One-Bit Compressed Sensing Using Untrained Network Prior

Abstract

In this paper, we address the problem of one-bit compressed sensing using the data-driven deep learning approach. Our approach uses an untrained neural network to reconstruct sparse vectors from their one-bit measurements. We define a new cost function using the untrained network, which maximizes the consistency between one-bit measurements and the corresponding linear measurements. The resulting optimization problem is solved using the projected gradient descent scheme and the backpropagation method. Our algorithm offers superior empirical performance compared to the existing model-based algorithms. Also, unlike the other deep learning-based algorithms that use learned generative priors, our algorithm does not require a large training set. Further, we empirically show that the proposed algorithm exhibits performance that is comparable to the learned generative network-based method.