# Image restoration using sparse approximations of spatially varying blur operators in the wavelet domain

arXiv: https://arxiv.org/abs/1302.6105 · HTML: https://mlsanity.com/paper/1302.6105/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2013.

## Built on by (most cited first, 2 of 2)

- [Deep Model-Based Super-Resolution with Non-uniform Blur](https://mlsanity.com/paper/2204.10109/) (2022)
- [Provably Convergent Plug & Play Linearized ADMM, applied to Deblurring Spatially Varying Kernels](https://mlsanity.com/paper/2210.10605/) (2022)

## Abstract (arXiv)

Restoration of images degraded by spatially varying blurs is an issue of increasing importance in the context of photography, satellite or microscopy imaging. One of the main difficulty to solve this problem comes from the huge dimensions of the blur matrix. It prevents the use of naive approaches for performing matrix-vector multiplications. In this paper, we propose to approximate the blur operator by a matrix sparse in the wavelet domain. We justify this approach from a mathematical point of view and investigate the approximation quality numerically. We finish by showing that the sparsity pattern of the matrix can be pre-defined, which is central in tasks such as blind deconvolution.