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Recovery of Noisy Points on Bandlimited Surfaces: Kernel Methods Re-Explained
Conference proceeding

Recovery of Noisy Points on Bandlimited Surfaces: Kernel Methods Re-Explained

Sunrita Poddar and Mathews Jacob
2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vol.2018-, pp.4024-4028
04/2018
DOI: 10.1109/ICASSP.2018.8462186
PMID: 33584147
url
https://arxiv.org/pdf/1801.00890View
Open Access

Abstract

We introduce a continuous domain framework for the recovery of points on a surface in high dimensional space, represented as the zero-level set of a bandlimited function. We show that the exponential maps of the points on the surface satisfy annihilation relations, implying that they lie in a finite dimensional subspace. The subspace properties are used to derive sampling conditions, which will guarantee the perfect recovery of the surface from finite number of points. We rely on nuclear norm minimization to exploit the low-rank structure of the maps to recover the points from noisy measurements. Since the direct estimation of the surface is computationally prohibitive in very high dimensions, we propose an iterative reweighted algorithm using the "kernel trick". The iterative algorithm reveals deep links to Laplacian based algorithms widely used in graph signal processing; the theory and the sampling conditions can serve as a basis for discrete-continuous domain processing of signals on a graph.
denoising Laplace equations Shape Signal processing algorithms Bandwidth superresolution kernels Noise measurement Kernel Surface treatment

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