"Plug-and-Play" Edge-Preserving Regularization

TL;DR

This paper introduces a simple, modular regularization method for inverse problems that preserves edges in reconstructions using standard matrix computation tools, making it more accessible than traditional complex algorithms.

Contribution

It proposes a plug-and-play framework for edge-preserving regularization that simplifies implementation without sacrificing key properties.

Findings

Uses standard matrix operations for regularization

Achieves edge-preserving reconstructions similar to TV methods

Offers an easier alternative to complex optimization algorithms

Abstract

In many inverse problems it is essential to use regularization methods that preserve edges in the reconstructions, and many reconstruction models have been developed for this task, such as the Total Variation (TV) approach. The associated algorithms are complex and require a good knowledge of large-scale optimization algorithms, and they involve certain tolerances that the user must choose. We present a simpler approach that relies only on standard computational building blocks in matrix computations, such as orthogonal transformations, preconditioned iterative solvers, Kronecker products, and the discrete cosine transform -- hence the term "plug-and-play." We do not attempt to improve on TV reconstructions, but rather provide an easy-to-use approach to computing reconstructions with similar properties.