One-Bit Compressive Sensing: Can We Go Deep and Blind?
This work addresses a key limitation in compressive sensing for signal processing applications by enabling blind recovery, though it is incremental as it builds on existing deep unfolding techniques.
The paper tackles the problem of one-bit compressive sensing without prior knowledge of the sensing matrix, achieving blind recovery through a model-driven deep neural architecture that learns an alternative sensing matrix, resulting in accurate and fast signal recovery with enhanced interpretability, small parameter counts, and minimal training samples.
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.