球面上带限信号球谐变换的迭代残差拟合：推广与分析
Iterative Residual Fitting for Spherical Harmonic Transform of Band-Limited Signals on the Sphere: Generalization and Analysis
摘要：
提出了一种广义迭代残差拟合（IRF）方法，用于计算球面上带限信号的球谐变换（SHT）。所提出的方法是基于带限信号的子空间划分成正交子空间。存在支持精确计算SHT的球体上的采样方案。然而，存在由于信号和/或采集设置的性质而不在预定义网格上进行采样（或测量）的应用。为了支持这样的应用程序，建议IRF方法能够精确计算随机分布的足够数量的样本的信号的SHT。为了提高SHT的计算精度，我们还提出了所谓的多通道IRF，它增加了多个迭代通道的IRF。我们分析了不同采样方案和不同大小分区的多通IRF。此外，我们进行数值实验，以说明多通IRF允许足够准确的计算SHT。
英文摘要：
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.
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