Extrapolation of Bandlimited Multidimensional Signals from Continuous Measurements

Frankenbach C, Martínez-Nuevo P, Møller M, Kellermann W (2021)

Publication Type: Conference contribution, Conference Contribution

Publication year: 2021

Pages Range: 2309-2313

Conference Proceedings Title: European Signal Processing Conference (EUSIPCO)

Event location: Amsterdam, NLD

ISBN: 9789082797053

DOI: 10.23919/Eusipco47968.2020.9287729

Abstract

Conventional sampling and interpolation commonly rely on discrete measurements. In this paper, we develop a theoretical framework for extrapolation of signals in higher dimensions from knowledge of the continuous waveform on bounded high-dimensional regions. In particular, we propose an iterative method to reconstruct bandlimited multidimensional signals based on truncated versions of the original signal to bounded regions-herein referred to as continuous measurements. In the proposed method, the reconstruction is performed by iterating on a convex combination of region-limiting and bandlimiting operations. We show that this iteration consists of a firmly nonexpansive operator and prove strong convergence for multidimensional bandlimited signals. In order to improve numerical stability, we introduce a regularized iteration and show its connection to Tikhonov regularization. The method is illustrated numerically for two-dimensional signals.

Authors with CRIS profile

Cornelius Frankenbach Professur für Signalverarbeitung Walter Kellermann Professur für Signalverarbeitung

Involved external institutions

Bang & Olufsen A/S DK Denmark (DK)

How to cite

APA:

Frankenbach, C., Martínez-Nuevo, P., Møller, M., & Kellermann, W. (2021). Extrapolation of Bandlimited Multidimensional Signals from Continuous Measurements. In European Signal Processing Conference (EUSIPCO) (pp. 2309-2313). Amsterdam, NLD.

MLA:

Frankenbach, Cornelius, et al. "Extrapolation of Bandlimited Multidimensional Signals from Continuous Measurements." Proceedings of the 2020 28th European Signal Processing Conference (EUSIPCO), Amsterdam, NLD 2021. 2309-2313.

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