CN106374935A

CN106374935A - A Block Sparse Signal Reconstruction Method Using Adaptive Coupling Parameters

Info

Publication number: CN106374935A
Application number: CN201610751105.XA
Authority: CN
Inventors: 段惠萍; 崔虹雨; 殷允杰; 刘豪
Original assignee: University of Electronic Science and Technology of China
Current assignee: University of Electronic Science and Technology of China
Priority date: 2016-08-29
Filing date: 2016-08-29
Publication date: 2017-02-01
Anticipated expiration: 2036-08-29
Also published as: CN106374935B

Abstract

The invention belongs to the field of compressed sensing, and provides a block sparse signal reconstruction method using adaptive coupling parameters, which is used for improving the accuracy of block sparse reconstruction under the condition of unknown block structure. The present invention first introduces adaptive coupling parameters β ₁ and β ₂ , establishes a new coupling layered Bayesian model, and estimates block sparse signals according to the maximum a posteriori probability criterion; then applies the expectation maximization criterion to estimate hyperparameters and coupling parameters ; Then re-estimate the block sparse signal according to the hyperparameters and coupling parameters; iterate until the stop condition is met to obtain the reconstructed block sparse signal. The present invention introduces adaptive coupling parameters, so that the coupling degree between each hyperparameter is controlled by different coupling coefficients, thereby encouraging the aggregation of non-zero signal elements to form a block structure with higher flexibility, and significantly improving the accuracy of block sparse reconstruction Spend.

Description

A Block Sparse Signal Reconstruction Method Using Adaptive Coupling Parameters

技术领域technical field

本发明属于压缩感知领域，针对具有未知块结构的块稀疏信号重构问题，提出了一种采用自适应耦合参数的块稀疏信号重构方法。The invention belongs to the field of compressed sensing, and aims at the reconstruction problem of block sparse signals with unknown block structure, and proposes a block sparse signal reconstruction method using adaptive coupling parameters.

技术背景technical background

稀疏信号重构是压缩感知领域的一个重要研究课题。传统的稀疏重构理论通常假定稀疏信号中非零项的分布都是随机且任意的，但是实际应用中，稀疏信号往往具有一定的块结构特征，称为块稀疏信号。针对具有块结构的稀疏信号重构问题，已有方法中，块正交匹配追踪(Block Orthogonal Matching Pursuit，OMP)方法、混合l₂/l₁范数最小化(Mixed l₂/l₁ Norm Minimization)方法等均需要已知块的大小或者分布等信息，而这些信息在实际的信号重构中往往是未知的。针对具有未知块结构的情况，扩展的块稀疏贝叶斯(Expanded Block Sparse Learning，EBSBL)方法假设信号由具有相同结构的块堆叠而成，并且每个块都服从高斯分布，将信号的后验协方差矩阵扩展为块对角阵结构，从而应用传统的块贝叶斯方法进行稀疏重构；模式耦合的稀疏贝叶斯(Pattern Coupled SparseBayesian Learning，PCSBL)方法使用相互耦合的超参数来控制信号元素，使其产生块稀疏的结构，即信号元素的稀疏性不仅与其自身的超参数有关，而且还受临近的超参数影响，但是该方法只引入一个固定的耦合参数来控制信号元素受相邻元素的影响程度，使其性能受到局限。Sparse signal reconstruction is an important research topic in the field of compressed sensing. Traditional sparse reconstruction theory usually assumes that the distribution of non-zero items in sparse signals is random and arbitrary, but in practical applications, sparse signals often have certain block structure characteristics, which are called block sparse signals. For the sparse signal reconstruction problem with a block structure, among the existing methods, Block Orthogonal Matching Pursuit (OMP) method, Mixed l ₂ /l ₁ Norm Minimization (Mixed l ₂ /l ₁ Norm Minimization ) methods, etc., all require information such as the size or distribution of known blocks, which are often unknown in actual signal reconstruction. For the case of unknown block structure, the Expanded Block Sparse Learning (EBSBL) method assumes that the signal is stacked by blocks with the same structure, and each block obeys a Gaussian distribution, and the posterior of the signal The covariance matrix is extended to a block diagonal matrix structure, thereby applying the traditional block Bayesian method for sparse reconstruction; the pattern coupled sparse Bayesian (Pattern Coupled SparseBayesian Learning, PCSBL) method uses mutually coupled hyperparameters to control the signal elements, so that it produces a block-sparse structure, that is, the sparsity of signal elements is not only related to its own hyperparameters, but also affected by adjacent hyperparameters, but this method only introduces a fixed coupling parameter to control the influence of signal elements by adjacent hyperparameters. The extent to which an element is affected makes its performance limited.

