  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.
