Recovery of point clouds on surfaces: Application to image reconstruction

Sunrita Poddar; Mathews Jacob

doi:10.1109/ISBI.2018.8363803

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Conference proceeding

Recovery of point clouds on surfaces: Application to image reconstruction

Sunrita Poddar and Mathews Jacob

2018 IEEE 15th International Symposium on Biomedical Imaging (ISBI 2018), Vol.2018-, pp.1272-1275

04/2018

DOI: 10.1109/ISBI.2018.8363803

PMID: 33619441

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https://arxiv.org/pdf/1801.00886View

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Abstract

We introduce a framework for the recovery of points on a smooth surface in high-dimensional space, with application to dynamic imaging. We assume the surface to be 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. We rely on nuclear norm minimization of the maps to recover the points from noisy and undersampled measurements. Since this direct approach suffers from the curse of dimensionality, we introduce an iterative reweighted algorithm that uses the "kernel trick". The resulting algorithm has similarities to iterative algorithms used in graph signal processing (GSP); this framework can be seen as a continuous domain alternative to discrete GSP theory. The use of the algorithm in recovering free breathing and ungated cardiac data shows the potential of this framework in practical applications.

denoising

Three-dimensional displays

Magnetic resonance imaging

Noise reduction

Signal processing algorithms

superresolution

kernels

Noise measurement

machine learning

Kernel

Surface treatment

dynamic MRI

Details

Title: Subtitle: Recovery of point clouds on surfaces: Application to image reconstruction
Creators: Sunrita Poddar - Department of Electrical and Computer Engineering, University of Iowa, IA, USA
Mathews Jacob - Department of Electrical and Computer Engineering, University of Iowa, IA, USA
Resource Type: Conference proceeding
Publication Details: 2018 IEEE 15th International Symposium on Biomedical Imaging (ISBI 2018), Vol.2018-, pp.1272-1275
DOI: 10.1109/ISBI.2018.8363803
PMID: 33619441
NLM abbreviation: Proc IEEE Int Symp Biomed Imaging
ISSN: 1945-7928
eISSN: 1945-8452
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: 9984070574102771

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