不确定量测联合信号重构的稳定性

STABILITY OF JOINTLY SPARSE SIGNAL RECOVERY WITH UNCERTAIN MEASUREMENTS

研究了分布式压缩感知(Distributed Compressed Sensing,DCS)理论对联合稀疏信号进行联合重构的稳定性问题.文中讨论的联合稀疏信号模型中含有两个近似稀疏信号,且信号的量测过程中带有噪声.证明利用分布式压缩感知思想对近似稀疏的联合稀疏信号的联合稀疏重构具有稳定性,刻画了重构信号的误差,并与单个信号的稀疏重构导致的误差进行了比较,证明了在一定条件下,利用分布式压缩感知思想对信号进行联合重构的误差界小于单个信号重构的误差界.

This paper considers the stability of jointly recovery for jointly sparse signals with distributed compressed sensing theory. The jointly sparse model studied in this paper contains two approximate sparse signals with approximate sparse common components and innovations. The measurements to the signals contain noises. Inspired by the stability of single-signal recovery, this paper characterizes the error of jointly signal recovery and makes a comparison with the case of single-signal recovery. Furthermore, the condition is demonstrated jointly recovery is smaller than that induced that under which the error induced by by single-signal recovery.