Deconvolution in diffusion spectrum imaging

Diffusion spectrum magnetic resonance imaging (DSI) allows the estimation of the displacement probability density function (pdf) of water molecules, which contain valuable information about the microgeometry of the medium where the diffusion process occurs. It provides a more general approach to disentangle complex fiber structures in biological tissues because it does not assume any particular model of diffusion; even so, it has a number of limitations that remain unstudied. For instance, the theoretical model used to compute the displacement pdf is based on a Fourier transformation defined in the whole measurement space; however, in practice, it is computed using discrete signals with a finite support. As a consequence, the displacement pdf obtained from the experiments is the convolution between the true pdf and a point spread function (PSF) that completely depends on the experimental sampling scheme. In this work, a general framework to rectify and decontaminate the displacement pdf reconstructed from DSI is introduced. This framework is based on model-free deconvolution techniques that allow obtaining clearer and sharper DSI estimates. The method was tested in synthetic data as well as in real data measured from a healthy human volunteer. The results demonstrated that the angular resolution of DSI can be increased, potentially revealing new real fiber components and reducing both the artefactual peaks and the uncertainty of the local diffusion orientational distribution. Furthermore, the deconvolution process provides scalar maps of quantities derived from the propagator, such as the zero displacement probability, with higher tissue contrast.