Encoder Blind Combinatorial Compressed Sensing

In its most elementary form, compressed sensing studies the design of decoding algorithms to recover a sufficiently sparse vector or code from lower dimensional linear measurement vector. Typically it is assumed that decoder has access encoder matrix, which in combinatorial case and binary. this paper we consider problem designing set codes their measurements alone, without matrix. To end study matrix factorisation task recovering both coding matrices associated The contribution computationally efficient algorithm, Decoder-Expander Based Factorisation, with strong performance guarantees. Under mild assumptions on by deploying novel random prove Factorisation recovers at optimal rate high probability near number vectors. addition, our experiments demonstrate efficacy computational efficiency algorithm practice. Beyond sensing, results may be interest for researchers working areas as diverse sketching, theory, compression dictionary learning.