IRLS and Slime Mold: Equivalence and Convergence
This addresses an open convergence problem in signal processing for sparse recovery, offering a novel biological-inspired perspective.
The paper establishes an equivalence between the Iteratively Reweighted Least Squares (IRLS) algorithm and slime mold dynamics, both aimed at finding minimum l1-norm solutions, and uses this connection to prove convergence and complexity bounds for a damped IRLS version.
In this paper we present a connection between two dynamical systems arising in entirely different contexts: one in signal processing and the other in biology. The first is the famous Iteratively Reweighted Least Squares (IRLS) algorithm used in compressed sensing and sparse recovery while the second is the dynamics of a slime mold (Physarum polycephalum). Both of these dynamics are geared towards finding a minimum l1-norm solution in an affine subspace. Despite its simplicity the convergence of the IRLS method has been shown only for a certain regularization of it and remains an important open problem. Our first result shows that the two dynamics are projections of the same dynamical system in higher dimensions. As a consequence, and building on the recent work on Physarum dynamics, we are able to prove convergence and obtain complexity bounds for a damped version of the IRLS algorithm.