A Deep Learning Approach to Structured Signal Recovery

Abstract--In this paper, we develop a new framework for sensing and recovering structured signals. In contrast to compressive sensing (CS) systems that employ linear measurements, sparse representations, and computationally complex convex/greedy algorithms, we introduce a deep learning framework that supports both linear and mildly nonlinear measurements, that learns a structured representation from training data, and that efficiently computes a signal estimate. In particular, we apply a stacked denoising autoencoder (SDA), as an unsupervised feature learner. SDA enables us to capture statistical dependencies between the different elements of certain signals and improve signal recovery performance as compared to the CS approach. Many configurations for x and Γ(.) have been explored in the literature for this problem; however, one of the most useful ones is to have a sparse signal x and a linear Γ(.), i.e., y Γ(x) Φx. Compressive sensing (CS) [1]-[3] is a field that tries to solve this linear inverse problem in case that x has a sparse representation, i.e., there exists an N N basis matrix Ψ [ψ Department of Electrical and Computer Engineering Rice University Houston, TX 77005 (i) How to recover the signal x from a given measurement vector y and operator Γ(.)? (ii) How to design the measurement operator Γ(.)? (iii) If we are concerned with any type of structure, How could we find a representation in which the signal x has that structure? Although there has been a considerable progress in CS and particularly in the answers of aforementioned questions, our goal is to go beyond the state-of-the-art results.