  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.
