Bi-Linear Modeling of Data Manifolds for Dynamic-MRI Recovery

This paper puts forth a novel bi-linear modeling framework for data recovery via manifold-learning and sparse-approximation arguments and considers its application to dynamic magnetic-resonance imaging (dMRI). Each temporal-domain MR image is viewed as a point that lies onto or close to a smooth man...

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Bibliographic Details
Published in:IEEE transactions on medical imaging 2020-03, Vol.39 (3), p.688-702
Main Authors: Shetty, Gaurav Nagesh, Slavakis, Konstantinos, Bose, Abhishek, Nakarmi, Ukash, Scutari, Gesualdo, Ying, Leslie
Format: Article
Language:English
Subjects:
Algorithms
Computer Simulation
Data acquisition
Data models
Data recovery
Decompression
Dimensionality reduction
Dynamic MRI
Humans
Image Processing, Computer-Assisted - methods
Image reconstruction
Laplace equations
Learning algorithms
Linear Models
low rank
Machine Learning
Magnetic resonance imaging
Magnetic Resonance Imaging - methods
manifold learning
Manifolds
Manifolds (mathematics)
Operators (mathematics)
Optimization
Phantoms, Imaging
Recovery (Medical)
sparsity
Task analysis
Three dimensional models
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Summary:This paper puts forth a novel bi-linear modeling framework for data recovery via manifold-learning and sparse-approximation arguments and considers its application to dynamic magnetic-resonance imaging (dMRI). Each temporal-domain MR image is viewed as a point that lies onto or close to a smooth manifold, and landmark points are identified to describe the point cloud concisely. To facilitate computations, a dimensionality reduction module generates low-dimensional/compressed renditions of the landmark points. Recovery of high-fidelity MRI data is realized by solving a non-convex minimization task for the linear decompression operator and affine combinations of landmark points which locally approximate the latent manifold geometry. An algorithm with guaranteed convergence to stationary solutions of the non-convex minimization task is also provided. The aforementioned framework exploits the underlying spatio-temporal patterns and geometry of the acquired data without any prior training on external data or information. Extensive numerical results on simulated as well as real cardiac-cine MRI data illustrate noteworthy improvements of the advocated machine-learning framework over state-of-the-art reconstruction techniques.
ISSN:0278-0062
1558-254X
DOI:10.1109/TMI.2019.2934125