ACQUIRE: an inexact iteratively reweighted norm approach for TV-based Poisson image restoration

TL;DR

ACQUIRE is a novel line-search algorithm that efficiently solves TV-based Poisson image restoration problems by combining smoothed TV regularization with second-order information, demonstrating competitive performance.

Contribution

The paper introduces ACQUIRE, a new inexact iterative method leveraging a smoothed TV approach and second-order approximations for improved Poisson image restoration.

Findings

ACQUIRE converges to a minimizer without exact subproblem solutions.

The method is computationally efficient compared to existing techniques.

Numerical results show high-quality restored images.

Abstract

We propose a method, called ACQUIRE, for the solution of constrained optimization problems modeling the restoration of images corrupted by Poisson noise. The objective function is the sum of a generalized Kullback-Leibler divergence term and a TV regularizer, subject to nonnegativity and possibly other constraints, such as flux conservation. ACQUIRE is a line-search method that considers a smoothed version of TV, based on a Huber-like function, and computes the search directions by minimizing quadratic approximations of the problem, built by exploiting some second-order information. A classical second-order Taylor approximation is used for the Kullback-Leibler term and an iteratively reweighted norm approach for the smoothed TV term. We prove that the sequence generated by the method has a subsequence converging to a minimizer of the smoothed problem and any limit point is a minimizer. Furthermore, if the problem is strictly convex, the whole sequence is convergent. We note that convergence is achieved without requiring the exact minimization of the quadratic subproblems; low accuracy in this minimization can be used in practice, as shown by numerical results. Experiments on reference test problems show that our method is competitive with well-established methods for TV-based Poisson image restoration, in terms of both computational efficiency and image quality.