Research On Image Processing Based On "Convex-Nonconvex" Statistical Prior

In the information age,images have become an important way for people to obtain and disseminate information.However,in the process of image acquisition,storage and dissemination,many unavoidable factors can lead to image quality degradation,such as noise,imaging environment,imaging equipment,etc.Digital image processing technology is rapidly developing in this era and is helping to improve and develop many industries(medical,aerospace,military,etc.).Digital image processing is the method of image restoration,enhancement,segmentation,feature extraction by using computer technology.This paper focuses on image restoration and segmentation in image processing,which mainly include image denoising,phase retrieval and image segmentation.Image denoising is the basis of the whole image processing,which refers to the restoration of the original image from the noise-polluted image;phase retrieval refers to the recovery of the phase information containing the image structure from the acquired image magnitude information;image segmentation is the division of the target and background of the image with their unique properties.For these three tasks,the following work is carried out in this paper.1.With the development and application of magnetic resonance imaging(MRI)techniques in recent years,more and more attention has been paid to the Rician noise removal problem in MRI.Rician noise,which often appears in medical images,leads to an interesting nonconvex optimization problem,namely the MAP-Rician model based on the Maximum a posteriori(MAP)and Bayes’ law.We need to understand carefully the mathematical meaning of this model and need to choose appropriately the suitable algorithm to solve this nonconvex problem.In this paper,we investigate these two problems.First,we give a theoretical result on the existence of minimal solutions to the MAP-Rician model under mild conditions.Second,we use an efficient and convergence-guaranteed boosted difference of convex algorithm(BDCA)to deal with this challenging problem.We also prove that the sequence generated by the proposed algorithm converges to a stationary point with the objective function values decreasing monotonically.Numerical experiments demonstrate that our strategy outperforms existing Rician noise removal methods.2.Since phase retrieval can be applied in many aspects such as signal recovery and holographic imaging,it has become a very important research area.During phase retrieval,the amplitude measurements are subject to noise interference during the measurement process.Many existing methods have obtained better results by adding the total variation(TV)to the phase retrieval model.Considering that regularization can reduce the influence of noise on ill-posed problems,we propose an implicit regularization-based phase retrieval model.In particular,we apply a smoothing scheme to handle the non-smooth implicitly regular terms in the discrete model.Since this nonconvex phase retrieval model presents a decomposable form,we apply BDCA to solve it.Theoretically,the convergence of the numerical algorithm is effectively guaranteed based on the Kurdyka-Lojasiewicz(KL)property.Numerical experiments also verify the validity and robustness of the proposed model.3.Image segmentation is a crucial pre-processing for image recognition and computer vision.In order to improve the quality of image segmentation,we need to describe the local information of the target in the image as much as possible.In this paper,we propose a two-stage segmentation strategy based on adaptive TV.First,we propose a smooth model based on adaptive TV to process the noise and blur in the image.Among them,the adaptive TV combines a weighting matrix with a gradient operator,which can simultaneously achieve the function of maintaining the local features of the image and filtering the noise.We apply a fast and efficient semi-proximal alternating direction method of multipliers(sPADMM)with convergence guarantee to solve the proposed smooth model.Next,we perform segmentation on the smooth results using a simple and effective thresholding method,i.e.Kmeans.Numerical experiments show that our method outperforms existing image segmentation methods both in terms of quantitative metrics and visual quality.