Sampling and Galerkin reconstruction in reproducing kernel spaces

2014/10/07 by Cheng Cheng, Cheng, Cheng, Yingchun Jiang +3
Computer Science · Earth and Planetary Sciences · Mathematics · #46E22 #65J22 #94A20 #FOS: Computer and information sciences #FOS: Mathematics #Image and Signal Denoising Methods #Information Theory (cs.IT) #Mathematical Analysis and Transform Methods #Numerical Analysis (math.NA) #Seismic Imaging and Inversion Techniques

paper · pdf · doi:10.48550/arxiv.1410.1828

openalex publication_date 2014/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider sampling in a reproducing kernel subspace of L^p. We introduce a pre-reconstruction operator associated with a sampling scheme and propose a Galerkin reconstruction in general Banach space setting. We show that the proposed Galerkin method provides a quasi-optimal approximation, and the corresponding Galerkin equations could be solved by an iterative approximation-projection algorithm. We also present detailed analysis and numerical simulations of the Galerkin method for reconstructing signals with finite rate of innovation.

Citations

• Weighted frames of exponentials and stable recovery of multidimensional functions from nonuniform Fourier samples

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