Manifold Recovery Using Kernel Low-Rank Regularization: Application to Dynamic Imaging

Sunrita Poddar; Yasir Q Mohsin; Deidra Ansah; Bijoy Thattaliyath; Ravi Ashwath; Mathews Jacob

doi:10.1109/TCI.2019.2893598

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Journal article

Manifold Recovery Using Kernel Low-Rank Regularization: Application to Dynamic Imaging

Sunrita Poddar, Yasir Q Mohsin, Deidra Ansah, Bijoy Thattaliyath, Ravi Ashwath and Mathews Jacob

IEEE transactions on computational imaging, Vol.5(3), pp.478-491

09/2019

DOI: 10.1109/TCI.2019.2893598

PMCID: PMC7990121

PMID: 33768137

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https://www.ncbi.nlm.nih.gov/pmc/articles/7990121View

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Abstract

In this paper, we introduce a novel kernel low-rank algorithm to recover free-breathing and ungated dynamic MRI data from highly undersampled measurements. The image frames in the free breathing and ungated dataset are assumed to be points on a bandlimited manifold. We show that the nonlinear features of these images satisfy annihilation conditions, which implies that the kernel matrix derived from the dataset is low-rank. We penalize the nuclear norm of the feature matrix to recover the images from highly undersampled measurements. The regularized optimization problem is solved using an iterative reweighted least squares (IRLS) algorithm, which alternates between the update of the Laplacian matrix of the manifold and the recovery of the signals from the noisy measurements. To improve computational efficiency, we use a two-step algorithm using navigator measurements. Specifically, the Laplacian matrix is estimated from the navigators using the IRLS scheme, followed by the recovery of the images using a quadratic optimization. We show the relation of this two-step algorithm with our recent SToRM approach, thus reconciling SToRM and manifold regularization methods with algorithms that rely on explicit lifting of data to a high dimensional space. The IRLS-based estimation of the Laplacian matrix is a systematic and noise-robust alternative to current heuristic strategies based on exponential maps. We also approximate the Laplacian matrix using a few eigenvectors, which results in a fast and memory efficient algorithm. The proposed scheme is demonstrated on several patients with different breathing patterns and cardiac rates.

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Magnetic Resonance Imaging

Manifolds

Laplace equations

Storms

Cardiac reconstruction

manifold models

kernel methods

free-breathing

Kernel

Details

Title: Subtitle: Manifold Recovery Using Kernel Low-Rank Regularization: Application to Dynamic Imaging
Creators: Sunrita Poddar - Electrical and Computer Engineering, The University of Iowa, Iowa City, IA, USA
Yasir Q Mohsin - Electrical and Computer Engineering, The University of Iowa, Iowa City, IA, USA
Deidra Ansah - Pediatric Cardiology, The University of Iowa, Iowa City, IA, USA
Bijoy Thattaliyath - Pediatric Cardiology, The University of Iowa, Iowa City, IA, USA
Ravi Ashwath - Pediatric Cardiology, The University of Iowa, Iowa City, IA, USA
Mathews Jacob - Electrical and Computer Engineering, The University of Iowa, Iowa City, IA, USA
Resource Type: Journal article
Publication Details: IEEE transactions on computational imaging, Vol.5(3), pp.478-491
DOI: 10.1109/TCI.2019.2893598
PMID: 33768137
PMCID: PMC7990121
NLM abbreviation: IEEE Trans Comput Imaging
ISSN: 2573-0436
eISSN: 2333-9403
Publisher: IEEE
Grant note: 1R01EB019961-01A1 / National Institutes of Health (10.13039/100000002)
Language: English
Date published: 09/2019
Academic Unit: Roy J. Carver Department of Biomedical Engineering; Radiology; Electrical and Computer Engineering; Cardiology; Stead Family Department of Pediatrics; Iowa Neuroscience Institute; Radiation Oncology
Record Identifier: 9984071705602771

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