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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.
The stability problem of joint reconstruction of joint sparse signals is studied by Distributed Compressed Sensing (DCS) theory.The joint sparse signal model discussed in this paper contains two approximate sparse signals, and the signal band It is proved that the joint sparse reconstruction of sparse sparse signals with approximate sparsity is stable by using the distributed compressive sensing idea and the errors of reconstructed signals are described and compared with the errors caused by the sparse reconstruction of single signals, Under certain conditions, the error bound of joint reconstruction using distributed compressive sensing is smaller than the error bound of single signal reconstruction.