Algorithms For Simultaneous Sparse Approximation Problems Of Array Signal

Sparse representation problem is important for information transmission, signal encoding and compression. The theoretical study claims that a signal can be represented with its sparse representation is good for compressed highly; in practice, algorithms for sparse representation problem directly promote the application of this theory. Simultaneous sparse approximation of array signal is a newly emerged problem in sparse signal representation. In this paper we will extend some efficient methods and theories of simple sparse approximation to this problem, and get two effective methods of simultaneous sparse approximation. The work of this paper can be outlined below:1. We structure a near convex function of the objective function of simultaneous sparse approximation, so we transform the combinatorial optimization problem into a convex case, and we analyse the optimal path and the optimum conditions about this problem.2. We extend the classical Homotopy algorithm developed for the simple sparse case. The generalized algorithm keeps advantages of the classical Homotopy algorithm:when there is a sparse solution of this problem, it can be used to get the sparse solution through a few iterative times. And we take some numerical experiments demonstrating the viability of generalized Homotopy for simultaneous sparse approximation.3. We develop another algorithmic approach called Simultaneous Stagewise Orthogonal Matching Pursuit based on the methods of Simultaneous Orthogonal Matching Pursuit and Stagewise Orthogonal Matching Pursuit. And the numerical experiments demonstrate that it gives advantages in computing time and its accuracy for simultaneous sparse approximation.