MRI/fMRI noise reduction and data analysis

The thesis addresses two critical issues in the processing of Magnetic Resonance Images (MRI) which have a wide-ranging impact in the deployment of MRI in clinical and scientific settings viz. the reduction of noise in MR images, and a subsequent noise-robust clustering process for analyzing critical aspects of functional MRI (fMRI). MR images acquired with fast acquisition techniques often display low signal-to-noise ratios (SNRs). In addition to the problem of relatively poor SNR in MR in general, fMRI often exhibit a low contrast to noise ratio (CNR). Therefore efficient MR denoising techniques and noise robust methods for detecting small and localized brain activations are critical both in clinical and in more general scientific use of MRI/fMRI. Since noise in MR magnitude images is known to be signal-dependent Rician distributed, standard approaches, which assume Gaussian noise model, are at best sub-optimal and at worst significantly in error. In this thesis, we develop a novel Non-Local Maximum Likelihood Estimation (NLML) method for Rician noise reduction in MRI/fMRI. We assume that the underpinning noise is in fact Rician, and posit that pixels which have similar neighborhoods come from the same distribution. By comparing NLML to a wide variety of standard denoising approaches, we show that it outperforms most traditional smoothing algorithms, non-local means and wavelet-based algorithms in recovering the true signal from Rician noise in terms of: SNR, contrast, the preservation of sharp tissue boundaries in terms of visual appearance, method error and a well-defined sharpness metric. In addition, in order to improve the accuracy of the detection of brain activation regions in fMRI, we develop a novel noise-robust Spatial Fuzzy Clustering (SFC) algorithm, which incorporates spatial regularization by means of a Markov Random Field (MRF) model. We assume that fMRI Statistical Parametric Map (SPM) to be best modeled by an MRF and couple the MRF to the fuzzy model by defining a fuzzy neighborhood energy function that describes the interaction between neighboring voxels. By comparing the clustering performance of our method to extant brain activation clustering strategies, we demonstrate that the SFC algorithm outperforms standard approaches, both on simulated and actual data.