Discrete Signal Reconstruction by Sum of Absolute Values

In this letter, we consider a problem of reconstructing an unknown discrete signal taking values in a finite alphabet from incomplete linear measurements. The difficulty of this problem is that the computational complexity of the reconstruction is exponential as it is. To overcome this difficulty, we extend the idea of compressed sensing, and propose to solve the problem by minimizing the sum of weighted absolute values. We assume that the probability distribution defined on an alphabet is known, and formulate the reconstruction problem as linear programming. Examples are shown to illustrate that the proposed method is effective.Comment: IEEE Signal Processing Letters (to appear

Efficient recovery algorithm for discrete valued sparse signals using an ADMM approach

Motivated by applications in wireless communications, in this paper we propose a reconstruction algorithm for sparse signals whose values are taken from a discrete set, using a limited number of noisy observations. Unlike conventional compressed sensing algorithms, the proposed approach incorporates knowledge of the discrete valued nature of the signal in the detection process. This is accomplished through the alternating direction method of the multipliers which is applied as a heuristic to decompose the associated maximum likelihood detection problem in order to find candidate solutions with a low computational complexity order. Numerical results in different scenarios show that the proposed algorithm is capable of achieving very competitive recovery error rates when compared with other existing suboptimal approaches.info:eu-repo/semantics/publishedVersio