Accelerated reconstruction of a compressively sampled data stream

The traditional compressed sensing approach is naturally offline, in that it amounts to sparsely sampling and reconstructing a given dataset. Recently, an online algorithm for performing compressed sensing on streaming data was proposed: the scheme uses recursive sampling of the input stream and recursive decompression to accurately estimate stream entries from the acquired noisy measurements. In this paper, we develop a novel Newton-type forward-backward proximal method to recursively solve the regularized Least-Squares problem (LASSO) online. We establish global convergence of our method as well as a local quadratic convergence rate. Our simulations show a substantial speed-up over the state of the art which may render the proposed method suitable for applications with stringent real-time constraints.