进化系统中空间欠采样信号的精确重构
Exact Reconstruction of Spatially Undersampled Signals in Evolutionary Systems
摘要：
我们认为时空采样的问题，其中的初始状态$f$的进化过程$f_t=A_tf$是从一组组合的粗样本从不同的时间水平$\{t_1,\dots,t_N\}$恢复。这种新的采样方式，我们称之为动态采样，不同于标准采样，因为在任何固定时间$t_i$都没有足够的样本来恢复函数$f$或状态$f_{t_i}$。虽然动态采样是一个反问题，它不同于典型的反问题，其中$f$是从$A_Tf$恢复一个单一的时间$T$。在本文中，我们考虑由$\ell^2(\mathbb Z)$或移位不变空间$V\subset L^2(\mathbb R)$建模的信号。
英文摘要：
We consider the problem of spatiotemporal sampling in which an initial state $f$ of an evolution process $f_t=A_tf$ is to be recovered from a combined set of coarse samples from varying time levels $\{t_1,\dots,t_N\}$. This new way of sampling, which we call dynamical sampling, differs from standard sampling since at any fixed time $t_i$ there are not enough samples to recover the function $f$ or the state $f_{t_i}$. Although dynamical sampling is an inverse problem, it differs from the typical inverse problems in which $f$ is to be recovered from $A_Tf$ for a single time $T$. In this paper, we consider signals that are modeled by $\ell^2(\mathbb Z)$ or a shift invariant space $V\subset L^2(\mathbb R)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
