The Implicit Convex Feasibility Problem and Its Application to Adaptive Image Denoising

TL;DR

This paper introduces methods for solving the implicit convex feasibility problem, where some convex sets are not explicitly defined, and applies these methods to improve adaptive image denoising in medical imaging.

Contribution

It develops projection algorithms for implicit convex sets and demonstrates their application to adaptive image denoising, generalizing previous work to include transformations like scaling, shifting, and rotation.

Findings

Effective projection methods for implicit convex sets

Successful application to medical image denoising

Generalization of previous convex feasibility models

Abstract

The implicit convex feasibility problem attempts to find a point in the intersection of a finite family of convex sets, some of which are not explicitly determined but may vary. We develop simultaneous and sequential projection methods capable of handling such problems and demonstrate their applicability to image denoising in a specific medical imaging situation. By allowing the variable sets to undergo scaling, shifting and rotation, this work generalizes previous results wherein the implicit convex feasibility problem was used for cooperative wireless sensor network positioning where sets are balls and their centers were implicit.