Edge-adaptive l2 regularization image reconstruction from non-uniform Fourier data

TL;DR

This paper introduces a non-iterative, edge-adaptive l2 regularization method for image reconstruction from non-uniform Fourier data, aiming to improve accuracy and speed over traditional reweighted TV methods.

Contribution

It proposes a novel non-iterative regularization approach that uses pre-processing edge detection to enhance reconstruction quality and computational efficiency.

Findings

Outperforms reweighted TV in accuracy

Reduces computational runtime

Effectively detects edges for regularization

Abstract

Total variation regularization based on the l1 norm is ubiquitous in image reconstruction. However, the resulting reconstructions are not always as sparse in the edge domain as desired. Iteratively reweighted methods provide some improvement in accuracy, but at the cost of extended runtime. In this paper we examine these methods for the case of data acquired as non-uniform Fourier samples. We then develop a non-iterative weighted regularization method that uses a pre-processing edge detection to find exactly where the sparsity should be in the edge domain. We show that its performance in terms of both accuracy and speed has the potential to outperform reweighted TV regularization methods.