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

We present an operator formulation for linear transformations in the joint spatial-Slepian domain, which is enabled by the spatial-Slepian transform. The operator is an integral type and is specified by the spatial-Slepian transformation kernel, which is also utilized in finding a matrix representation for the operator using the orthogonal basis of Wigner-D functions. Conditions for the compactness and self-adjointness of the operator are presented and spectral analysis is carried out. The formulation is illustrated by choosing a Gaussian form for the spectral representation of the kernel to smooth out the noise in a bandlimited Earth topography map.