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

3rd International Workshop on New Computational Methods for Inverse Problems

物理学;计算机科学

Escande, Paul^1 ; Weiss, Pierre^1 ; Malgouyres, François^2

ITAV-USR3505, Université de Toulouse, CNRS, Toulouse, France^1

IMT-UMR5219, Université de Toulouse, CNRS, Toulouse, France^2

关键词: Approximation quality;    Blind deconvolution;    Matrix vector multiplication;    Microscopy imaging;    Restoration of images;    Sparse approximations;    Sparsity patterns;    Wavelet domain;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/464/1/012004/pdf
DOI  :  10.1088/1742-6596/464/1/012004

学科分类：计算机科学（综合）

来源: IOP

【 摘 要 】

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.