Family Constraining of Iterative Algorithms

TL;DR

This paper explores a method of constraining iterative algorithms using a family of operators, allowing the incorporation of prior knowledge to improve solutions in image processing tasks.

Contribution

It introduces a novel approach of constraining iterative algorithms with multiple operators, extending previous single-operator methods for better image reconstruction.

Findings

Enhanced image reconstruction quality with multiple constraints

Theoretical framework for family-constrained iterative processes

Potential applications in various image processing tasks

Abstract

In constraining iterative processes, the algorithmic operator of the iterative process is pre-multiplied by a constraining operator at each iterative step. This enables the constrained algorithm, besides solving the original problem, also to find a solution that incorporates some prior knowledge about the solution. This approach has been useful in image restoration and other image processing situations when a single constraining operator was used. In the field of image reconstruction from projections a priori information about the original image, such as smoothness or that it belongs to a certain closed convex set, may be used to improve the reconstruction quality. We study here constraining of iterative processes by a family of operators rather than by a single operator.