One-Bit Compressive Sensing: Can We Go Deep and Blind?

TL;DR

This paper introduces a novel deep unfolding-based method for blind one-bit compressive sensing that learns an alternative sensing matrix, enabling accurate signal recovery without prior knowledge of the sensing matrix, with enhanced interpretability and efficiency.

Contribution

It presents the first data-driven, model-based deep neural architecture for blind one-bit compressive sensing that learns sensing matrices and improves recovery performance.

Findings

Achieves accurate signal recovery from one-bit noisy measurements.

Requires fewer training samples and has fewer parameters than black-box models.

Provides an interpretable, efficient recovery algorithm.

Abstract

One-bit compressive sensing is concerned with the accurate recovery of an underlying sparse signal of interest from its one-bit noisy measurements. The conventional signal recovery approaches for this problem are mainly developed based on the assumption that an exact knowledge of the sensing matrix is available. In this work, however, we present a novel data-driven and model-based methodology that achieves blind recovery; i.e., signal recovery without requiring the knowledge of the sensing matrix. To this end, we make use of the deep unfolding technique and develop a model-driven deep neural architecture which is designed for this specific task. The proposed deep architecture is able to learn an alternative sensing matrix by taking advantage of the underlying unfolded algorithm such that the resulting learned recovery algorithm can accurately and quickly (in terms of the number of iterations) recover the underlying compressed signal of interest from its one-bit noisy measurements. In addition, due to the incorporation of the domain knowledge and the mathematical model of the system into the proposed deep architecture, the resulting network benefits from enhanced interpretability, has a very small number of trainable parameters, and requires very small number of training samples, as compared to the commonly used black-box deep neural network alternatives for the problem at hand.