Blind Image Deblurring Using Row-Column Sparse Representations

TL;DR

This paper introduces BD-RCS, a novel method for blind image deblurring that effectively handles large motions by modeling the problem as a rank-one matrix recovery using row-column sparsity, outperforming existing techniques.

Contribution

The paper proposes a new approach that models the blur kernel and image as a rank-one matrix and introduces two optimization problems based on row and column sparsity for automatic support determination.

Findings

BD-RCS outperforms state-of-the-art methods in large motion deblurring.

The method effectively estimates blur kernel and image support sequentially.

Experimental results show improved visual and quantitative deblurring quality.

Abstract

Blind image deblurring is a particularly challenging inverse problem where the blur kernel is unknown and must be estimated en route to recover the deblurred image. The problem is of strong practical relevance since many imaging devices such as cellphone cameras, must rely on deblurring algorithms to yield satisfactory image quality. Despite significant research effort, handling large motions remains an open problem. In this paper, we develop a new method called Blind Image Deblurring using Row-Column Sparsity (BD-RCS) to address this issue. Specifically, we model the outer product of kernel and image coefficients in certain transformation domains as a rank-one matrix, and recover it by solving a rank minimization problem. Our central contribution then includes solving {\em two new} optimization problems involving row and column sparsity to automatically determine blur kernel and image support sequentially. The kernel and image can then be recovered through a singular value decomposition (SVD). Experimental results on linear motion deblurring demonstrate that BD-RCS can yield better results than state of the art, particularly when the blur is caused by large motion. This is confirmed both visually and through quantitative measures.