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

Daniela di Serafino (daniela.diserafino***at***unicampania.it)
Germana Landi (germana.landi***at***unibo.it)
Marco Viola (marco.viola***at***uniroma1.it)

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.

Keywords: Image restoration, Poisson noise, TV regularization, iteratively reweighted norm, quadratic approximation.

Category 1: Applications -- Science and Engineering (Other )

Category 2: Convex and Nonsmooth Optimization


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Entry Submitted: 07/27/2018
Entry Accepted: 07/27/2018
Entry Last Modified: 08/21/2019

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