Optimized JPEG image decompression with super-resolution interpolation using multi-order total variation

We propose a novel framework to obtain an artifact-free enlarged image from a given JPEG image. The proposed formulation based on a newly introduced JPEG image acquisition model realizes decompression and super-resolution interpolation simultaneously using multi-order total variation, so that we can drastically reduce artifacts appearing in JPEG images such as block noise and mosquito noise, without generating staircasing effect, which is typical in existing total variation-based JPEG decompression methods. We also present a computationally-efficient optimization scheme, derived as a special case of a primal-dual splitting type algorithm, for solving the convex optimization problem associated with the proposed formulation. Numerical examples show that the proposed method works effectively compared with existing methods.