Gaussianization of Diffusion MRI Data Using Spatially Adaptive Filtering

Diffusion MRI magnitude data, typically Rician or noncentral χ distributed, is affected by the noise floor, which falsely elevates signal, reduces image contrast, and biases estimation of diffusion parameters. Noise floor can be avoided by extracting real-valued Gaussian-distributed data from complex diffusion-weighted images via phase correction, which is performed by rotating each complex diffusion-weighted image based on its phase so that the actual image content resides in the real part. The imaginary part can then be discarded, leaving only the real part to form a Gaussian-noise image that is not confounded by the noise floor. The effectiveness of phase correction depends on the estimation of the background phase associated with factors such as brain motion, cardiac pulsation, perfusion, and respiration. Most existing smoothing techniques, applied to the real and imaginary images for phase estimation, assume spatially-stationary noise. This assumption does not necessarily hold in real data. In this paper, we introduce an adaptive filtering approach, called multi-kernel filter (MKF), for image smoothing catering to spatially-varying noise. Inspired by the mechanisms of human vision, MKF employs a bilateral filter with spatially-varying kernels. Extensive experiments demonstrate that MKF significantly improves spatial adaptivity and outperforms various state-of-the-art filters in signal Gaussianization.