One-Bit Compressed Sensing Using Generative Models

Abstract

In this paper, we address the classical problem of one-bit compressed sensing. We present a deep learning based reconstruction algorithm that relies on a generative model. The generator which is a neural network, learns a mapping from a low dimensional space to a higher dimensional set comprising of sparse vectors. This pre-trained generator is used to reconstruct sparse vectors from their one-bit measurements by searching over the range of the generator. Hence, the algorithm presented in this paper provides excellent reconstruction accuracy by accounting for any other possible structure in the signal apart from sparsity. Further, we provide theoretical guarantees on the reconstruction accuracy of the presented algorithm. Using numerical results, we also demonstrate the efficacy of our algorithm compared to other existing algorithms.