Retinex Based On Exponent-type Total Variation And Its Application On MRI Restoration

Retinex theory deals with compensation for illumination effects in images,which has a number of applications including Retinex illusions,medical image intensity inhomogeneity and color image shadow effect etc..Such ill-posed problem has been studied by researchers for decades.However,most exiting methods paid little attention to the noises contained in the images and lost effectiveness when the noises increase.One of the main tasks of this paper is to present a general Retinex model to effectively and robustly restore images simultaneously corrupted by illusion and noises.Firstly,we propose a novel variational model by incorporating appropriate regularization technique for the reflectance component and illumination component accordingly.Although the proposed model is non-convex,we prove the existence of the minimizers theoretically.Next,we design a fast and efficient alternating minimization algorithm for the proposed model,where all subproblems have the closed-form solutions.Finally,applications of the algorithm to various gray images and color images with noises of different distributions yield promising results.The Retinex model can also be applied to the restoration of nuclear magnetic resonance images in medicine.Rician noise and intensity nonuniformity are two common artifacts and usually coexist in magnetic resonance imaging(MRI)data.Many methods have been proposed in the literature dealing with either Rician noise or intensity nonuniformity individually.Indeed,the existence of intensity nonuniformity influences the performance of denoising and vice versa.Thus,the other main task of this paper is to propose a novel restoration model via a Maximum a Posteriori(MAP)estimator by regarding MRI data as a combination of two multiplicative components,namely,the true intensity and the bias field,and a noise followed a Rician distribution.Meanwhile,the existence of minimizers of the proposed model is provided as well.Then,an efficient algorithm based on alternating minimization method is developed,all subproblems of which can be solved effectively by either primal-dual splitting scheme or closed-form solutions.Finally,intensive numerical results on synthetic and real MRI data confirm the robustness of the method and its better performance for MRI data restoration.