128 research outputs found
Acceleration Methods for MRI
Acceleration methods are a critical area of research for MRI. Two of the most important acceleration techniques involve parallel imaging and compressed sensing. These advanced signal processing techniques have the potential to drastically reduce scan times and provide radiologists with new information for diagnosing disease. However, many of these new techniques require solving difficult optimization problems, which motivates the development of more advanced algorithms to solve them. In addition, acceleration methods have not reached maturity in some applications, which motivates the development of new models tailored to these applications. This dissertation makes advances in three different areas of accelerations. The first is the development of a new algorithm (called B1-Based, Adaptive Restart, Iterative Soft Thresholding Algorithm or BARISTA), that solves a parallel MRI optimization problem with compressed sensing assumptions. BARISTA is shown to be 2-3 times faster and more robust to parameter selection than current state-of-the-art variable splitting methods. The second contribution is the extension of BARISTA ideas to non-Cartesian trajectories that also leads to a 2-3 times acceleration over previous methods. The third contribution is the development of a new model for functional MRI that enables a 3-4 factor of acceleration of effective temporal resolution in functional MRI scans. Several variations of the new model are proposed, with an ROC curve analysis showing that a combination low-rank/sparsity model giving the best performance in identifying the resting-state motor network.PhDBiomedical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120841/1/mmuckley_1.pd
Rapid, Robust, and Reliable Blind Deconvolution via Nonconvex Optimization
We study the question of reconstructing two signals and from their
convolution . This problem, known as {\em blind deconvolution},
pervades many areas of science and technology, including astronomy, medical
imaging, optics, and wireless communications. A key challenge of this intricate
non-convex optimization problem is that it might exhibit many local minima. We
present an efficient numerical algorithm that is guaranteed to recover the
exact solution, when the number of measurements is (up to log-factors) slightly
larger than the information-theoretical minimum, and under reasonable
conditions on and . The proposed regularized gradient descent algorithm
converges at a geometric rate and is provably robust in the presence of noise.
To the best of our knowledge, our algorithm is the first blind deconvolution
algorithm that is numerically efficient, robust against noise, and comes with
rigorous recovery guarantees under certain subspace conditions. Moreover,
numerical experiments do not only provide empirical verification of our theory,
but they also demonstrate that our method yields excellent performance even in
situations beyond our theoretical framework
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