Abstract
Signal compression is essential for energy and bandwidth efficient communication and storage systems. In this paper, we provide two practical approaches for source compression of noisy sparse and non-strictly sparse (compressible) sources. The proposed schemes are based on channel coding theory to construct a source encoder that decreases the number of transmitted bits while preserving the fidelity of the reconstructed signal at the receiver by exploiting its sparsity. In addition, a model order selection scheme is proposed to detect the nonzero elements of sparse vectors embedded in noise, or to find a nonlinear sparse approximation of compressible signals. As illustrated by numerical results, our approach provides a lower distortion-rate function compared to previously known methods. For example, the proposed schemes achieve a lower distortion, about 2 orders of magnitude, compared to compressed sensing, for the same rate.