基于多观测向量序列降采样恢复的稀疏矩阵重构

二维稀疏信号的重构可以通过解多观测向量的稀疏表示问题来实现。然而,当各向量的稀疏结构不同时,将稀疏恢复算法拓展到多观测向量模型的方法将不再有效。提出了一种序列降采样重构的方法用于实现稀疏矩阵的重构。该方法通过构造降采样矩阵,大幅降低稀疏矩阵信号的稀疏度,再通过多观测向量序列观测和恢复,完成对稀疏矩阵的重构。理论分析表明,所提方法能够实现对高稀疏度矩阵的高概率重构。实验表明,所提算法能够有效地实现二维稀疏信号和图像重构。

Sparse matrix reconstruction based on sequential down-sampling recovery of multiple measurement vectors

The two-dimensional (2D) sparse signals can be reconstructed by solving a sparse representation problem for multiple measurement vectors (MMVs). However, the extension of the sparse recovery algorithms to the MMV cases may be inefficient if the vectors do not have the same sparsity profile. A sequential down-sampling recovery (SDR) algorithm is proposed to reconstruct the 2D sparse matrix. This method can reduce the sparsity of the signal by constructing down-sampling matrices, and then reconstruct the sparse matrix by sequential observations and reconstructions. Theoretical analysis indicates that the sparse matrix with high sparsity level can be reconstructed with high probability. Experimental results verify the effectiveness of the proposed method in 2D sparse signal and image reconstruction.