1,665 research outputs found
PEAR: PEriodic And fixed Rank separation for fast fMRI
In functional MRI (fMRI), faster acquisition via undersampling of data can
improve the spatial-temporal resolution trade-off and increase statistical
robustness through increased degrees-of-freedom. High quality reconstruction of
fMRI data from undersampled measurements requires proper modeling of the data.
We present an fMRI reconstruction approach based on modeling the fMRI signal as
a sum of periodic and fixed rank components, for improved reconstruction from
undersampled measurements. We decompose the fMRI signal into a component which
a has fixed rank and a component consisting of a sum of periodic signals which
is sparse in the temporal Fourier domain. Data reconstruction is performed by
solving a constrained problem that enforces a fixed, moderate rank on one of
the components, and a limited number of temporal frequencies on the other. Our
approach is coined PEAR - PEriodic And fixed Rank separation for fast fMRI.
Experimental results include purely synthetic simulation, a simulation with
real timecourses and retrospective undersampling of a real fMRI dataset.
Evaluation was performed both quantitatively and visually versus ground truth,
comparing PEAR to two additional recent methods for fMRI reconstruction from
undersampled measurements. Results demonstrate PEAR's improvement in estimating
the timecourses and activation maps versus the methods compared against at
acceleration ratios of R=8,16 (for simulated data) and R=6.66,10 (for real
data). PEAR results in reconstruction with higher fidelity than when using a
fixed-rank based model or a conventional Low-rank+Sparse algorithm. We have
shown that splitting the functional information between the components leads to
better modeling of fMRI, over state-of-the-art methods
Orthonormal Expansion l1-Minimization Algorithms for Compressed Sensing
Compressed sensing aims at reconstructing sparse signals from significantly
reduced number of samples, and a popular reconstruction approach is
-norm minimization. In this correspondence, a method called orthonormal
expansion is presented to reformulate the basis pursuit problem for noiseless
compressed sensing. Two algorithms are proposed based on convex optimization:
one exactly solves the problem and the other is a relaxed version of the first
one. The latter can be considered as a modified iterative soft thresholding
algorithm and is easy to implement. Numerical simulation shows that, in dealing
with noise-free measurements of sparse signals, the relaxed version is
accurate, fast and competitive to the recent state-of-the-art algorithms. Its
practical application is demonstrated in a more general case where signals of
interest are approximately sparse and measurements are contaminated with noise.Comment: 7 pages, 2 figures, 1 tabl
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