发明内容Contents of the invention

本发明的目的在于提供一种采用自适应耦合参数的块稀疏信号重构方法，用于针对在未知块结构情况下提高块稀疏重构的精确度。本发明通过建立一个新的耦合分层贝叶斯模型，引入多个自适应耦合参数，使每个超参数之间的耦合程度受不同耦合系数控制，从而以更高的灵活性来鼓励非零信号元素聚集形成块结构，提高块稀疏重构的精确度。The purpose of the present invention is to provide a block sparse signal reconstruction method using adaptive coupling parameters, which is used to improve the accuracy of block sparse reconstruction in the case of unknown block structure. The present invention introduces multiple adaptive coupling parameters by establishing a new coupling hierarchical Bayesian model, so that the coupling degree between each hyperparameter is controlled by different coupling coefficients, thereby encouraging non-zero hyperparameters with higher flexibility The signal elements are aggregated to form a block structure, which improves the accuracy of block sparse reconstruction.

为实现上述目的，本发明采用的解决方案为：To achieve the above object, the solution adopted by the present invention is:

本发明的具体步骤为：Concrete steps of the present invention are:

一种采用自适应耦合参数的块稀疏信号重构方法，包括以下步骤：A block sparse signal reconstruction method using adaptive coupling parameters, comprising the following steps:

步骤1、设定接收信号为：y＝Ax+n，其中，A表示传感矩阵，x表示块稀疏信号，n表示高斯噪声；Step 1. Set the received signal as: y=Ax+n, where A represents the sensing matrix, x represents the block sparse signal, and n represents Gaussian noise;

初始化超参数α、耦合参数β₁与β₂以及噪声方差λ^-1，其中，α＝[α₁,α₁,…,α_n]，x中的每个元素服从高斯分布：Initialize hyperparameter α, coupling parameters β ₁ and β ₂ and noise variance λ ^-1 , where α=[α ₁ ,α ₁ ,…,α _n ], Each element in x follows a Gaussian distribution:

$p p (({x x}_{i i} | | {α α}_{i i},, {α α}_{i i - - 11},, {α α}_{i i + + 11},, {β β}_{i i - - 11}^{i i},, {β β}_{i i + + 11}^{i i})) = = N N (({x x}_{i i} | | 00,, {(({α α}_{i i} + + {β β}_{i i - - 11}^{i i} {α α}_{i i - - 11} + + {β β}_{i i + + 11}^{i i} {α α}_{i i + + 11}))}^{- - 11})),,$

其中，i＝1,2,…,n，块稀疏信号x有n个元素；Wherein, i=1,2,...,n, the block sparse signal x has n elements;

高斯噪声n服从均值为0、协方差矩阵为λ^-1I的高斯分布，则推出x的后验均值为：μ＝λΣA^Ty，协方差矩阵为：Σ＝(λA^TA+S)^-1，其中S是对角矩阵：Gaussian noise n obeys the Gaussian distribution with mean value 0 and covariance matrix λ ^-1 I, then the posterior mean of x is: μ= ^λΣAT y, and the covariance matrix is: Σ=(λA ^T A+S) ^{- 1} , where S is the diagonal matrix:

$S S = = d d i i a a g g (({α α}_{11} + + {β β}_{22}^{11} {α α}_{22},, {α α}_{22} + + {β β}_{11}^{22} {α α}_{11} + + {β β}_{33}^{22} {α α}_{33},, ... ...,, {α α}_{n no} + + {β β}_{n no - - 11}^{n no} {α α}_{n no - - 11}));;$

根据最大后验准则得到稀疏信号x的估计为 According to the maximum a posteriori criterion, the sparse signal x can be estimated as

