Sparse Signal Reconstruction using Weight Point Algorithm.

In this paper we propose a new approach of the compressive sensing (CS) reconstruction problem based on a geometrical interpretation of l₁-norm minimization. By taking a large l₁-norm value at the initial step, the intersection of l₁-norm and the constraint curves forms a convex polytope and by exploiting the fact that any convex combination of the polytope's vertexes gives a new point that has a smaller l₁-norm, we are able to derive a new algorithm to solve the CS reconstruction problem. Compared to the greedy algorithm, this algorithm has better performance, especially in highly coherent environments. Compared to the convex optimization, the proposed algorithm has simpler computation requirements. We tested the capability of this algorithm in reconstructing a randomly down-sampled version of the Dow Jones Industrial Average (DJIA) index. The proposed algorithm achieved a good result but only works on realvalued signals. [ABSTRACT FROM AUTHOR]