Spatially robust adaptive ensemble average propagator reconstruction via spherical polar Fourier imaging

The aim of this paper is to propose a robust multi-scale adaptive and sequential smoothing (MASS) method framework to spatially and adaptively infer the ensemble average propagator (EAP) of water diffusion in brain regions with complex fiber configurations. We consider Spherical Polar Fourier Imaging (SPFI), which is a model-free and fast analytical high angular resolution diffusion imaging (HARDI) technique, for EAP reconstruction. SPFI uses the combination of angular and radial elementary functions expressed in a spherical coordinate system, making it less reliant on data assumptions and sampling requirements than other HARDI techniques. We reformulate the EAP reconstruction as a robust regression problem using Huber’s loss function with Spherical Polar Fourier (SPF) basis as covariates. Similarity and distance weights are introduced to account for spatial smoothness of HARDI, while preserving the unknown discontinuities (e.g., edges between white matter and grey matter). Experimental results indicate that MASS can reduce the angle detection errors in fiber crossing area and provides more accurate reconstructions than standard voxelwise methods under the presence of outliers.