使用香农插值和泊松求和公式的随机采样
Random Sampling Using Shannon Interpolation and Poisson Summation Formulae
AI总结：
本文利用香农插值和泊松求和公式实现快速观测矩阵填充，结合正交匹配追踪和梯度总变分策略恢复随机采样信号，并通过三角信号、高斯调制正弦脉冲和方波的数值实验验证方法有效性。
摘要：
本报告主要关注随机采样的基本概念和恢复方法。恢复方法包括正交匹配追踪算法和基于梯度的总变分策略。特别地，通过经典的香农插值和泊松求和公式实现了一种快速高效的观测矩阵填充技术。文中展示并讨论了三角信号、高斯调制正弦脉冲和方波的数值结果。该工作可能对随机采样在理论研究和实际应用中的未来工作有所帮助。
英文摘要：
This report mainly focused on the basic concepts and the recovery methods for the random sampling. The recovery methods involve the orthogonal matching pursuit algorithm and the gradient-based total variation strategy. In particular, a fast and efficient observation matrix filling technique was implemented by the classic Shannon interpolation and Poisson summation formulae. The numerical results for the trigonometric signal, the Gaussian-modulated sinusoidal pulse, and the square wave were demonstrated and discussed. The work may give some help for future work in theoretical study and practical implementation of the random sampling.
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。
