Neighborly Polytopes and Sparse Solution of Underdetermined Linear Equations

@inproceedings{Donoho2005NeighborlyPA,
title={Neighborly Polytopes and Sparse Solution of Underdetermined Linear Equations},
author={David L. Donoho},
year={2005}
}

Consider a d × n matrix A, with d < n. The problem of solving for x in y = Ax is underdetermined, and has many possible solutions (if there are any). In several fields it is of interest to find the sparsest solution – the one with fewest nonzeros – but in general this involves combinatorial optimization. Let ai denote the i-th column of A, 1 ≤ i ≤ n. Associate to A the quotient polytope P formed by taking the convex hull of the 2n points (±ai) in R. P is centrosymmetric and is called (centrally… CONTINUE READING