Data Driven Measurement Matrix Learning for Sparse Reconstruction

In this work, we learn jointly how to sense and reconstruct a class of signals such as images through a deep learning structure within the compressive sensing (CS) framework. We develop a data driven approach and learn both the measurement matrix and the inverse reconstruction scheme instead of utilizing random linear projections as measurements and reconstruction via convex optimization with a given known sparsity in conventional CS framework. To achieve this goal, we have designed an end to end deep neural network structure consisting of fully connected layers with cascaded convolutional layers to be trained and tested over a publicly available image dataset. Results show that the proposed technique provides higher peak signal to noise ratio (PSNR) levels and hence learns better measurement matrices than that of the randomly selected or specifically designed for a known sparsity basis to reduce average coherence. The reconstruction performance on the test dataset also gets better as more train samples are utilized. We also observe that the learned measurement matrices achieve higher PSNR compared to random or designed cases when they are used in l 1 based recovery. Proposed reconstruction scheme has much less computational complexity compared to l 1 minimization based reconstruction with comparable results.