Constrained spherical deconvolution on signal and ODF values

For the purpose of the ISBI HARDI reconstruction challenge 2013 and for the categories DTI and HARDI acquisitions, we reconstructed the diffusion datasets using two well established methods: a) Spherical Deconvolution Transform (SDT) [1], [2] and b) Constrained Spherical Deconvolution (CSD) [3]. The SDT is a sharpening operation which transforms the smooth diffusion ODF into a sharper fiber ODF. The method is inspired by CSD [3] with, the main difference that the CSD is applied directly to the initial signal and the SDT directly to the ODF. The idea here is that an ODF, for example the analytical Q-ball ODF ψQBI , can be formed by the convolution between the single fiber diffusion ODF kernel R and the true fiber ODF ψSDT .