Extrapolation of Bandlimited Multidimensional Signals from Continuous Measurements
| Autor: | Walter Kellermann, Cornelius Frankenbach, Pablo Martinez-Nuevo, Martin Bo Møller |
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| Rok vydání: | 2021 |
| Předmět: |
Signal Processing (eess.SP)
Bandlimiting Computer science Iterative method Extrapolation 020206 networking & telecommunications 02 engineering and technology Tikhonov regularization Bounded function FOS: Electrical engineering electronic engineering information engineering 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Convex combination Electrical Engineering and Systems Science - Signal Processing Algorithm Numerical stability Interpolation |
| Zdroj: | EUSIPCO |
| Popis: | 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. Comment: Submitted to EUSIPCO 2020 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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