Sparsity and Low-Rank Constraints in Functional MRI

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Functional MRI (fMRI) has been slow to benefit from data acceleration techniques based on nonlinear image reconstruction for a number of reasons. This is in part due to the uncertain impact of nonlinear filtering effects on image and noise statistics, as well as the difficulty in implementing robust trajectories that satisfy the sampling requirements of the acceleration scheme (such as incoherence) while providing optimal blood oxygen level-dependent (BOLD) contrast and whole-brain coverage. More importantly, no consensus has been reached on the validity of different constraints used to regularise undersampled fMRI data reconstruction. Although early work in sparsity-constrained fMRI acceleration used the k-t FOCUSS framework, recently arguments have emerged for rank-constrained reconstruction. In this thesis, we compare the reconstruction performance of two techniques using temporal sparsity (k-t FOCUSS) and low-rank (k-t FASTER) on synthetic fMRI data based on realistic fMRI signal characteristics. We demonstrate that the strict rank-constraint method outperforms spectral sparsity and Karhunen-Lo`eve transform sparsity across different metrics. These results demonstrate the limitations of sparsity regularization on fMRI signals that, aside from simple block design task fMRI, are not spectrally sparse.


Type of resource text
Date created May 16, 2016


Author Guan, Charles
Advisor Pauly, John
Advisor Hargreaves, Brian
Degree granting institution Stanford University. Department of Electrical Engineering.


Subject MRI
Subject fMRI
Subject functional MRI
Subject resting-state functional MRI
Subject rsfMRI
Subject medical imaging
Subject compressed sensing
Subject sparsity
Subject matrix completion
Subject low-rank
Subject k-t FOCUSS
Subject k-t FASTER
Subject NMR
Genre Thesis

Bibliographic information

Related Publication Hong Jung, Jong Chul Ye, and Eung Yeop Kim. Improved k-t BLAST and SENSE using FOCUSS. Physics in Medicine and Biology, 52:3201–3226, May 2007.
Related Publication Mark Chiew, Stephen M. Smith, Peter J. Koopmans, Nadine N. Graedel, Thomas Blumensath, and Karla L. Miller. k-t FASTER: Acceleration of functional MRI data acquisition using low rank constraints. Magnetic Resonance in Medicine, 74(2):353–364, August 2014.
Related Publication Jeffrey Tsao and Sebastian Kozerke. MRI temporal acceleration techniques. Journal of Magnetic Resonance Imaging, 36:543–560, February 2012.

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Guan, Charles. (2016). Sparsity and Low-Rank Constraints in Functional MRI. Stanford Digital Repository. Available at:


Undergraduate Theses, School of Engineering

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