Theory and practice of irregular sampling

IF 0.9 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

International Journal of Wavelets Multiresolution and Information Processing Pub Date : 2021-01-01 DOI:10.1201/9781003210450-10

H. Feichtinger, K. Gröchenig

引用次数: 117

Abstract

This chapter presents methods for the reconstruction of bandlimited functions from irregular samples. The first part discusses algorithms for a constructive solution of the irregular sampling problem. An important aspect of these algorithms is the explicit knowledge of the constants involved and efficient error estimates. The second part discusses the numerical implementation of these algorithms and compares the performance of various reconstruction methods. Although most of the material has already appeared in print, several new results are included: (a) a new method to estimate frame bounds, (b) a reconstruction of band-limited functions from partial information, which is not just the samples; (c) a new result on the complete reconstruction of band-limited functions from local averages; (d) a systematic exposition of recent experimental results.

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不规则抽样的理论与实践

本章介绍了从不规则样本中重建带限函数的方法。第一部分讨论了不规则采样问题的构造解算法。这些算法的一个重要方面是明确了解所涉及的常数和有效的误差估计。第二部分讨论了这些算法的数值实现，并比较了各种重建方法的性能。虽然大多数材料已经出现在印刷品中，但包括几个新的结果:(a)估计帧边界的新方法;(b)从部分信息重建带限制函数，这不仅仅是样本;(c)关于局部平均完全重构带限函数的新结果;(d)对最近实验结果的系统阐述。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

International Journal of Wavelets Multiresolution and Information Processing 工程技术-计算机：软件工程

CiteScore

2.60

自引率

7.10%

发文量

审稿时长

2.7 months

期刊介绍： International Journal of Wavelets, Multiresolution and Information Processing (hereafter referred to as IJWMIP) is a bi-monthly publication for theoretical and applied papers on the current state-of-the-art results of wavelet analysis, multiresolution and information processing. Papers related to the IJWMIP theme are especially solicited, including theories, methodologies, algorithms and emerging applications. Topics of interest of the IJWMIP include, but are not limited to: 1. Wavelets: Wavelets and operator theory Frame and applications Time-frequency analysis and applications Sparse representation and approximation Sampling theory and compressive sensing Wavelet based algorithms and applications 2. Multiresolution: Multiresolution analysis Multiscale approximation Multiresolution image processing and signal processing Multiresolution representations Deep learning and neural networks Machine learning theory, algorithms and applications High dimensional data analysis 3. Information Processing: Data sciences Big data and applications Information theory Information systems and technology Information security Information learning and processing Artificial intelligence and pattern recognition Image/signal processing.