For radial basis function (RBF) kernel interpolation of scattered data,
Schaback in 1995 proved that the attainable approximation error and the
condition number of the underlying interpolation matrix cannot be made small
simultaneously. He referred to this finding as an "uncertainty relation", an
undesirable consequence of which is that RBF kernel interpolation is
susceptible to noisy data. In this paper, we propose and study a distributed
interpolation method to manage and quantify the uncertainty brought on by
interpolating noisy spherical data of non-negligible magnitude. We also present
numerical simulation results showing that our method is practical and robust in
terms of handling noisy data from challenging computing environments.

该研究论文介绍了一种分布式插值方法，用于管理和量化由插值具有非可忽略的大小的嘈杂球形数据引发的不确定性，并展示了对具有挑战性计算环境中的嘈杂数据进行处理时，该方法在实际应用中的实用性和鲁棒性。

在球面上的核插值分布式不确定性量化

Distributed Uncertainty Quantification of Kernel Interpolation on  Spheres

We investigate the recovery of signals exhibiting a sparse representation in
a general (i.e., possibly redundant or incomplete) dictionary that are
corrupted by additive noise admitting a sparse representation in another
general dictionary. This setup covers a wide range of applications, such as
image inpainting, super-resolution, signal separation, and recovery of signals
that are impaired by, e.g., clipping, impulse noise, or narrowband
interference. We present deterministic recovery guarantees based on a novel
uncertainty relation for pairs of general dictionaries and we provide
corresponding practicable recovery algorithms. The recovery guarantees we find
depend on the signal and noise sparsity levels, on the coherence parameters of
the involved dictionaries, and on the amount of prior knowledge about the
signal and noise support sets.

本文研究了在一般（即可能是冗余或不完整的）词典中表现出稀疏表示并受到另一种广义词典中的加性噪声干扰的信号的恢复方法。文章基于新的不确定性关系提供了确定性的恢复保证，并提供了相应的实用恢复算法。