步骤2、根据期望最大化准则估计超参数和耦合参数：Step 2. Estimate hyperparameters and coupling parameters according to the expectation maximization criterion:

${α α}_{i i} = = \frac{{κ κ}_{α α}}{0.5 0.5 (({ω ω}_{i i} + + {β β}_{i i}^{i i + + 11} {ω ω}_{i i + + 11} + + {β β}_{i i}^{i i - - 11} {ω ω}_{i i - - 11})) + + b b}$

${β β}_{i i}^{i i + + 11} = = \frac{{κ κ}_{{β β}_{11}}}{{α α}_{i i} {ω ω}_{i i + + 11}}$

${β β}_{i i}^{i i - - 11} = = \frac{{κ κ}_{{β β}_{22}}}{{α α}_{i i} {ω ω}_{i i - - 11}}$

$λ λ = = \frac{m m + + 22 ((c c - - 11))}{| | | | y the y - - A A μ μ | | {| |}_{22}^{22} + + T T r r (({ΣA ΣA}^{T T} A A)) + + 22 d d},,$

其中，κ_α∈(0.5,2)，a，b，c，d都是α和λ所服从的伽马分布中的参数，m为测量值个数；in, κ _α ∈ (0.5,2), a, b, c, d are all parameters in the gamma distribution that α and λ obey, and m is the number of measured values;

步骤3、根据步骤2估计的参数集合{α,β₁,β₂,λ}和步骤1得到的公式重新估计块稀疏信号，得到 Step 3. According to the parameter set {α, β ₁ , β ₂ , λ} estimated in step 2 and the formula obtained in step 1 Re-estimating the block-sparse signal, we get

步骤4、判断是否小于指定门限或者迭代次数是否达到指定次数，若是则输出重构信号否则回到步骤2继续迭代。Step 4. Judgment Whether it is less than the specified threshold or whether the number of iterations reaches the specified number, if so, output the reconstructed signal Otherwise, go back to step 2 and continue iterating.

本发明首先引入自适应的耦合参数β₁与β₂，建立一个新的耦合分层贝叶斯模型，根据最大后验概率准则估计块稀疏信号；然后应用期望最大化准则估计超参数和耦合参数；再根据超参数和耦合参数重新估计块稀疏信号；迭代直至满足停止条件即得到重构块稀疏信号。本发明引入自适应耦合参数，使每个超参数之间的耦合程度受不同耦合系数控制，从而以更高的灵活性来鼓励非零信号元素聚集形成块结构，显著提高块稀疏重构的精确度。The present invention first introduces adaptive coupling parameters β ₁ and β ₂ , establishes a new coupling layered Bayesian model, and estimates block sparse signals according to the maximum a posteriori probability criterion; then applies the expectation maximization criterion to estimate hyperparameters and coupling parameters ; Then re-estimate the block sparse signal according to the hyperparameters and coupling parameters; iterate until the stop condition is met to obtain the reconstructed block sparse signal. The present invention introduces adaptive coupling parameters, so that the coupling degree between each hyperparameter is controlled by different coupling coefficients, thereby encouraging the aggregation of non-zero signal elements to form a block structure with higher flexibility, and significantly improving the accuracy of block sparse reconstruction Spend.

附图说明Description of drawings

图1为本发明提供采用自适应耦合参数的块稀疏信号重构方法的流程示意图。FIG. 1 is a schematic flowchart of a block sparse signal reconstruction method using adaptive coupling parameters provided by the present invention.

图2为本发明与PCSBL方法和EBSBL方法的均方根误差(Root Mean Square Error，R MSE)随信号稀疏度K变化的比较图。Fig. 2 is a comparison diagram of the root mean square error (Root Mean Square Error, R MSE) of the present invention, the PCSBL method and the EBSBL method as a function of signal sparsity K.

图3为本发明与PCSBL方法和EBSBL方法的均方根误差(Root Mean Square Error，R MSE)随测量值个数m变化的比较图。Fig. 3 is a comparison diagram of the root mean square error (Root Mean Square Error, R MSE) of the present invention and the PCSBL method and the EBSBL method as the number of measured values changes.

