基于块A~＊正交匹配追踪的多传感器数据联合重构算法

A Joint Reconstruction Algorithm for Multiple Sensor Data Based on Block A＊ Orthogonal Matching Pursuit

针对A*正交匹配追踪(A*OMP)算法计算复杂高,且不能利用信号的结构稀疏性这一缺陷,该文提出了块A*OMP算法并将其用于解决分布式压缩感知中的信号联合重构问题。该算法用原子块取代单个原子作为搜索树中的节点,在计算路径代价时用搜索树中所有路径的最大长度取代信号的稀疏度。然后在块A*OMP算法的基础上,选择与残差矩阵投影误差最小的原子块作为新的节点,得到了一种用于解决MMV(Multiple Measurement Vector,MMV)问题的块A*OMP算法,并利用该算法对相邻区域内的多个传感器所测的温度信号进行了联合重构。实验结果表明,该算法的重构性能优于MMV正交匹配追踪(OMPMMV)算法。

Considering the disadvantage of the high complexity and ignoring signal＇s structural sparsity in A＊ Orthogonal Matching Pursuit （A＊OMP） algorithm, a block A＊OMP algorithm is proposed for block-sparse signals, and it is improved to solve the joint reconstruction problem for multiple signals in distributed compressed sensing. In the proposed algorithm, the single atom is replaced by a block that is composed of several atoms, and the sparsity is replaced by the maximum length of all the paths on the search tree when calculating the path cost. Then on the basis of block A＊OMP algorithm, a block A＊OMP algorithm for Multiple Measurement Vector （MMV） problem is presented by projecting all blocks onto the residual matrix and selecting the block with the smallest projection error as a new node. With this algorithm, the temperature signals which are measured by sensors in the adjacent region are jointly reconstructed perfectly. Experiments show that the reconstruction performance of this algorithm outperform Orthogonal Matching Pursuit for MMV （OMPMMV） algorithm.