Conference proceeding
Recovery of Noisy Points on Bandlimited Surfaces: Kernel Methods Re-Explained
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
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.
Details
- Title: Subtitle
- Recovery of Noisy Points on Bandlimited Surfaces: Kernel Methods Re-Explained
- Creators
- Sunrita Poddar - Department of Electrical and Computer Engineering, University of Iowa, IA, USAMathews Jacob - Department of Electrical and Computer Engineering, University of Iowa, IA, USA
- Resource Type
- Conference proceeding
- Publication Details
- 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Vol.2018-, pp.4024-4028
- DOI
- 10.1109/ICASSP.2018.8462186
- PMID
- 33584147
- NLM abbreviation
- Proc IEEE Int Conf Acoust Speech Signal Process
- ISSN
- 1520-6149
- eISSN
- 2379-190X
- Publisher
- IEEE
- Language
- English
- Date published
- 04/2018
- Academic Unit
- Roy J. Carver Department of Biomedical Engineering; Radiology; Electrical and Computer Engineering; Iowa Neuroscience Institute; Radiation Oncology
- Record Identifier
- 9984070346802771
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