Linear Transformations and Signal Estimation in the Joint Spatial-Slepian Domain

We develop a framework for generalized linear transformations of the joint spatial-Slepian domain representation of signals on the sphere. Such a representation is enabled by the spatial-Slepian transform on the sphere. We formulate a least-square signal estimation framework for reconstruction of the spherical signal from the modified (transformed) spatial-Slepian representation specified by the spatial-Slepian transformation kernel. We specialize the form of the kernel to present analytical expressions for the multiplicative and convolutive transformations, and use the latter to present illustrations on a Mars topography map.