We propose a scheme for Compressed Sensing in the noiseless setting that reconstructs the original signal operating on a binary graph where the samples are obtained sequentially. The proposed scheme has an affordable computational complexity and a large performance enhancement with respect to similar schemes in the literature, thanks to the proposed measurement matrix structure and enhanced decoding based on a message passing algorithm.
Ramirez, F.; Lamarca, M.; Villares, N. Binary graphs and message passing strategies for compressed sensing in the noiseless setting. A: IEEE International Symposium on Information Theory. "2012 IEEE International Symposium on Information Theory Proceedings: took place July 1-6, 2012, in Cambridge, Massachusetts, USA". Cambridge, Massachusetts: Institute of Electrical and Electronics Engineers (IEEE), 2012, p. 1867-1871.