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

Introduction: This work proposes a new linear transform method for estimating orientation distribution functions (ODFs) from multi-shell (MS) diffusion MRI data. MS data is becoming increasingly common, partly due to the fact that MS data often contains more information than standard single-shell acquisitions [1-7]. Existing methods for estimating ODFs from MS data have either used non-linear processing [1,4,6] or have used linear processing under specific modeling assumptions [3,5]. In each of these cases, the theoretical relationship between the estimated ODF and the original propagator has not been established for the common situation where modeling assumptions are violated. Since brain white matter characteristics can be quite complicated and can vary between different brain regions (e.g., axon radius, myelination, and packing density can all change), it is common for modeling assumptions to be at least partially violated in practice. Some approaches (particularly the nonlinear methods) can be sensitive to modeling violations, leading to inaccurate results [6,8].