具体实施方式detailed description

下面结合具体实施例和附图对本发明做进一步详细说明，但本发明并不局限于实施例。The present invention will be described in further detail below in conjunction with specific embodiments and drawings, but the present invention is not limited to the embodiments.

本发明的基本思想是建立一个新的耦合分层贝叶斯模型，引入多个自适应耦合参数，使信号先验分布的超参数之间相互耦合，以更高的灵活性来鼓励非零信号元素聚集形成块结构。The basic idea of the present invention is to establish a new coupled hierarchical Bayesian model, introduce multiple adaptive coupling parameters, and make the hyperparameters of the signal prior distribution be coupled with each other to encourage non-zero signals with higher flexibility Elements are aggregated to form a block structure.

步骤1、根据观测数据、假设模型及初始化的超参数和耦合参数对块稀疏信号进行估计；Step 1. Estimate the block sparse signal according to the observed data, hypothetical model, and initialized hyperparameters and coupling parameters;

假设接收信号为：y＝Ax+n，其中，A∈R^m×n表示传感矩阵，y∈R^m×1表示接收信号，x∈R^n×1表示块稀疏信号，n∈R^m×1表示高斯噪声；Suppose the received signal is: y=Ax+n, where A∈R ^m×n represents the sensing matrix, y∈R ^m×1 represents the received signal, x∈R ^n×1 represents the block sparse signal, n∈R ^{m× 1} means Gaussian noise;

假设信号x中的每个元素服从高斯分布：Assume that each element in the signal x follows a Gaussian distribution:

$p p (({x x}_{i i} | | {α α}_{i i},, {α α}_{i i - - 11},, {α α}_{i i + + 11},, {β β}_{i i - - 11}^{i i},, {β β}_{i i + + 11}^{i i})) = = N N (({x x}_{i i} | | 00,, {(({α α}_{i i} + + {β β}_{i i - - 11}^{i i} {α α}_{i i - - 11} + + {β β}_{i i + + 11}^{i i} {α α}_{i i + + 11}))}^{- - 11}))$

其中i＝1,2,…,n，α_i为传统稀疏重构方法中控制x_i稀疏性的超参数，其概率密度服从伽马分布：在本发明中，控制x_i稀疏性的变量不仅仅是α_i，其稀疏性还受到相邻系数的超参数α_i-1和α_i+1的影响，分别为α_i-1和α_i+1对α_i的超参数耦合系数，设置超参数耦合系数服从0到1的均匀分布；这样块稀疏信号中元素x_i的稀疏性便由来决定，即当趋于无穷的时候，x_i的值为0；设置向量α＝[α₁,α₁,…,α_n]，和 Where i=1,2,...,n, α _i is the hyperparameter controlling the sparsity of _xi in the traditional sparse reconstruction method, and its probability density obeys the gamma distribution: In the present invention, the variable controlling the sparsity of x _i is not only α _i , its sparsity is also affected by the hyperparameters α _i-1 and α _i+1 of adjacent coefficients, are the hyperparameter coupling coefficients of α _i-1 and α _i+1 to α _i respectively, and set the hyperparameter coupling coefficient to obey the uniform distribution from 0 to 1; in this way, the sparsity of element x _i in the block sparse signal is given by to decide when When it tends to infinity, the value of x _i is 0; set the vector α=[α ₁ ,α ₁ ,…,α _n ], and

假设噪声n服从均值为0，协方差矩阵为λ^-1I的高斯分布，根据接收信号的数学模型，可以得到p(y|x；λ)服从均值为Ax，协方差矩阵为λ^-1I的高斯分布，即p(y|x；λ)＝N(Ax,λ^-1I)；根据这些条件便可以得到x的后验概率密度为p(x|y)＝N(μ,Σ)，其中Assuming that the noise n obeys the Gaussian distribution with the mean value of 0 and the covariance matrix of λ ^-1 I, according to the mathematical model of the received signal, it can be obtained that p(y|x; λ) obeys the mean value of Ax and the covariance matrix is λ ^-1 I Gaussian distribution of x, that is, p(y|x;λ)=N(Ax,λ ^-1 I); according to these conditions, the posterior probability density of x can be obtained as p(x|y)=N(μ,Σ) ,in

