Scholarlink

<p>In this work, we investigate the sampling and reconstruction of spectrally <i>s</i>-sparse bandlimited graph signals governed by heat diffusion processes. We propose a random space-time sampling regime, referred to as randomized dynamical sampling, where a small subset of space-time nodes is randomly selected at each time step based on a probability distribution. To analyze the recovery problem, we establish a rigorous mathematical framework by introducing the parameter <i>the dynamic spectral graph weighted coherence</i>. This key parameter governs the number of space-time samples needed for stable recovery and extends the idea of variable density sampling to the context of dynamical systems. By optimizing the sampling probability distribution, we show that as few as <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41_2025_10177_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="81" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {O}(s \log (k))\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">O</mi> <mo stretchy="false">(</mo> <mi>s</mi> <mo>log</mo> <mo stretchy="false">(</mo> <mi>k</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> space-time samples are sufficient for accurate reconstruction in optimal scenarios, where <i>k</i> denotes the bandwidth of the signal. Our framework encompasses both static and dynamic cases, demonstrating a reduction in the number of spatial samples needed at each time step by exploiting temporal correlations. Furthermore, we provide a computationally efficient and robust algorithm for signal reconstruction. Numerical experiments validate our theoretical results and illustrate the practical efficacy of our proposed methods.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Random Space-Time Sampling and Reconstruction of Sparse Bandlimited Graph Diffusion Field

  • 期刊论文

  • 发表日期：

    2025年6月4日

查看全文
  • Longxiu Huang,
  • Dongyang Li,
  • Sui Tang,
  • Qing Yao

摘要

In this work, we investigate the sampling and reconstruction of spectrally s-sparse bandlimited graph signals governed by heat diffusion processes. We propose a random space-time sampling regime, referred to as randomized dynamical sampling, where a small subset of space-time nodes is randomly selected at each time step based on a probability distribution. To analyze the recovery problem, we establish a rigorous mathematical framework by introducing the parameter the dynamic spectral graph weighted coherence. This key parameter governs the number of space-time samples needed for stable recovery and extends the idea of variable density sampling to the context of dynamical systems. By optimizing the sampling probability distribution, we show that as few as \(\mathcal {O}(s \log (k))\) O ( s log ( k ) ) space-time samples are sufficient for accurate reconstruction in optimal scenarios, where k denotes the bandwidth of the signal. Our framework encompasses both static and dynamic cases, demonstrating a reduction in the number of spatial samples needed at each time step by exploiting temporal correlations. Furthermore, we provide a computationally efficient and robust algorithm for signal reconstruction. Numerical experiments validate our theoretical results and illustrate the practical efficacy of our proposed methods.