Regularized Q-Ball Reconstruction: Robust Estimation, Model Selection, and Spatial Denoising

Jaime E. Cisternas¹, Pedro Daza¹, Takeshi Asahi², Tim B. Dyrby³, Klaus Fritzsche⁴

Diffusion weighted MRI offers the possibility of measuring the random motion of water molecules, revealing important microscopic features of anisotropic tissue such as the orientation of white matter fiber tracts. For high angular resolution acquisitions, recently proposed methods such as Q-ball describe the directional heterogeneity of complex voxels and should in principle detect fiber crossings. Now the Q-ball model, in its different implementations, has a large number of degrees of freedom that are difficult to estimate in the presence of noise, leading to overfitting and artefacts. The present work proposes a variational framework for the estimation, spatial smoothing and model selection, that greatly reduces the impact of noise on the estimated parameters and on other quantities such as the principal and secondary diffusion orientations. Some of the key ingredients of the approach are the use of an expansion in terms of real spherical harmonics to describe the orientation distribution, and a rotationally invariant metric of the coefficients of the expansion.