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The Study Of Algorithm In Image Processing Based On Multiscale Resolution Analysis And Partial Differential Equations

Posted on:2013-01-13Degree:DoctorType:Dissertation
Country:ChinaCandidate:Y WangFull Text:PDF
GTID:1118330371482969Subject:Computational Mathematics
Abstract/Summary:PDF Full Text Request
Image science is an inter-discipline subject and has a great relationshipwith the successful applications of multi-subject, especially mathematics. Inimage processing, no matter image modeling, representation of image contents,description of image feature, all can be upgraded to a mathematic problem.Especially in recent years, as a representation of mathematic tools, WaveletTransform (WT) and Partial Diferential Equations (PDE) are active in manyimage-processing felds, making the name of"Image Science" gradually beingaccepted by people. In this paper, we will study some aspects of algorithms ofwavelets and PDE, and obtain some new instructive algorithms:(1) A3D extension of the wavelet transform based bilateral fltering ideafor Rician noise removal was proposed. Considering the delineating capabilityof wavelet,3D wavelet transform is employed to provide efective represen-tation of the noisy coefcients. Then, bilateral fltering of the approxima-tion coefcients in a modifed neighborhood improves the denoising efciencyand efectively preserves the relevant edge features. Meanwhile, the detailedsubbands are processed with a weighted NeighShrink thresholding algorithm.The experimental results over synthetic images demonstrate that our proposalachieves good performance with respect to the other MRI denoising fltersbeing compared.(2) Based on the3D Radon transform, a wavelet denoising method is pro-posed for MRI images. Based on noise statistics, we apply the3D Radon trans- form to the original MRI images and use the Gaussian noise model to processthe projected image. A translation invariant wavelet transform is employed todecompose the projected image into multiscales in order to efectively denoisethe images. For the fnal denoised projected image, we apply the inverse Radontransform in order to reconstruct the original MRI images. Simulation brainMRI images were used to validate our method. The experiment results showthe superiority of the proposed scheme over the methods being compared.(3) A new fltering method to remove Rician noise from magnetic reso-nance imaging is presented. This flter relies on a robust estimation of thestandard deviation of the noise and a new difusion coefcient based on theedge-preserving method is proposed. The parameter of the flter are auto-matically chosen from image's local statistics. This property improves theconvergence rate of the difusion while preserving contours, leading to morerobust and intuitive fltering. The numerical scheme is explained and visualand quantitative result on simulated datasets are presented. In the experi-ments, the new flter leads to the best results.(4) Total variation was recently introduced in many diferent magneticresonance imaging appications. The assumption of total variation is that im-ages consist of areas, which are piecewise constant. However, in many praticalmagnetic resonance imaging situations, this assumptions is not valid due tothe inhomogeneities of the exciting B1feld and the receive coils. In this chap-ter, we propose a variational model to restore images degraded by Rician noise.This model uses total variation regularization with a fdelity term involving theRician probability distribution. The quantitative and the qualitative measuresused as the quality metrics demonstrate the ability of the proposed methodfor noise suppression.
Keywords/Search Tags:Magnetic Resonance Imaging, Rician noise, Image denoising, 3DWavelet Transform, Bilateral flter, NeighShrink, 3D Radon Transform, Trans-lation invariant wavelet, Bayesian estimation, Anisotropic Difusion, PartialDiferential Equations
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