Wenting Long, Yao Lu, Lixin Shen and Yuesheng Xu
Abstract: High-resolution image reconstruction obtains one high-resolution image from multiple low resolution, shifted, degraded samples of a true scene. This is a typical ill-posed problem and optimization models such as the ℓ2/TV model are previously studied for solving this problem. It is based on the assumption that during acquisition digital images are polluted by Gaussian noise. In this work, we propose a new optimization model arising from the statistical assumption for mixed Gaussian and impulse noises, which leads us to choose the Moreau envelop of the ℓ1-norm as the fidelity term. The developed envℓ1 /TV model is effective to suppress mixed noises, combining the advantages of the ℓ1/TV and the ℓ2/TV models. Furthermore, a fixed-point proximity algorithm is developed for solving the proposed optimization model and convergence analysis is provided. An adaptive parameter choice strategy for the developed algorithm is also proposed for fast convergence. The experimental results confirm the superiority of the proposed model compared to the previous ℓ2/TV model besides the robustness and effectiveness of the derived algorithm.
Journal: International Journal of Numerical Analysis & Modeling, Volume 14 (2017), Number 2, Pages 255–282
URL: http://www.math.ualberta.ca/ijnam/Volume-14-2017/No-2-17/2017-02-06.pdf