Wavelet Based Denoising Methods For Magnetic Resonance Images

Abstract

Magnetic resonance medical imaging is one of the diagnostic methods used today in cardiograph, mammography and brain tumor analysis as well as many other applications. They are acquired using gradient coil when magnetic moments in body tissues resonate with a very high magnetic field of the Magnetic Resonance Imaging (MRI) scanner. To obtain the image, the raw data acquired is inverse Fourier transformed which results in a complex image which has Rician distributed noise. Most conventional noise removal methods are not suited for MRI denoising since they do not take in consideration the Rician nature of this noise .Various wavelet based methods that have modeled Rician noise have been developed but with short comings .The objective of this research is to develop an efficient and effective solution for denoising a Magnetic Resonance Image. A detailed analysis of MRI formation is presented and then a mathematical model is formulated for an image that is corrupted by Rician noise. Using statistical data of the images, a number of wavelet based filter algorithms have been developed to denoise the images. The bilateral filter in its adaptive form is used to enhance image features and edges to minimize smoothing effects of noise filtering process. Other processes include signal and noise estimation using various methods including Chi square unbiased risk estimator (CURE), Poisson unbiased Risk Estimator with Linear Estimation of Thresholds (PURE-LET),Steinbeck unbiased Risk Estimator with Linear Estimation of Thresholds (SURE-LET), Linear Minimum Mean square error (LMMSE) and also parameter estimation for various filters used as building blocks in different combination filters. The experimental investigation involves structural MRI, functional MRI and Diffusion weighted MRI images of brain, torso, cranium, hip and knee as test images. Four combinational denoising methods have been developed, these are the wavelet based Haar denoising method using non-local means filter and bilateral enhancement, A wavelet based MRI denoising method using LMMSE estimation and bilateral filter enhancement. Others are a total variational wavelet based structural MRI denoising with bilateral feature enhancement and a Haar wavelet magnetic resonance image denoising with optimized chi-square Rician estimation and bilateral filter enhancement. MATLAB simulation platform has been used in testing their effectiveness against Rician noise. Results obtained show that most of the new methods perform better than the stand alone filters and wavelet thresholding in all forms. This is for both subjective comparison and using various objective measures of quality such as the Peak Signal to noise Ratio (PSNR) and Structural Similarlity Index Measure (SSIM). For example in Table 5.1 and Table 5.2 where SNR is very high, MSE relatively low, UQI almost 1, SSIM 0.984 and EPI 0.89 which is an improvement from 0.70 of the noisy image. It also shows that edge preservation is very sensitive even for low noise