Neumann Network with Recursive Kernels for Single Image Defocus Deblurring

Single image defocus deblurring (SIDD) refers to recovering an all-in-focus image from a defocused blurry one. It is a challenging recovery task due to the spatially-varying defocus blurring effects with significant size variation. Motivated by the strong correlation among defocus kernels of different sizes and the blob-type structure of defocus kernels, we propose a learnable recursive kernel representation (RKR) for defocus kernels that expresses a defocus kernel by a linear combination of recursive, separable and positive atom kernels, leading to a compact yet effective and physics-encoded parametrization of the spatially-varying defocus blurring process. Afterwards, a physics-driven and efficient deep model with a cross-scale fusion structure is presented for SIDD, with inspirations from the truncated Neumann series for approximating the matrix inversion of the RKR-based blurring operator. In addition, a reblurring loss is proposed to regularize the RKR learning. Extensive experiments show that, our proposed approach significantly outperforms existing ones, with a model size comparable to that of the top methods.