Sparse image recovery using compressed sensing over finite alphabets

In this paper we present F² OMP, 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.