Robust regression for mixed Poisson-Gaussian model
Provides a robust regression approach for inverse problems with mixed noise and outliers, but the contribution is incremental as it combines existing techniques.
The paper develops efficient computational methods for linear inverse problems with mixed Poisson-Gaussian noise and outliers, using a Talwar robust regression function and a projected Newton algorithm with preconditioning. Numerical experiments on image deblurring demonstrate effectiveness.
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.