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

arXiv: https://arxiv.org/abs/1811.08487 · HTML: https://mlsanity.com/paper/1811.08487/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2018.

## Built on by (most cited first, 1 of 1)

- [Sequential edge detection using joint hierarchical Bayesian learning](https://mlsanity.com/paper/2302.14247/) (2023)

## Abstract (arXiv)

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.