Robust maximum likelihood estimation in Q-space MRI

Q-space imaging is an emerging diffusion weighted MR imaging technique to estimate molecular diffusion probability density functions (PDF's) without the need to assume a Gaussian distribution. We present a robust M-estimator, Q-space Estimation by Maximizing Rician Likelihood (QEMRL), for diffusion PDFs based on maximum likelihood. PDFs are modeled by constrained Gaussian mixtures. In QEMRL, robust likelihood measures mitigate the impacts of imaging artifacts. In simulation and in vivo human spinal cord, the method improves reliability of estimated PDFs and increases tissue contrast. QEMRL enables more detailed exploration of the PDF properties than prior approaches and may allow acquisitions at higher spatial resolution.