μ＝λΣA^Ty，Σ＝(λA^TA+S)^-1，μ=λΣA ^T y, Σ=(λA ^T A+S) ^-1 ,

S是一个对角矩阵： S is a diagonal matrix:

步骤2、根据期望最大化准则估计超参数和耦合参数： Step 2. Estimate hyperparameters and coupling parameters according to the expectation maximization criterion:

忽略与超参数不相关的系数，Q中的第一项可以重新改写为：Ignoring coefficients that are not correlated with hyperparameters, the first term in Q can be rewritten as:

$\begin{matrix} {Q Q}_{11} = = {E E.}_{x x | | y the y} {{ln ln [[p p ((α α)) p p (({β β}_{11})) p p (({β β}_{22})) p p ((x x | | α α,, {β β}_{11},, {β β}_{22}))]]}} \\ = = {Σ Σ}_{i i = = 11}^{n no} ((a a {lnα lnα}_{i i} - - {bα bα}_{i i} + + \frac{11}{22} ln ln (({α α}_{i i} + + {β β}_{i i - - 11}^{i i} {α α}_{i i - - 11} + + {β β}_{i i + + 11}^{i i} {α α}_{i i + + 11})) \\ - - \frac{11}{22} (({α α}_{i i} + + {β β}_{i i - - 11}^{i i} {α α}_{i i - - 11} + + {β β}_{i i + + 11}^{i i} {α α}_{i i + + 11})) (({μ μ}_{i i}^{22} + + {Σ Σ}_{i i,, i i})))) \end{matrix}$

其中，μ_i为均值μ的第i个元素，Σ_i,i为协方差矩阵Σ对角线上的第i个元素，利用λ的概率密度p(λ)＝Γ^-1(c)d^cλ^c-1e^-dλ，Q中的第二项可以表示为：Among them, μ _i is the i-th element of the mean value μ, Σ _i,i is the i-th element on the diagonal of the covariance matrix Σ, using the probability density of λ p(λ)=Γ ^-1 (c)d ^c λ ^c-1 e ^-dλ , the second term in Q can be expressed as:

$\begin{matrix} {Q Q}_{22} = = {E E.}_{x x | | y the y} {{l l n no [[p p ((y the y | | x x,, λ λ)) p p ((λ λ))]]}} \\ = = ((\frac{m m}{22} + + c c - - 11)) ln ln λ λ - - \frac{λ λ}{22} {E E.}_{x x | | y the y} [[| | | | y the y - - A A x x | | {| |}_{22}^{22}]] - - d d λ λ \end{matrix}$

将Q₁分别对α_i，和求偏导，得到的偏导数为：Put Q ₁ against α _i , respectively, and Find the partial derivative, and the obtained partial derivative is:

$\begin{matrix} \frac{\partial \partial {Q Q}_{11}}{\partial \partial {α α}_{i i}} = = \frac{a a}{{α α}_{i i}} - - b b + + \frac{11}{22 (({α α}_{i i} + + {β β}_{i i - - 11}^{i i} {α α}_{i i - - 11} + + {β β}_{i i + + 11}^{i i} {α α}_{i i + + 11}))} - - \frac{{ω ω}_{i i}}{22} \\ + + \frac{{β β}_{i i}^{i i - - 11}}{22 (({α α}_{i i - - 11} + + {β β}_{i i - - 22}^{i i - - 11} {α α}_{i i - - 22} + + {β β}_{i i}^{i i - - 11} {α α}_{i i}))} - - \frac{{ω ω}_{i i - - 11}}{22} {β β}_{i i}^{i i - - 11} \\ + + \frac{{β β}_{i i}^{i i + + 11}}{22 (({α α}_{i i + + 11} + + {β β}_{i i}^{i i + + 11} {α α}_{i i} + + {β β}_{i i + + 22}^{i i + + 11} {α α}_{i i + + 22}))} - - \frac{{ω ω}_{i i + + 11}}{22} {β β}_{i i}^{i i + + 11} \\ \frac{\partial \partial {Q Q}_{11}}{\partial \partial {β β}_{i i}^{i i - - 11}} = = \frac{{α α}_{i i}}{22 (({α α}_{i i - - 11} + + {β β}_{i i - - 22}^{i i - - 11} {α α}_{i i - - 22} + + {β β}_{i i}^{i i - - 11} {α α}_{i i}))} - - \frac{{ω ω}_{i i - - 11}}{22} {α α}_{i i} \\ \frac{\partial \partial {Q Q}_{11}}{\partial \partial {β β}_{i i}^{i i + + 11}} = = \frac{{α α}_{i i}}{22 (({α α}_{i i + + 11} + + {β β}_{i i}^{i i + + 11} {α α}_{i i} + + {β β}_{i i + + 22}^{i i + + 11} {α α}_{i i + + 22}))} - - \frac{{ω ω}_{i i + + 11}}{22} {α α}_{i i} \end{matrix}$

