We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix ensemble. By design, the fixed points of the algorithm obey the Thouless-Anderson-Palmer (TAP) equations corresponding to the ensemble. Using a dynamical functional approach we are able to derive an effective stochastic process for the marginal statistics of a single component of the dynamics. This allows us to design memory terms in the algorithm in such a way that the resulting fields become Gaussian random variables allowing for an explicit analysis. The asymptotic statistics of these fields are consistent with the replica ansatz of the compressed sensing problem.
|Title of host publication||2017 IEEE International Symposium on Information Theory (ISIT)|
|Number of pages||5|
|Publication status||Published - 2017|
|Event||2017 IEEE International Symposium on Information Theory - Aachen, Germany|
Duration: 25 Jun 2017 → 30 Jun 2017
|Conference||2017 IEEE International Symposium on Information Theory|
|Period||25/06/2017 → 30/06/2017|