A boundary condition based deconvolution framework for image deblurring

• Various BC based deconvolution methods are re-derived.
• We propose a repeated BC based deconvolution method.
• The repeated BC can outperform undetermined BC in some cases.

In image deconvolution, various boundary conditions (BC) based deconvolution methods have been proposed to reduce boundary artifacts. However, most of them are not considering the accuracy of BC due to computation limitation. In this paper, we propose a BC based deconvolution framework, which considers the convolution matrix as a product of partial convolution matrix and boundary condition matrix. By computing the adjoint matrix of boundary condition matrix, we can solve this large linear system with conjugate gradient algorithm. With this framework, we can easily derive two efficient non-blind image deconvolution algorithms, which treat the borders of image as repeated instances of the edge pixel values and unknown variables, respectively. Experiments on synthetic data and real data are both presented to show the performance of various BCs. Our conclusion is that undetermined BC usually has the best performance, and repeated BC outperforms undetermined BC if the latent image has high local similarity around the boundary.