其中，使这三个偏导数为0，运用不等式和得到α_i，和的取值范围为：in, To make these three partial derivatives 0, apply the inequality and get α _i , and The value range of is:

$\frac{a a}{0.5 0.5 (({ω ω}_{i i} + + {β β}_{i i}^{i i + + 11} {ω ω}_{i i + + 11} + + {β β}_{i i}^{i i - - 11} {ω ω}_{i i - - 11})) + + b b} < < {α α}_{i i} < < \frac{a a + + 1.5 1.5}{0.5 0.5 (({ω ω}_{i i} + + {β β}_{i i}^{i i + + 11} {ω ω}_{i i + + 11} + + {β β}_{i i}^{i i - - 11} {ω ω}_{i i - - 11})) + + b b}$

$00 < < {β β}_{i i}^{i i - - 11} < < \frac{11}{{ω ω}_{i i - - 11} {α α}_{i i}}$

$00 < < {β β}_{i i}^{i i + + 11} < < \frac{11}{{ω ω}_{i i + + 11} {α α}_{i i}}$

经过实验，本实施例选取a＝0.5，b＝10^-4，并且使用如下公式更新α_i，和 After experiments, this embodiment selects a=0.5, b=10 ^-4 , and uses the following formula to update α _i , and

${β β}_{i i}^{i i - - 11} = = \frac{{κ κ}_{{β β}_{11}}}{{ω ω}_{i i - - 11} {α α}_{i i}}$

${β β}_{i i}^{i i + + 11} = = \frac{{κ κ}_{{β β}_{22}}}{{ω ω}_{i i + + 11} {α α}_{i i}}$

其中，κ_α∈(0.5,2)， where, κ _α ∈ (0.5,2),

将Q₂对λ求导数并且使导数为0，求出λ的值为Take the derivative of Q ₂ to λ and make the derivative 0, and find the value of λ

$λ λ = = \frac{m m + + 22 ((c c - - 11))}{| | | | y the y - - A A μ μ | | {| |}_{22}^{22} + + T T r r (({ΣA ΣA}^{T T} A A)) + + 22 d d}$

其中，参数c与d都取10^-4；Among them, the parameters c and d both take 10 ^-4 ;

本发明的效果通过仿真结果图2和图3进行说明：Effect of the present invention is illustrated by simulation result Fig. 2 and Fig. 3:

仿真试验中将α初始化为1，将β₁和β₂初始化为0，噪声的方差初始化为λ^-1＝1；设置信号元素的个数n为100；并且固定非零块的个数L为3，信噪比SNR为2dB；进行500次蒙特卡罗实验。用均方根误差RMSE来比较每个方法的性能，其定义为：In the simulation experiment, α is initialized to 1, β ₁ and β ₂ are initialized to 0, and the variance of noise is initialized to λ ^-1 = 1; the number n of signal elements is set to 100; and the number L of fixed non-zero blocks is 3. The signal-to-noise ratio (SNR) is 2dB; conduct 500 Monte Carlo experiments. The performance of each method is compared with the root mean square error RMSE, which is defined as:

其中为第k次蒙特卡罗实验中真实信号的第i个元素； in is the i-th element of the real signal in the k-th Monte Carlo experiment;

图2和图3分别是本发明与其他方法(PCSBL方法和EBSBL方法)的均方根误差随信号稀疏度K和测量值个数m变化的比较图，从图中可以看出，相较于近期提出的块稀疏重构方法，本发明具有最小的均方根误差，说明本发明相较其他方法具有更高的重构精度。Fig. 2 and Fig. 3 are the comparison figure that the root mean square error of the present invention and other methods (PCSBL method and EBSBL method) changes with signal sparseness K and the number of measured values m respectively, as can be seen from the figure, compared with In the block sparse reconstruction method recently proposed, the present invention has the smallest root mean square error, indicating that the present invention has higher reconstruction accuracy than other methods.

