混合范数条件下平移不变信号的非均匀平均采样

L~p平移不变子空间中的采样研究通常要求生成函数属于一个不依赖于p的Wiener amalgam空间,此条件因不能控制p而显得太强.本文主要讨论生成函数属于混合范数空间时,非衰减平移不变空间中的非均匀平均采样与重构.生成函数属于混合范数空间的条件弱于Wiener amalgam空间且依赖于参数p.基于混合范数空间中的一些引理,针对两种平均采样泛函建立了采样稳定性,并给出了对应的具有指数收敛的迭代重构算法.

Nonuniform Average Sampling of Shift-invariant Signals with Generators in a Hybrid-norm Space

Sampling in shift-invariant subspaces of L_p is commonly studied under the requirement that the generator is in a Wiener amalgam space independent of p, but such condition is too strong because it does not allow us to control p. In this paper, we mainly discuss the nonuniform average sampling and reconstruction of signals in a non-decaying shift-invariant space under the assumption that the generator is in a hybrid-norm space. The new condition is weaker than the Wiener amalgam space and depends on the parameter p. Based on some lemmas in hybrid-norm spaces, we first give the sampling stability for two kinds of average sampling functionals, and then the corresponding iterative reconstruction algorithms with exponential convergence are established.