非平稳Gabor框架--近似对偶框架与重构误差
Nonstationary Gabor Frames - Approximately Dual Frames and Reconstruction Errors
摘要：
非平稳的Gabor框架，最近引入的自适应信号分析，代表了一个自然的推广经典的Gabor框架，允许窗口和格在时间或频率的自适应性。由于缺乏一个完全格结构，完美的重建一般是不可行的系数从非平稳的Gabor帧。在本文中，它表明，非平稳的Gabor框架，相关的一些已知的框架，对偶框架可以计算，可以实现良好的近似重建诉诸近似对偶框架。特别是，我们给建设性的例子，所谓的几乎无痛非平稳框架，即框架密切相关的非平稳框架与companies支持的窗口。理论结果通过具体的计算和数值例子说明。
英文摘要：
Nonstationary Gabor frames, recently introduced in adaptive signal analysis, represent a natural generalization of classical Gabor frames by allowing for adaptivity of windows and lattice in either time or frequency. Due to the lack of a complete lattice structure, perfect reconstruction is in general not feasible from coefficients obtained from nonstationary Gabor frames. In this paper it is shown that for nonstationary Gabor frames that are related to some known frames for which dual frames can be computed, good approximate reconstruction can be achieved by resorting to approximately dual frames. In particular, we give constructive examples for so-called almost painless nonstationary frames, that is, frames that are closely related to nonstationary frames with compactly supported windows. The theoretical results are illustrated by concrete computational and numerical examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
