Efficient non-uniform deblurring based on generalized additive convolution model

Abstract

Image with non-uniform blurring caused by camera shake can be modeled as a linear combination of the homographically transformed versions of the latent sharp image during exposure. Although such a geometrically motivated model can well approximate camera motion poses, deblurring methods in this line usually suffer from the problems of heavy computational demanding or extensive memory cost. In this paper, we develop generalized additive convolution (GAC) model to address these issues. In GAC model, a camera motion trajectory can be decomposed into a set of camera poses, i.e., in-plane translations (slice) or roll rotations (fiber), which can both be formulated as convolution operation. Moreover, we suggest a greedy algorithm to decompose a camera motion trajectory into a more compact set of slices and fibers, and together with the efficient convolution computation via fast Fourier transform (FFT), the proposed GAC models concurrently overcome the difficulties of computational cost and memory burden, leading to efficient GAC-based deblurring methods. Besides, by incorporating group sparsity of the pose weight matrix into slice GAC, the non-uniform deblurring method naturally approaches toward the uniform blind deconvolution.