We present the generalized iterative residual fitting (IRF) for the
computation of the spherical harmonic transform (SHT) of band-limited signals
on the sphere. The proposed method is based on the partitioning of the subspace
of band-limited signals into orthogonal subspaces. There exist sampling schemes
on the sphere which support accurate computation of SHT. However, there are
applications where samples~(or measurements) are not taken over the predefined
grid due to nature of the signal and/or acquisition set-up. To support such
applications, the proposed IRF method enables accurate computation of SHTs of
signals with randomly distributed sufficient number of samples. In order to
improve the accuracy of the computation of the SHT, we also present the
so-called multi-pass IRF which adds multiple iterative passes to the IRF. We
analyse the multi-pass IRF for different sampling schemes and for different
size partitions. Furthermore, we conduct numerical experiments to illustrate
that the multi-pass IRF allows sufficiently accurate computation of SHTs.Comment: 5 Pages, 7 Figure
