Learning to Sense and Reconstruct A Class of Signals

Abstract

In this paper, we propose a deep learning structure to jointly learn both how to sense and reconstruct a class of signals. In contrast to classical compressive sensing (CS) framework that utilizes pre-determined linear projections as measurements and convex optimization with a known sparsity basis to reconstruct the signal, instead we develop a data driven approach and learn both the measurement matrix and the inverse reconstruction scheme. To achieve this, an end to end deep neural network with fully connected and convolutional layers are designed and trained over an image dataset. Our initial results show that the measurement matrix learned through the proposed technique provides higher peak signal to noise ratio (PSNR) levels compared to both randomly selected matrices or designed measurement matrices for an assumed sparsity basis for the dataset. Learned measurement matrices are tested in both $\ell_{1}$ minimization based sparse recovery and deep neural network structures and for both recovery schemes highest PSNR values are obtained with the learned measurement matrix. The $\ell_{1}$ based recovery achieves higher PSNR results compared to inversion with deep neural network, their results are comparable.