Graph-based iterative reconstruction of sparse signals for compressed sensing

In this paper, we consider the problem of reconstruction of sparse signals in compressed sensing. In particular, we introduce a novel iterative algorithm based on graph-based decoding of low-density parity-check codes which possesses desirable properties like good performance, low complexity and running time, and ease of implementation. In this work, we outline the reconstruction algorithm, and analyze its performance on some measurement matrices. Furthermore, we also provide some initial results on the theoretical performance limits of this algorithm.