A Non-Negative and Sparse Enough Solution of an Underdetermined Linear System of Equations is Unique

@inproceedings{Bruckstein2007ANA,
title={A Non-Negative and Sparse Enough Solution of an Underdetermined Linear System of Equations is Unique},
author={Alfred M. Bruckstein and Michael Elad and Michael Zibulevsky},
year={2007}
}

In this paper we consider an underdetermined linear system of equations Ax = b with non-negative entries of A and b, and the solution x being also required to be nonnegative. We show that if there exists a sufficiently sparse solution to this problem, it is necessarily unique. Furthermore, we present a greedy algorithm – a variant of the matching pursuit – that is guaranteed to find this sparse solution. We also extend the existing theoretical analysis of the basis pursuit problem, i.e. min ‖x… CONTINUE READING