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

Recovery of binary sparse signals from compressed linear measurements via polynomial optimization

The recovery of signals with finite-valued components from few linear measurements is a problem with widespread applications and interesting mathematical characteristics. In the compressed sensing framework, tailored methods have been recently proposed to deal with the case of finite-valued sparse signals. In this work, we focus on binary sparse signals and we propose a novel formulation, based on polynomial optimization. This approach is analyzed and compared to the state-of-the-art binary compressed sensing methods

Advances in the recovery of binary sparse signals

Recently, the recovery of binary sparse signals from compressed linear systems has received attention due to its several applications. In this contribution, we review the latest results in this framework, that are based on a suitable non-convex polynomial formulation of the problem. Moreover, we propose novel theoretical results. Then, we show numerical results that highlight the enhancement obtained through the non-convex approach with respect to the state-of-the-art methods

Sparse image recovery using compressed sensing over finite alphabets

In this paper we present F2OMP, a recovery algorithm for Compressed Sensing over finite fields. Classical recovery algorithms do not exploit the fact that a signal may belong to a finite alphabet, while we show that this information can lead to more efficient reconstruction algorithms. As an application, we use the proposed algorithm to recover sparse grayscale images, showing that performing CS operation over a finite field can outperform classical recovery algorithms from visual quality, memory occupation and complexity point of view