2016/01/07 by Rongrong Lin, Lin, Rongrong, Haizhang Zhang +1
Computer Science · Earth and Planetary Sciences · Mathematics · #FOS: Computer and information sciences #Image and Signal Denoising Methods #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Seismic Imaging and Inversion Techniques
paper · pdf · doi:10.48550/arxiv.1601.01363
openalex publication_date 2016/01/07 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We consider the reconstruction of a bandlimited function from its finite localized sample data. Truncating the classical Shannon sampling series results in an unsatisfactory convergence rate due to the slow decayness of the sinc function. To overcome this drawback, a simple and highly effective method, called the Gaussian regularization of the Shannon series, was proposed in the engineering and has received remarkable attention. It works by multiplying the sinc function in the Shannon series with a regularized Gaussian function. L. Qian (Proc. Amer. Math. Soc., 2003) established the convergence rate of O(√(n)exp(-\fracπ-δ2n)) for this method, where δ