arXiv subjects

Yingchun Jiang

Publications and source records attributed to Yingchun Jiang.

5 recordsLinked to original sources

arXiv2022

Random sampling stability in weighted reproducing kernel subspaces of $L_ν^p(\mathbb{R}^d)$

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.

math.FA↗

arXiv2020

$(p,q)$-frames in shift-invariant subspaces of mixed Lebesgue spaces $L^{p,q}(\mathbf{R}\times \mathbf{R}^{d})$

In this paper, we mainly discuss the $(p,q)$-frame in shift-invariant subspace \begin{equation*} V_{p,q}(Φ)=\left\{\sum\limits_{i=1}^{r}\sum\limits_{j_{1}\in \mathbf{Z}}\sum\limits_{j_{2}\in \mathbf{Z}^{d}}d_{i}(j_{1},j_{2})ϕ_{i}(\cdot-j_{1},\cdot-j_{2}):\Big(d_{i}(j_{1},j_{2})\Big)_{(j_{1},j_{2})\in \mathbf{Z}\times\mathbf{Z}^{d}}\in \ell^{p,q}(\mathbf{Z}\times\mathbf{Z}^d)\right\} \end{equation*} of mixed Lebesgue space $L^{p,q}(\mathbf{R}\times \mathbf{R}^{d})$. Some equivalent conditions for $\{ϕ_{i}(\cdot-j_{1},\cdot-j_{2}):(j_{1},j_{2})\in\mathbf{Z}\times\mathbf{Z}^d,1\leq i\leq r\}$ to constitute a $(p,q)$-frame of $V_{p,q}(Φ)$ are given. Moreover, the result shows that $V_{p,q}(Φ)$ is closed under these equivalent conditions of $(p,q)$-frame for the family $\{ϕ_{i}(\cdot-j_{1},\cdot-j_{2}):(j_{1},j_{2})\in\mathbf{Z}\times\mathbf{Z}^d,1\leq i\leq r\}$, although the general result is not correct.

math.FA↗

arXiv2019

Adaptive sampling of time-space signals in a reproducing kernel subspace of mixed Lebesgue space

The Mixed Lebesgue space is a suitable tool for modelling and measuring signals living in time-space domains. And sampling in such spaces plays an important role for processing high-dimensional time-varying signals. In this paper, we first define reproducing kernel subspaces of mixed Lebesgue spaces. Then, we study the frame properties and show that the reproducing kernel subspace has finite rate of innovation. Finally, we propose a semi-adaptive sampling scheme for time-space signals in a reproducing kernel subspace, where the sampling in time domain is conducted by a time encoding machine. Two kinds of timing sampling methods are considered and the corresponding iterative approximation algorithms with exponential convergence are given.

cs.IT↗

arXiv2015

Spatially Distributed Sampling and Reconstruction

A spatially distributed system contains a large amount of agents with limited sensing, data processing, and communication capabilities. Recent technological advances have opened up possibilities to deploy spatially distributed systems for signal sampling and reconstruction. In this paper, we introduce a graph structure for a distributed sampling and reconstruction system by coupling agents in a spatially distributed system with innovative positions of signals. A fundamental problem in sampling theory is the robustness of signal reconstruction in the presence of sampling noises. For a distributed sampling and reconstruction system, the robustness could be reduced to the stability of its sensing matrix. In a traditional centralized sampling and reconstruction system, the stability of the sensing matrix could be verified by its central processor, but the above procedure is infeasible in a distributed sampling and reconstruction system as it is decentralized. In this paper, we split a distributed sampling and reconstruction system into a family of overlapping smaller subsystems, and we show that the stability of the sensing matrix holds if and only if its quasi-restrictions to those subsystems have uniform stability. This new stability criterion could be pivotal for the design of a robust distributed sampling and reconstruction system against supplement, replacement and impairment of agents, as we only need to check the uniform stability of affected subsystems. In this paper, we also propose an exponentially convergent distributed algorithm for signal reconstruction, that provides a suboptimal approximation to the original signal in the presence of bounded sampling noises.

cs.IT↗

arXiv2014

Sampling and Galerkin reconstruction in reproducing kernel spaces

In this paper, we consider sampling in a reproducing kernel subspace of $L^p$. We introduce a pre-reconstruction operator associated with a sampling scheme and propose a Galerkin reconstruction in general Banach space setting. We show that the proposed Galerkin method provides a quasi-optimal approximation, and the corresponding Galerkin equations could be solved by an iterative approximation-projection algorithm. We also present detailed analysis and numerical simulations of the Galerkin method for reconstructing signals with finite rate of innovation.

cs.IT↗