抽样定理在数字信号处理和图像处理中具有重要的作用,古典Shannon抽样定理因其局限性而限制了它的应用.本文研究了二维平移不变子空间中以任意点作为抽样点的规则抽样定理.首先,抽样空间的一些特征被给出;接着,平移不变子空间的决定集的一个刻画被得到.然后,通过平移不变子空间的决定集,函数属于一个抽样空间的充要条件被证明. The sampling theorem plays an important role in the digital signal processing and image processing, and the classical Shannon sampling theorem limits its application due to its limitation.In this paper, we study the regular sampling of arbitrary points in a two-dimensional translationally invariant subspace as sampling points Theorem. First, some features of the sampling space are given. Then, a description of the set of translation invariant subspaces is obtained. Then, by transforming the deterministic set of invariant subspaces, the function belongs to a sampling space proved.