非均匀块稀疏信号的压缩采样与盲重构算法

摘要

The lowest compressive sampling rate for non-uniform block sparse signals and the decay property of restricted isometry constant of measure matrix is theoretically analyzed.A blind recovery algorithm without knowing the order and distribution of blocks is proposed.The algorithm improves the estimation precision of nonzero values positions by dividing the block sparse signal uniformly for several times according to successive decreasing block length,and then eliminating the zero value positions in the uniform blocks using Orthogonal Matching Pursuit (OMP) method,which leads to a better recovery result.The performance of the blind recovery algorithm is analyzed and simulation results verify the effectiveness and practicality further.%该文对非均匀块稀疏信号的压缩采样速率下限进行了分析,并对测量矩阵的约束等距常数衰减特性进行了理论证明.在此基础上,提出了一种块稀疏阶数和块分布未知情况下的非均匀块稀疏信号盲重构算法,按照逐次递减的块长度,对非均匀块稀疏信号进行多次均匀切割,利用正交匹配追踪算法逐次剔除均匀块中的零值位置,从而精确估计信号中非零块位置,实现信号的准确重构.理论分析了算法的性能,仿真实验进一步验证了算法的有效性和实用性.