Real-time $\ell^1$ -- $\ell^2$ deblurring using wavelet expansions of operators

TL;DR

This paper introduces a fast, real-time method for image deblurring by exploiting wavelet-based sparse representations of images and blur operators, combined with preconditioning and parallel computing.

Contribution

The authors propose a novel wavelet-based approach that significantly accelerates $ ext{l}^1$--$ ext{l}^2$ deblurring, enabling real-time performance on standard hardware.

Findings

Achieved acceleration factors of 30 to 250 times.

Deblurred 1024x1024 images in 0.15 seconds.

Method suitable for real-time imaging applications.

Abstract

Image deblurring is a fundamental problem in imaging, usually solved with com-putationally intensive optimization procedures. We show that the minimization can be significantly accelerated by leveraging the fact that images and blur operators are compressible in the same orthogonal wavelet basis. The proposed methodology consists of three ingredients: i) a sparse approximation of the blur operator in wavelet bases, ii) a diagonal preconditioner and iii) an implementation on massively parallel architectures. Combing the three ingredients leads to acceleration factors ranging from 30 to 250 on a typical workstation. For instance, a 1024 x 1024 image can be deblurred in 0.15 seconds, which corresponds to real-time.