论文标题
加权重现$l_ν^p（\ mathbb {r}^d）$的加权复制子空间的随机抽样稳定性
Random sampling stability in weighted reproducing kernel subspaces of $L_ν^p(\mathbb{R}^d)$
论文作者
论文摘要
在本文中，我们主要研究了$l_ν^p（\ mathbb {r}^d）$的加权再现子空间中信号的随机采样稳定性，而无需其他要求内核函数具有对称性。采样集是从$ \ mathbb {r}^d $上的一般概率分布中独立和随机绘制的。基于加权再现内核子空间的框架表征，我们首先通过在任何有界域上的有限尺寸子空间近似加权繁殖的内核空间。然后，我们证明，随机采样稳定性对于加权再现子空间中所有信号的可能性很高，当采样大小足够大时，其能量集中在立方体上。
In this paper, we mainly study the random sampling stability for signals in a weighted reproducing kernel subspace of $L_ν^p(\mathbb{R}^d)$ without the additional requirement that the kernel function has symmetry. The sampling set is independently and randomly drawn from a general probability distribution over $\mathbb{R}^d$. Based on the frame characterization of weighted reproducing kernel subspaces, we first approximate the weighted reproducing kernel space by a finite dimensional subspace on any bounded domains. Then, we prove that the random sampling stability holds with high probability for all signals in weighted reproducing kernel subspaces whose energy concentrate on a cube when the sampling size is large enough.
