Variational Methods for Magnetic Resonance Image Denoising

Abstract

The research works carried out in this thesis is proposed to develop methodologies newlinefor the enhancement of MRI data using well-known variational methods such as variational mode decomposition (VMD), total variation (TV) method, and wavelet Galerkin method (WGM). The research works presented in the newlinethesis explore Rician and herringbone noise characteristics that occur at the newlinetime of acquisition of MRI data. Post-acquisition image denoising model based newlineon VMD is proposed for removing Rician and herringbone noise from MRI. VMD is an adaptive variational method that sparsely decomposes the image into its principal components or modes based on frequency. The proposed denoising methods e_ectively utilize the properties of the VMD in capturing newlinethe high-frequency noise characteristics from the noisy MRI. In the VMD-TV model for Rician noise, a non-convex optimization-based TV image smoothing is performed in the second stage for removing the remnant noise details newlinefrom the _rst stage. The e_ectiveness of the proposed VMD-TV method is con_rmed based on improved objective quality metrics such as peak signal-tonoise ratio (PSNR), structural similarity index (SSIM), quality index based newlineon local variance (QILV) and the hattacharrya coe_cient (BC). In addition newlineto objective quality assessments, the subjective evaluations carried out by a newlineradiologist and a neurologist show relatively better visual quality of the proposed newlinemethod compared to the methods such as linear minimum mean square error (LMMSE) and bilateral _ltering (BF). The e_ciency of the proposed VMD approach in removing the herringbone noise characteristics from MRI newlinewas further demonstrated by improved non-reference image quality metrics. By exploiting the regularity, vanishing moments and smoothing properties of wavelets and properties of Galerkin method, WGM method is proposed as a postprocessing stage for the MRI Rician denoising. Since WGM relies on the newlinenumerical solution of the partial di_erential equations, the performance of the proposed method is ....