Research Of Image Retinex Problem Based On The Non-convex TV-type Regularization

In the imaging process,due to the effect of the light source or the reflection of the surface of the object and other factors,non-uniform illumination often occurs in the acquired images,such as underexposure areas and overexposure areas.To some extent,illumination inhomogeneity changes the original appearance of the image,resulting in poor visual effect,and is not conducive to the subsequent image processing.Retinex technology can make the interesting part more prominent,so that the processed images are more suitable for observation or other engineering applications.Based on total variation(TV)type functional space,this paper proposes a new non-convex Retinex model and solves it by effective numerical method.The main contents are as follows:· In order to more effectively describe the sparsity of the image,we propose a new image retinex model based on the non-convex total variation(TV)-type regularization,where the data fitting term and regularization term based on the exponent transform are used to describe image details efficiently.Especially in the model,one regularization term based on the non-convex total variation ?pquasi-norm with p ?(0,1)is used to penalize the sparsity of the piecewise constants and one regularization term based on the non-convex high-order total variation ?qquasi-norm with q ?(0,1)is used to penalize the piecewise smoothing regions.· Since the proposed model is non-convex,non-smooth and non-Lipschitz,we employ the alternating minimization(Alternating Minimization,AM)method,where the iteratively re-weighted ?1algorithm(Iteratively Re-weighted ?1Algorithm,IRLA)and the alternating direction method of multipliers(Alternating Direction Method of Multipliers,ADMM)are used in the sub-minimization problems.In addition,this paper discusses some mathematical properties of the proposed model and numerical algorithm.Finally,experiments on the simulated and real images illustrate the effectiveness and the robustness of our proposed model both visually and quantitatively by compared with some Retinex variational models.