Robust regression for mixed Poisson-Gaussian model

TL;DR

This paper develops robust computational methods for solving inverse problems contaminated with mixed Poisson-Gaussian noise and outliers, using Talwar regression and efficient algorithms, with applications in image deblurring.

Contribution

It introduces a robust regression approach with a projected Newton algorithm and preconditioning for mixed noise inverse problems, addressing outliers and solution-dependent weights.

Findings

Effective handling of outliers in mixed noise models

Improved convergence with preconditioned algorithms

Successful application to image deblurring problems

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.