论文标题
迭代执行离散和逆离散傅立叶变换，并使用信号通过稀疏来信号deno
Iterative execution of discrete and inverse discrete Fourier transforms with applications for signal denoising via sparsification
论文作者
论文摘要
我们描述了一个迭代算法的家族，其中涉及反复执行离散和离散傅立叶变换。该家族中一个有趣的成员是由离散的傅立叶变换不确定性原理的动机，涉及将稀疏操作应用于真实域和频域数据，当真实域稀疏达到稳定模式时，获得的收敛性。这种稀疏变体具有信号降解的实用性，特别是在存在高斯噪声的情况下恢复了周期性尖峰信号。使用仿真研究证明了相对于现有方法的一般收敛性能和降解性能。可以在https://hrfrost.host.dartmouth.edu/iterativeft上找到实施此技术和相关资源的R软件包。
We describe a family of iterative algorithms that involve the repeated execution of discrete and inverse discrete Fourier transforms. One interesting member of this family is motivated by the discrete Fourier transform uncertainty principle and involves the application of a sparsification operation to both the real domain and frequency domain data with convergence obtained when real domain sparsity hits a stable pattern. This sparsification variant has practical utility for signal denoising, in particular the recovery of a periodic spike signal in the presence of Gaussian noise. General convergence properties and denoising performance relative to existing methods are demonstrated using simulation studies. An R package implementing this technique and related resources can be found at https://hrfrost.host.dartmouth.edu/IterativeFT.
