Robust regression for mixed Poisson–Gaussian model

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.

Flexible GMRES for total variation regularization

“…We also consider a preconditioner built around the idea of approximating the row scaling W 2d by a diagonal column scaling W 2d (see [22]), so that…”

Efficient learning methods for large-scale optimal inversion design

“…Gaussian distribution and that 0 < p < 2 should be considered when the available data are perturbed by non-Gaussian noise, it is unclear what to use when there is a mixture of noise corrupting the data. For specific statistical models of noise, e.g., mixed Gaussian and Poisson noise that arise from Charge Coupled Device detectors, a reformulation to a weighted least-squares problem has been considered, see e.g., [6,9,13,46] and references therein. However, the reformulation relies on an approximation using knowledge about the noise statistics, which is not necessarily available in practice.…”