Disjoint sparsity for signal separation and applications to hybrid inverse problems in medical imaging

摘要

The main focus of this work is the reconstruction of the signals f and g(i), i = 1,, N, from the knowledge of their sums h(i) = f + g(i), under the assumption that f and the g(i)'s can be sparsely represented with respect to two different dictionaries A(f) and A(g). This generalizes the well-known "morphological component analysis" to a multi-measurement setting. The main result of the paper states that f and the gi's can be uniquely and stably reconstructed by finding sparse representations of hi for every i with respect to the concatenated dictionary [A(f), A(g)], provided that enough incoherent measurements gi are available. The incoherence is measured in terms of their mutual disjoint sparsity.