Fast proximal splitting algorithm for constrained TGV-regularised image restoration and reconstruction.

A fast algorithm is proposed to tackle the constrained total generalised variation (TGV)-based image-restoration and reconstruction problems. The proposed algorithm proceeds by splitting: the non-smooth constrained TGV model is first decomposed into several sub-problems easier to solve, and then the linear gradient or proximity operators, including projections and shrinkages, of the sub-problems are individually called without inner iteration. The algorithm is highly parallel since most of its steps can be executed simultaneously. Image-restoration and reconstruction experiments demonstrate that the proposed algorithm outperforms several state-of-the-art TV-based methods both in accuracy and high-speed efficiency. Besides, the proposed method efficiently suppresses staircase effects and presents better visual impression.