Binary input-output compressive sensing: A sub-gradient reconstruction

Compressive sensing (CS) for sparse binary signals applications is subject of a growing interest especially in the wireless communication field. In practice, a reconstruction of binary input signals from binary measurements will enable a lot of attractive application. However such problem is a challenging task. In this paper, we address this special group of sparse signals with binary entries. Our approach is based on extreme quantized sensing instead of conventional CS. We introduce a simple binary sparse matrix to model the acquisition system. Thereafter, the obtained measurements are quantized severely to one bit. As a result, we enhance the spectral efficiency and reduce the acquisition cost. Moreover, an adapted Binary input-output Iterative Hard Threshold (Bio-IHT) algorithm which does not require complex optimization process is proposed for decoding. Our method is justified by mathematical analysis and numerical simulations.