A New Linear Transform Approach for Estimating ODFs from Multi-Shell Diffusion Data

The Funk-Radon and Cosine Transform (FRACT) is a recent linear method for estimating orientation distribution functions (ODFs) from single-shell diffusion MRI data. Compared to previous single-shell ODF estimation techniques, the FRACT offers predictable performance, strong theoretical characterization, and does not require any tissue modeling assumptions (that can confound nonlinear ODF estimation methods when the modeling assumptions are violated). In this work, we propose an extension of FRACT for multi-shell diffusion MRI (MS-FRACT). We show theoretically and empirically that MS-FRACT yields more accurate ODF estimates than conventional FRACT, while still being predictable with strong theoretical characterization, and without requiring tissue-modeling assumptions.

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