Wavelet Frame Method For Medical Image Restoration And Its Application

Medical imaging models such as MRI and CT are affected by artifacts and noise.The tiny particles in the air will cause noise in the image.The hands shaking of the cameraman or the motion of the imaging object will cause the motion artifacts.The motion artifacts will blur the image.This dissertation aims to restore the original images from the blurred and noisy images.Minimizing the energy functional formed by fidelity term is commonly used.However,this minimization model is ill-posed,it will amplify the noise to recover the image.Adding the regularization terms is a common method to overcome its ill-posedness.The common regularization methods include Tikhonov regularization,TV regularization,etc.However,with the increasing demand for small details in some areas of medical imaging,these methods can’t meet the demand.Considering that the first or second derivative of some images is sparse,sparse regularization is valued and has been widely used.The wavelet frame method generally describes the image through sparseness.The various filters in the wavelet frame systems can capture the first-order and second-order derivative features of the images.Under the a priori assumption of the sparsity of the coefficients of the medical image in the wavelet transform domain,we construct a minimization model with an l1/2 regularization term including the wavelet frames.This is a sparse regularization problem with non-convex optimization.In this dissertation,the alternating direction method of multipliers is used to solve the minimization problem of l1/2 regularization under the wavelet frames.We give the convergence analysis of the iterative scheme.We do numerical experiments using the sparsity of the coefficients of the medical image in the wavelet transform domain to validate the proposed theory.