector of the sound field, the auxiliary variables, and the dual variables are updated sequentially.
7. The sensor network sound field reconstruction method based on graph signals and distributed optimization as described in claim 6, characterized in that: The formula for updating the sparse coefficient vector of the sound field during one outer iteration is as follows: （1）； in, Indicates the first During the next outer iteration process, the first The update results of the sparse coefficient vector of the sound field at each node. Indicates the first During the next outer iteration process, the first Auxiliary variables for each node, Indicates the first During the next outer iteration process, the first The node to the first The dual variables of the directed edges of each node; Combining the linear and quadratic terms of formula (1) and completing the square coordination, formula (1) is equivalent to: （2）； Formula (2) is solved using a fast iterative shrinkage threshold algorithm: Perform sparse coefficient vector of sound field The process involves one iteration, and this iteration is called the inner iteration: In one inner iteration, the sparse coefficient vector of the sound field is updated as follows: ； in, ； ； ； ； ； in, For the first The first step in the inner layer iteration process The update results of the sparse coefficient vector of the sound field at each node. For the first Momentum point during the inner iteration process. For function gradient, For the first Smoothing terms in the inner iteration process. The momentum coefficient, For the first Momentum parameters during the inner-layer iteration process. For the first The inner iteration step size of each node, For the first The intermediate parameters of each node, It is a matrix spectral norm, For the gradient descent step, For the first The number of neighboring nodes of a node. This is a component-wise soft thresholding operator; The inner iteration employs an accelerated gradient strategy, where the momentum parameter... Dynamically adjust based on local gradient changes: when Reset when the value exceeds the preset threshold. To avoid oscillation, otherwise press Update; Inner iteration step size A backtracking search mechanism is used: the initial step size is In each inner iteration, if Then shrink the inner iteration step size , until the Armijo condition is met; Adaptive adjustment is achieved through backtracking search, with an initial step size of [value missing]. However, in each inner iteration, the function dynamically shrinks or expands based on the effect of local gradient descent to ensure that the objective function decreases monotonically. When the number of inner iterations reaches the maximum When the time comes, terminate the inner iteration and output the result. For the last inner iteration That is, the first During the next outer iteration process, the first The update result of the sparse coefficient vector of the sound field at each node is the result of the last inner iteration in the current inner iteration. ,in , All are preset values.
8. The sensor network sound field reconstruction method based on graph signals and distributed optimization as described in claim 7, characterized in that: In one outer iteration, the update obtained in the current outer iteration is... It is sent to all neighboring nodes and used to update auxiliary variables, and the update formula for the auxiliary variables is as follows: （3）； Formula (3) is about , The convex problem has a unique closed-form solution. By setting the gradient of equation (3) to zero, we obtain a system of linear equations, as follows: right Find the partial derivative and set it to zero: ； get: （4）； right Find the partial derivative and set it to zero: ； get: （5）； Combining formulas (4) and (5), we obtain a system of linear equations: ； Solving for: ； ； in, For the first During the next outer iteration process, the first Auxiliary variables for each node, For the first During the next outer iteration process, the first Auxiliary variables for each node, It is the identity matrix; when and hour, ,at this time: 。 9. The sensor network sound field reconstruction method based on graph signals and distributed optimization as described in claim 8, characterized in that: In one outer iteration, the update obtained in the current outer iteration is... and To update the dual variable, the update formula for the dual variable is as follows: ； in, For the first During the next outer iteration process, the first The node to the first The dual variables of the directed edges of each node.
10. The sensor network sound field reconstruction method based on graph signals and distributed optimization as described in claim 8, characterized in that: When the outer iteration termination condition is met, the sparse coefficient vector of the sound field at each node corresponding to the last outer iteration is taken as the final sparse coefficient vector of the sound field at each node. and through Reconstruct the sound field at each node; The outer iteration termination condition is: when the constraint residual is less than the first threshold. And the dual residual is less than the second threshold. ,Right now: ,and If the outer iteration terminates, then the outer iteration terminates. Alternatively, the outer iteration will terminate when the number of outer iterations reaches the preset maximum number.