Nonuniform average sampling in multiply generated shift-invariant subspaces of mixed Lebesgue spaces

Qingyue Zhang

Nonuniform average sampling in multiply generated shift-invariant subspaces of mixed Lebesgue spaces

Classical Analysis and ODEs 2018-06-14 v1

Authors: Qingyue Zhang

Abstract

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 $\{\left \langle f,\psi_{a}(\cdot-x_{j},\cdot-y_{k}) \right \rangle:j,k\in\mathbb{J}\}$ generated by single averaging function and average sampled values $\left\{\left \langle f,\psi_{x_{j},y_{k}}\right \rangle:j,k\in\mathbb{J}\right\}$ generated by multiple averaging functions. Two fast reconstruction algorithms for this two types of average sampled values are provided.

Cite

@article{arxiv.1806.05055,
  title  = {Nonuniform average sampling in multiply generated shift-invariant subspaces of mixed Lebesgue spaces},
  author = {Qingyue Zhang},
  journal= {arXiv preprint arXiv:1806.05055},
  year   = {2018}
}

Comments

16 pages. arXiv admin note: text overlap with arXiv:1801.05715

Nonuniform average sampling in multiply generated shift-invariant subspaces of mixed Lebesgue spaces

Abstract

Cite

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