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 setof coarse samples from varying time levels $\{t_1,\dots,t_N\}$. This new way ofsampling, which we call dynamical sampling, differs from standard samplingsince at any fixed time $t_i$ there are not enough samples to recover thefunction $f$ or the state $f_{t_i}$. Although dynamical sampling is an inverseproblem, it differs from the typical inverse problems in which $f$ is to berecovered from $A_Tf$ for a single time $T$. In this paper, we consider signalsthat are modeled by $\ell^2(\mathbb Z)$ or a shift invariant space $V\subsetL^2(\mathbb R)$.
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机译：我们考虑时空采样的问题，其中将从不同时间级别$ \ {t_1，\ dots，t_N \} $的一组组合的粗糙样本中恢复演化过程$ f_t = A_tf $的初始状态$ f $ 。这种称为动态采样的新采样方式与标准采样不同，因为在任何固定时间$ t_i $都没有足够的采样来恢复函数$ f $或状态$ f_ {t_i} $。尽管动态采样是一个反问题，但它与典型的反问题不同，在典型的反问题中，一次要从$ A_Tf $中恢复$ f $。在本文中，我们考虑由$ \ ell ^ 2（\ mathbb Z）$或移位不变空间$ V \ subsetL ^ 2（\ mathbb R）$建模的信号。
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