Robust regression for mixed Poisson-Gaussian model

• ID: 2800, RIV: 10385080
• ISSN: 1017-1398, ISBN: not specified
• source: Numerical Algorithms
• keywords: Image restoration; Poisson-Gaussian model; Preconditioner; Robust regression; Weighted least squares
• authors: Marie Kubínová, James G. Nagy
• authors from KNM: not assigned

Abstract

This paper focuses on efficient computational approaches to compute approximate solutions of a linear inverse problem that is contaminated with mixed Poisson-Gaussian noise, and when there are additional outliers in the measured data. The Poisson-Gaussian noise leads to a weighted minimization problem, with solution-dependent weights. To address outliers, the standard least squares fit-to-data metric is replaced by the Talwar robust regression function. Convexity, regularization parameter selection schemes, and incorporation of non-negative constraints are investigated. A projected Newton algorithm is used to solve the resulting constrained optimization problem, and a preconditioner is proposed to accelerate conjugate gradient Hessian solves. Numerical experiments on problems from image deblurring illustrate the effectiveness of the methods.