A full technical description is available from:
J. P. Haldar, R. M. Leahy. Linear Transforms for Fourier Data on the Sphere: Application to High Angular Resolution Diffusion MRI of the Brain. NeuroImage 71:233-247, 2013.
http://dx.doi.org/10.1016/j.neuroimage.2013.01.022
Some relationships to spherical deconvolution are discussed in:
J. P. Haldar, R. M. Leahy. The Equivalence of Linear Spherical Deconvolution and Model-Free Linear Transform Methods for Diffusion MRI. IEEE International Symposium on Biomedical Imaging: From Nano to Macro, San Francisco, 2013, pp. 504-507.
http://dx.doi.org/10.1109/ISBI.2013.6556523