Nonconvex relaxation for Poisson intensity reconstruction
Lasith Adhikari, Roummel F. Marcia
Abstract
Critical to accurate reconstruction of sparse signals from low-dimensional Poisson observations is the solution of nonlinear optimization problems that promote sparse solutions. Theoretically, non-convex ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm minimization (0 ≤ p <; 1) would lead to more accurate reconstruction than the convex ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm relaxation commonly used in sparse signal recovery. In this paper, we propose an extension to the existing SPIRAL-ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> algorithm based on the Generalized Soft-Thersholding (GST) function to better recover signals with mostly nonzero entries from Poisson observations. This approach is based on iteratively minimizing a sequence of separable subproblems of the nonnegatively constrained, ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -penalized negative Poisson log-likelihood objective function using the GST function. We demonstrate the effectiveness of the proposed method, called SPIRAL-ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> , through numerical experiments.
BibTeX
@inproceedings{icassp2015_nonconvexrelaxat,
title = {Nonconvex relaxation for Poisson intensity reconstruction},
author = {Lasith Adhikari and Roummel F. Marcia},
booktitle = {ICASSP 2015},
year = {2015}
}