Regularized Super-resolution Image Restoration Algorithm

Super-resolution image restoration is ill-posed inverse problem;it should be resolved by regularization method. Super-resolution image restoration involves in multi-frame low resolution image and a frame high resolution image, so its computational complexity is large. While, the estimation of degrade model and its parameter and the sub-pixel motion estimation are liable to create error. The additional noise type in degrade process is difficult to determine. Consequently, we need to find fast algorithm and we expect it have robustness to above errors.In traditional approach, people use l₂ -norm to measure data approximation item and regularization item in regularized image restoration and super-restoration in spatial domain. S.Farsiu et al point out use l₁ -norm to measure data approximation item and regularization item and provide us a robust super-resolution method, while we can't obtain so robustness by l₂ -norm. They didn't discuss the uniqueness of minimum point of objective functional in theory. Besides this problem, the convergence of steepest descend algorithm used to find the minimum point of objective functional and how to choose step size parameter and regularization parameter aren't discussed. This paper give further discuss and obtain some important conclusion.We discuss the uniqueness of minimum point of objective functional obtained by using l_p -norm (1 ≤ p ≤ 2) to measure data approximation item and regularization item in theory. If1 < p ≤ 2, the objective functional has unique minimum point;if p=l, we can't determine the uniqueness easily. For making up this bug, we use l_p -norm, p is a little larger than 1, and obtain similar image restoration effect.This paper gives a method to choose regularization parameter. Discuss the performance of steepest descend algorithm, introduce the idea that set the step size parameter in phase in order to reduce iterative time and improve the effect. Adopt Roberts cross gradient operator, we get super-resolution algorithm with lower computational complexity and get better effect than bilateral total variation operator at some case. We discover the regularization method with l₁, -norm is more robust to the blur estimation error than that with l₂ -norm. Therefore, we apply it to blind super-resolution and get robust blind super-resolution method.