Message passing for multidimensional inverse problems

Abstract

Numerous algorithms for the recovery of sparse, high-dimensional signals with independent, identically distributed samples have been discussed in the literature. Some of the most advanced ones are based on approximated message passing algorithms and have been shown to perform well in terms of mean-squared error. Restrictions such as the independence of signal samples as well as rigid requirements imposed upon the measurement matrix often limit the practical usability and performance of these algorithms. This thesis attempts to lift some of these restrictions without constraining the solutions to specific problems. The resulting algorithms maintain or surpass the performance of Bayesian approximate message passing under adverse conditions, while retaining reasonable computational complexity for practical applications.

Numerous algorithms for the recovery of sparse, high-dimensional signals with independent, identically distributed samples have been discussed in the literature. Some of the most advanced ones are based on approximated message passing algorithms and have been shown to perform well in terms of mean-squared error. Restrictions such as the independence of signal samples as well as rigid requirements imposed upon the measurement matrix often limit the practical usability and performance of these algorithms. This thesis attempts to lift some of these restrictions without constraining the solutions to specific problems. The resulting algorithms maintain or surpass the performance of Bayesian approximate message passing under adverse conditions, while retaining reasonable computational complexity for practical applications.