以上所述为本发明具体实施方式，本说明书中所公开的任一特征，除非特别叙述，均可被其他等效或具有类似目的的替代特征加以替换；所公开的所有特征、或所有方法或过程中的步骤，除了互相排斥的特征和/或步骤以外，均可以任何方式组合。The above is a specific implementation of the present invention, and any feature disclosed in this specification, unless specifically stated, can be replaced by other equivalent or alternative features with similar purposes; all disclosed features, or all methods or The steps of the processes may be combined in any way, except for mutually exclusive features and/or steps.

Claims

1. A block sparse signal reconstruction method employing adaptive coupling parameters, comprising the following steps:

Step 1. Set the received signal as: y=Ax+n, where A represents the sensing matrix, x represents the block sparse signal, and n represents Gaussian noise;

Initialize hyperparameter α, coupling parameters β ₁ and β ₂ and noise variance λ ^-1 , where α=[α ₁ ,α ₁ ,…,α _n ], Each element in x follows a Gaussian distribution:

p p (({x x}_{i i} | | {α α}_{i i},, {α α}_{i i - - 11},, {α α}_{i i + + 11},, {β β}_{i i - - 11}^{i i},, {β β}_{i i + + 11}^{i i})) = = N N (({x x}_{i i} | | 00,, {(({α α}_{i i} + + {β β}_{i i - - 11}^{i i} {α α}_{i i - - 11} + + {β β}_{i i + + 11}^{i i} {α α}_{i i + + 11}))}^{- - 11})),,

Wherein, i=1,2,...,n, the block sparse signal x has n elements;

Gaussian noise n obeys the Gaussian distribution with mean value 0 and covariance matrix λ ^-1 I, then the posterior mean of x is: μ= ^λΣAT y, and the covariance matrix is: Σ=(λA ^T A+S) ^{- 1} , where S is the diagonal matrix:

S S = = d d i i a a g g (({α α}_{11} + + {β β}_{22}^{11} {α α}_{22},, {α α}_{22} + + {β β}_{11}^{22} {α α}_{11} + + {β β}_{33}^{22} {α α}_{33},, ... ...,, {α α}_{n no} + + {β β}_{n no - - 11}^{n no} {α α}_{n no - - 11}));;

According to the maximum a posteriori criterion, the sparse signal x can be estimated as

Step 2. Estimate hyperparameters and coupling parameters according to the expectation maximization criterion:

{α α}_{i i} = = \frac{{κ κ}_{α α}}{0.5 0.5 (({s the s}_{i i} + + {β β}_{i i}^{i i + + 11} {s the s}_{i i + + 11} + + {β β}_{i i}^{i i - - 11} {s the s}_{i i - - 11})) + + b b}

{β β}_{i i}^{i i + + 11} = = \frac{{κ κ}_{{β β}_{11}}}{{α α}_{i i} {s the s}_{i i + + 11}}

{β β}_{i i}^{i i - - 11} = = \frac{{κ κ}_{{β β}_{22}}}{{α α}_{i i} {s the s}_{i i - - 11}}

λ λ = = \frac{m m + + 22 ((c c - - 11))}{| | | | y the y - - A A μ μ | | {| |}_{22}^{22} + + T T r r (({ΣA ΣA}^{T T} A A)) + + 22 d d},,

in, κ _α ∈ (0.5,2), a, b, c, and d are all parameters in the gamma distribution that α and λ obey, and m is the number of measured values;

Step 3. According to the parameter set {α, β ₁ , β ₂ , λ} estimated in step 2 and the formula obtained in step 1 Re-estimating the block-sparse signal, we get

Step 4. Judgment Whether it is less than the specified threshold or whether the number of iterations reaches the specified number, if so, output the reconstructed signal Otherwise, go back to step 2 and continue iterating.