L阶Markov信号的稀疏表示

Sparse Representation for L-order Markov Signals

在现实生活中,很多信号(比如语音信号)都具有有色性,即信号相邻采样点之间具有统计相关性,通常可采用L阶Markov过程进行较好的描述,然而已有的稀疏表示算法并没有充分考虑到这种统计特性。因此,针对L阶Markov信号,采用l(p≤1)-范数的广义平均值作为稀疏度量,并提出了基于重叠采样的稀疏表示算法。仿真结果表明,相比现有的线性规划稀疏表示方法、最短路径法和FOCUSS法,新算法的精度更高。

In real life,many signals are non-white with temporal structure such as speech signals.These signals usually can be modeled as an L-order Markov process.However,the existing sparse representation methods ignore the property of these signals.The general mean of l（p≤1）-norm is adopted as the sparse measure and a sparse representation algorithm based on overlapping sampling is proposed for L-order Markov signals.The simulation shows that the proposed algorithm can achieve more accurate results compared with the existing methods such as linear programming,shortest path decomposition,and standard FOCUSS algorithm.