混合Lebesgue空间的多重生成移位不变子空间中的非均匀平均采样
Nonuniform average sampling in multiply generated shift-invariant subspaces of mixed Lebesgue spaces
摘要：
本文研究了混合Lebesgue空间的多重生成移位不变子空间中的非均匀平均采样问题。本文讨论了两类平均采样值：由单个平均函数产生的平均采样值$\{\left \langle f,ψ_{a}(\cdot-x_{j},\cdot-y_{k}) \right \rangle:j,k\in\mathbb{J}\}$和由多个平均函数产生的平均采样值$\left\{\left \langle f,ψ_{x_{j},y_{k}}\right \rangle:j,k\in\mathbb{J}\right\}$。针对这两类平均采样值，提出了两种快速重构算法。
英文摘要：
In this paper, we study nonuniform average sampling problem in multiply generated shift-invariant subspaces of mixed Lebesgue spaces. We discuss two types of average sampled values: average sampled values $\{\left \langle f,ψ_{a}(\cdot-x_{j},\cdot-y_{k}) \right \rangle:j,k\in\mathbb{J}\}$ generated by single averaging function and average sampled values $\left\{\left \langle f,ψ_{x_{j},y_{k}}\right \rangle:j,k\in\mathbb{J}\right\}$ generated by multiple averaging functions. Two fast reconstruction algorithms for this two types of average sampled values are provided.
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