Image Recovery Based On Statistical Priors And Their Deep Learning Algorithms

Digital image processing refers to the methods of image restoration,enhancement,segmentation and feature extraction by using computer technology.This dissertation mainly studies the image recovery of digital image processing,including image restoration and reconstruction.Image restoration is a technique of restoring the original contents of the low-quality observed image caused by noise,environment,atmospheric turbulence and imaging equipment itself by simulating their degradation process.It is the basis of the whole image processing.Image reconstruction is the reconstruction of the image through the part of the image information.It is widely used in radiological medical equipment.Based on different statistical assumptions,this dissertation uses the total variation(TV)and deep learning algorithms for image restoration and reconstruction tasks.This dissertation mainly studies the restoration of multiplicative structure noise and blur,and the restoration of Cauchy noise and blur.The other part of this dissertation mainly studies the reconstruction of magnetic resonance imaging(MRI)and positron emission computed tomography(PET).The main innovations of this dissertation are as follows:In view of the problem of structure noise and blur restoration,many literatures only focus on the restoration of additive structure noise and blur or multiplicative structured noise.It is still a challenge to restore degraded images with blur and multiplicative structured noise,simultaneously.Based on TV,the statistical property of the Gamma noise,using Bayes rule and maximum posterior estimation method,this dissertation proposes a convex multiplicative structure noise and blur restoration model.In particular,we reformulate the prior assumption of the image degradation model by using division instead of multiplication in this dissertation,which can get a convex model and avoid the difficulty of numerical solution.Moreover,the alternating direction method of multipliers(ADMM)is adopted to solve the problem.Numerical experiments prove the validity and robustness of the proposed model.Cauchy noise is a typical non-Gaussian noise,which often appears in radar,medical and biomedical imaging.Aiming at solving the problem of Cauchy noise and blur,a deep learning-based image denoiser prior is adopted in this dissertation to replace the traditional TV or low-rank prior.In order to maintain a more detailed texture and better balance the size of the receiving domain and the computational cost,multi-level wavelet convolutional neural network(MWCNN)is used to train the denoisers.In addition,the forward-backward splitting algorithm(FBS)is used to solve the proposed model.This algorithm can solve the problem effectively without introducing any auxiliary variables.In this dissertation,a series of denoisers are trained by multi-noise level strategy to recover images degraded by Cauchy noise and blur.Numerical experiments show that our method is superior to the existing image restoration methods both in terms of the quantitative index and visual quality.As a basic and important task,medical image reconstruction has attracted more and more attention in clinical diagnosis.Aiming at the problem of medical image reconstruction,we consider to combine advanced deep learning method with traditional variational model for medical image reconstruction.Specifically,this dissertation proposes a hybrid model which combining MWCNN and tight frame regularization,and uses the proximal alternating minimization(PAM)algorithm to solve the problem effectively.To demonstrate the robustness and effectiveness of the proposed algorithm and model,we used two classic medical image reconstruction tasks,namely magnetic resonance imaging(MRI)and positron emission tomography(PET)to test.Numerical experiments show that the performance of our method is superior to that of the existing methods.