Blind Image Deblurring
Using Structured Sparse Representations

Blind image deblurring is a particularly challenging inverse problem where the blur kernel is unknown and must be estimated en route to recovering the de-blurred 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 Sparse Representations (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 via a rank minimization problem. Our central contribution then involves solving {m two new} optimization problems involving row and column sparsity to automatically determine blur kernel and image support respectively. 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.