Sampling of Planar Curves: Theory and Fast Algorithms

Qing Zou; Sunrita Poddar; Mathews Jacob

doi:10.1109/TSP.2019.2954508

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Sampling of Planar Curves: Theory and Fast Algorithms

Journal article

Open access

Peer reviewed

Sampling of Planar Curves: Theory and Fast Algorithms

Qing Zou, Sunrita Poddar and Mathews Jacob

IEEE transactions on signal processing, Vol.67(24), pp.6455-6467

12/15/2019

DOI: 10.1109/TSP.2019.2954508

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https://arxiv.org/pdf/1810.11575View

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Abstract

We introduce a continuous domain framework for the recovery of a planar curve from a few samples. We model the curve as the zero level set of a trigonometric polynomial. We show that the exponential feature maps of the points on the curve lie on a low-dimensional subspace. We show that the null-space vector of the feature matrix can be used to uniquely identify the curve, given a sufficient number of samples. The worst-case theoretical guarantees show that the number of samples required for unique recovery depends on the bandwidth of the underlying trigonometric polynomial, which is a measure of the complexity of the curve. We introduce an iterative algorithm that relies on the low-rank property of the feature maps to recover the curves when the samples are noisy or when the true bandwidth of the curve is unknown. We also demonstrate the preliminary utility of the proposed curve representation in the context of image segmentation.

denoising

Image segmentation

Level set

nuclear norm

Noise reduction

Signal processing algorithms

Bandwidth

kernels

Noise measurement

band-limited function

Kernel

Curve recovery

Details

Title: Subtitle: Sampling of Planar Curves: Theory and Fast Algorithms
Creators: Qing Zou - Applied Mathematics & Computational Sciences program, University of Iowa, Iowa City, IA, USA
Sunrita Poddar - Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA, USA
Mathews Jacob - Department of Electrical and Computer Engineering, University of Iowa, Iowa City, IA, USA
Resource Type: Journal article
Publication Details: IEEE transactions on signal processing, Vol.67(24), pp.6455-6467
DOI: 10.1109/TSP.2019.2954508
ISSN: 1053-587X
eISSN: 1941-0476
Publisher: IEEE
Grant note: 1R01EB019961-01A1; R01 EB019961-02S1 / National Institutes of Health (10.13039/100000002)
Language: English
Date published: 12/15/2019
Academic Unit: Roy J. Carver Department of Biomedical Engineering; Radiology; Electrical and Computer Engineering; Iowa Technology Institute; Iowa Neuroscience Institute; Radiation Oncology
Record Identifier: 9984070150702771

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