Phase diagram of matrix compressed sensing.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 28085338.
- Also identified by DOI 10.1103/PhysRevE.94.062136.
- No licence information is recorded for this record.
- Because redistribution is not established, this page shows the abstract only. Follow the links below for the full text.
Abstract
In the problem of matrix compressed sensing, we aim to recover a low-rank matrix from a few noisy linear measurements. In this contribution, we analyze the asymptotic performance of a Bayes-optimal inference procedure for a model where the matrix to be recovered is a product of random matrices. The results that we obtain using the replica method describe the state evolution of the Parametric Bilinear Generalized Approximate Message Passing (P-BiG-AMP) algorithm, recently introduced in J. T. Parker and P. Schniter [IEEE J. Select. Top. Signal Process. 10, 795 (2016)1932-455310.1109/JSTSP.2016.2539123]. We show the existence of two different types of phase transition and their implications for the solvability of the problem, and we compare the results of our theoretical analysis to the numerical performance reached by P-BiG-AMP. Remarkably, the asymptotic replica equations for matrix compressed sensing are the same as those for a related but formally different problem of matrix factorization.