Research On Mathematical Model And Fast Algorithm Of Image Enhancement

Image enhancement has always been one of the key research problems in image processing,especially color images processing.We use those images in contact all the time.In image enhancement,the Retinex theory studies human perception of color,and explains how the human visual system perceives color with respect to a slowly varying illumination.Land et al found that actual color sensations are related to the intrinsic reflectance of objects rather than to the radiance values captured by the eyes.Therefore,the Retinex theory is to create a decomposition that separates the varying illumination from the observed image,and gets the actual color of the object with the details coverd by illumination.The study of Retinex theory has undergone many stages and has been in progress and development.First of all,this thesis introduces the path-based methods and single/multi-scale Retinex for solving the Retinex problem.However,these methods have high complexity and contain a lot of parameters,which are not practical.With the development of PDE methods,the computational efficiency is greatly enhanced by fast Fourier transform.Meanwhile,the Retinex problem was decomposed into the point multiplication form of reflectance and illumination,which provides the basis for the later models.After that,the variational models are based on different regularization terms,such as total variation(TV),Tikhonov,high order TV and reweighted TV,making the final results significantly improved in visual and computational speed.In this thesis,based on the analysis of the margin distribution curves of reflectance and illumination,we proposed two new regularization terms: for reflectance,we use the hyper-Laplacian prior to ensure that the edges and details are not lost;for illumination,we use the hybrid regularization term,which combines the advantages of hyper-Laplacian and Tikhonov regularization.It can not only ensure that different lightness regions are clearly differentiated,but also maintain smoothness within the illumination area.After establishing the Retinex model in this thesis,we use the alternating directional multiplier algorithm(ADMM)framework to solve the proposed model.For the hyper-Laplacian subproblem,we use the GST algorithm to guarantee the speed and precision of solution of the sub-problem compared by other algorithms.In the numerical experiments,the proposed method is compared with four state-of-the-art algorithms in different scenes.The proposed method can recover the most details under different illumination,and it is better than the competing methods quantitatively and qualitatively.