科研之友
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摘要
In this paper, the problem of sparse representation is addressed: we consider a linear model X=AS , where the data matrix X=[x(1),....,x(T)]∈Rm×TT»M)and basis matrix A=a[a1,...,a2]∈Rm×Tare given, and the objective is to estimate the sparse sources matrix S∈Rn×Twherem<n. Although several algorithms have been proposed to solve this problem, still their performance is often not desirable. The goal of this paper is to develop a new algorithm for this problem. In engineering applications, many signals are non-white (with temporal structure) and can be modeled as an L -order Markov process. However, the existing sparse representation methods don't exploit the Lorder Markov property of signals. To overcome this drawback, a new sparse representation framework is developed in this paper: first, the available T samples are segmented (split) into several frames, where the length of each frame is L(1&leL&leT)secondly, to make the estimated signals to be smooth, we set an appropriate percentage of overlapping between two neighbor frames (typically, 50% - 70% over-lapping); finally, we perform sparse representation for each frame. Under the proposed framework, it is convenient to take advantage of L -order Markov property to improve the performance. In addition, a new optimization criterion is proposed for the sparse representation problem with multiple measurement vectors. The new criterion is also particularly suitable for L - order Markov signals. A modified basis pursuit based algorithm is developed to minimize the proposed objective function. Compared with the existing methods such as linear programming, shortest path decomposition, and standard FOCUSS algorithm, the proposed algorithm can achieve more accurate results.
- 出版日期2013--
- 单位暨南大学
