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.

中文翻译：

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联合空间-Slepian 域中的线性变换和信号估计


我们开发了一个用于球体上信号的联合空间-Slepian 域表示的广义线性变换的框架。这种表示是通过球体上的空间-Slepian 变换实现的。我们制定了一个最小二乘信号估计框架，用于根据空间-Slepian 变换内核指定的修改（变换）空间-Slepian 表示来重建球形信号。我们专门采用核的形式来呈现乘法和卷积变换的解析表达式，并使用后者在火星地形图上呈现插图。