In this paper, we consider (random) sampling of signals concentrated on a bounded Corkscrew domain Ω of a metric measure space, and reconstructing concentrated signals approximately from their (un)corrupted sampling data taken on a sampling set contained in Ω. We establish a weighted stability of bi-Lipschitz type for a (random) sampling scheme on the set of concentrated signals in a reproducing kernel space. The weighted stability of bi-Lipschitz type provides a weak robustness to the sampling scheme, however due to the nonconvexity of the set of concentrated signals, it does not imply the unique signal reconstruction. From (un)corrupted samples taken on a finite sampling set contained in Ω, we propose an algorithm to find approximations to signals concentrated on a bounded Corkscrew domain Ω. Random sampling is a sampling scheme where sampling positions are randomly taken according to a probability distribution. Next we show that, with high probability, signals concentrated on a bounded Corkscrew domain Ω can be reconstructed approximately from their uncorrupted (or randomly corrupted) samples taken at i.i.d. random positions drawn on Ω, provided that the sampling size is at least of the order $\mu (\mathrm{\Omega })\ln (\mu (\mathrm{\Omega }))$, where $\mu (\mathrm{\Omega })$ is the measure of the concentrated domain Ω. Finally, we demonstrate the performance of proposed approximations to the original concentrated signals when the sampling procedure is taken either with large density or randomly with large size.

在本文中，我们考虑（随机）集中在度量度量空间的有界Corkscrew域Ω上的信号采样，并从在Ω中包含的采样集上获取的（未）损坏的采样数据近似重构集中的信号。我们为重现核空间中的集中信号集上的（随机）采样方案建立了双Lipschitz类型的加权稳定性。bi-Lipschitz类型的加权稳定性为采样方案提供了较弱的鲁棒性，但是由于集中信号集的非凸性，它并不意味着唯一的信号重构。通过对包含在Ω中的有限采样集进行采样的（未破坏的）采样，我们提出了一种算法来查找集中在有限的Corkscrew域Ω上的信号的近似值。随机采样是一种采样方案，其中根据概率分布随机获取采样位置。接下来，我们证明，只要采样大小至少为阶数，集中在有限的Corkscrew域Ω上的信号就可以近似地从在Ω上绘制的iid随机位置处获取的未损坏（或随机损坏）的样本中进行重构。$\mu （\mathrm{\Omega }）\ln （\mu （\mathrm{\Omega }））$， 在哪里 $\mu （\mathrm{\Omega }）$是集中域Ω的量度。最后，当以大密度或随机大尺寸采样时，我们证明了对原始集中信号的拟议近似性能。