Model-free and analytical EAP reconstruction via spherical polar Fourier diffusion MRI

How to estimate the diffusion Ensemble Average Propagator (EAP) from the DWI signals in q-space is an open problem in diffusion MRI field. Many methods were proposed to estimate the Orientation Distribution Function (ODF) that is used to describe the fiber direction. However, ODF is just one of the features of the EAP. Compared with ODF, EAP has the full information about the diffusion process which reflects the complex tissue micro-structure. Diffusion Orientation Transform (DOT) and Diffusion Spectrum Imaging (DSI) are two important methods to estimate the EAP from the signal. However, DOT is based on mono-exponential assumption and DSI needs a lot of samplings and very large b values. In this paper, we propose Spherical Polar Fourier Imaging (SPFI), a novel model-free fast robust analytical EAP reconstruction method, which almost does not need any assumption of data and does not need too many samplings. SPFI naturally combines the DWI signals with different b-values. It is an analytical linear transformation from the q-space signal to the EAP profile represented by Spherical Harmonics (SH). We validated the proposed methods in synthetic data, phantom data and real data. It works well in all experiments, especially for the data with low SNR, low anisotropy, and non-exponential decay.