Plug-and-play superiorization

TL;DR

This paper extends the superiorization methodology by integrating plug-and-play operations like denoisers and neural networks, enabling improved solutions in imaging problems with better efficiency and quality.

Contribution

It introduces a flexible plug-and-play framework for superiorization, allowing the use of arbitrary procedures such as neural networks within the optimization heuristic.

Findings

Plug-and-play superiorization achieves comparable or better image quality.

The approach offers advantages in computational efficiency.

It improves data fidelity in image reconstruction.

Abstract

The superiorization methodology (SM) is an optimization heuristic in which an iterative algorithm, which aims to solve a particular problem, is ``superiorized'' to promote solutions that are improved with respect to some secondary criterion. This superiorization is achieved by perturbing iterates of the algorithm in nonascending directions of a prescribed function that penalizes undesirable characteristics in the solution; the solution produced by the superiorized algorithm should therefore be improved with respect to the value of this function. In this paper, we broaden the SM to allow for the perturbations to be introduced by an arbitrary procedure instead, using a plug-and-play approach. This allows for operations such as image denoisers or deep neural networks, which have applications to a broad class of problems, to be incorporated within the superiorization methodology. As proof of concept, we perform numerical simulations involving low-dose and sparse-view computed tomography image reconstruction, comparing the plug-and-play approach to two conventionally superiorized algorithms, as well as a post-processing approach. The plug-and-play approach provides comparable or better image quality in most cases, while also providing advantages in terms of computing time, and data fidelity of the solutions.