A discrete Funk transform on the Cubed Sphere

Computing accurately Funk transforms from discrete values is crucial in some applications, such as Q-Ball Imaging medicine. This paper deals with a transform devoted to computation. The studied based on spectral method applied least squares fitting, the special feature that regularization not performed. We investigate several mathematical and numerical aspects this context, including stability pseudoinversion. As specific instance, we introduce simple framework equiangular Cubed Sphere guarantee stability. Various experiments attest accuracy convergence of approach, particular for synthetic Gaussian signals Imaging.