Abstract: A method of sampling and decoding of a signal of interest x comprising, at a training stage: acquiring a set of training signals {xi}i=1M, providing a sampling operator P? and a decoder g?g(.), training operator P? on signals {xi}i=1M to obtain a learned sampling operator P{circumflex over (?)}; and, at a sampling stage: applying P{circumflex over (?)} in a transform domain ? to signal x, resulting in observation signal y; applying the decoder g?g(.) to y, to produce an estimate {circumflex over (x)} of signal x to decode and/or, decide about, the signal. Decoder g?g(.) is trained jointly with P? on signals {xi}i=1M, to obtain a learned decoder g{circumflex over (?)}g, by jointly determining, during a cost minimization step, sampling parameters ? and decoding parameters ?g according to a cost function, and wherein the step of applying the decoder g?g(.) uses decoding parameters ?g, such that estimate {circumflex over (x)} is produced by the learned decoder g{circumflex over (?)}g.

Abstract: A method of sampling and decoding of a signal of interest x comprising, at a training stage: acquiring a set of training signals {xi}i=1M, providing a sampling operator P? and a decoder g?g(.), training operator P? on signals {xi}i=1M to obtain a learned sampling operator P{circumflex over (?)}; and, at a sampling stage: applying P{circumflex over (?)} in a transform domain ? If to signal x, resulting in observation signal y; applying the decoder g?g(.) to y, to produce an estimate {circumflex over (x)} of signal x to decode and/or, decide about, the signal. Decoder g?g(.) is trained jointly with P? on signals {xi}i=1M, to obtain a learned decoder g?g, by jointly determining, during a cost minimization step, sampling parameters ? and decoding parameters ?gaccording to a cost function, and wherein the step of applying the decoder g?g(.) uses decoding parameters ?g, such that estimate {circumflex over (x)} is produced by the learned decoder g{circumflex over (?)}g.