96 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
Solution Path Clustering with Adaptive Concave Penalty
Fast accumulation of large amounts of complex data has created a need for
more sophisticated statistical methodologies to discover interesting patterns
and better extract information from these data. The large scale of the data
often results in challenging high-dimensional estimation problems where only a
minority of the data shows specific grouping patterns. To address these
emerging challenges, we develop a new clustering methodology that introduces
the idea of a regularization path into unsupervised learning. A regularization
path for a clustering problem is created by varying the degree of sparsity
constraint that is imposed on the differences between objects via the minimax
concave penalty with adaptive tuning parameters. Instead of providing a single
solution represented by a cluster assignment for each object, the method
produces a short sequence of solutions that determines not only the cluster
assignment but also a corresponding number of clusters for each solution. The
optimization of the penalized loss function is carried out through an MM
algorithm with block coordinate descent. The advantages of this clustering
algorithm compared to other existing methods are as follows: it does not
require the input of the number of clusters; it is capable of simultaneously
separating irrelevant or noisy observations that show no grouping pattern,
which can greatly improve data interpretation; it is a general methodology that
can be applied to many clustering problems. We test this method on various
simulated datasets and on gene expression data, where it shows better or
competitive performance compared against several clustering methods.Comment: 36 page
X-ray CT Image Reconstruction on Highly-Parallel Architectures.
Model-based image reconstruction (MBIR) methods for X-ray CT use accurate
models of the CT acquisition process, the statistics of the noisy measurements,
and noise-reducing regularization to produce potentially higher quality images
than conventional methods even at reduced X-ray doses. They do this by
minimizing a statistically motivated high-dimensional cost function; the high
computational cost of numerically minimizing this function has prevented MBIR
methods from reaching ubiquity in the clinic. Modern highly-parallel hardware
like graphics processing units (GPUs) may offer the computational resources to
solve these reconstruction problems quickly, but simply "translating" existing
algorithms designed for conventional processors to the GPU may not fully
exploit the hardware's capabilities.
This thesis proposes GPU-specialized image denoising and image reconstruction
algorithms. The proposed image denoising algorithm uses group coordinate
descent with carefully structured groups. The algorithm converges very
rapidly: in one experiment, it denoises a 65 megapixel image in about 1.5
seconds, while the popular Chambolle-Pock primal-dual algorithm running on the
same hardware takes over a minute to reach the same level of accuracy.
For X-ray CT reconstruction, this thesis uses duality and group coordinate
ascent to propose an alternative to the popular ordered subsets (OS) method.
Similar to OS, the proposed method can use a subset of the data to update the
image. Unlike OS, the proposed method is convergent. In one helical CT
reconstruction experiment, an implementation of the proposed algorithm using
one GPU converges more quickly than a state-of-the-art algorithm converges
using four GPUs. Using four GPUs, the proposed algorithm reaches near
convergence of a wide-cone axial reconstruction problem with over 220 million
voxels in only 11 minutes.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113551/1/mcgaffin_1.pd
Regularized Interpolation for Noisy Images
Interpolation is the means by which a continuously defined model is fit to discrete data samples. When the data samples are exempt of noise, it seems desirable to build the model by fitting them exactly. In medical imaging, where quality is of paramount importance, this ideal situation unfortunately does not occur. In this paper, we propose a scheme that improves on the quality by specifying a tradeoff between fidelity to the data and robustness to the noise. We resort to variational principles, which allow us to impose smoothness constraints on the model for tackling noisy data. Based on shift-, rotation-, and scale-invariant requirements on the model, we show that the Lp-norm of an appropriate vector derivative is the most suitable choice of regularization for this purpose. In addition to Tikhonov-like quadratic regularization, this includes edge-preserving total-variation-like (TV) regularization. We give algorithms to recover the continuously defined model from noisy samples and also provide a data-driven scheme to determine the optimal amount of regularization. We validate our method with numerical examples where we demonstrate its superiority over an exact fit as well as the benefit of TV-like nonquadratic regularization over Tikhonov-like quadratic regularization
Topics in Steady-state MRI Sequences and RF Pulse Optimization.
Small-tip fast recovery (STFR) is a recently proposed rapid steady-state magnetic resonance imaging (MRI) sequence that has the potential to be an alternative to the popular balanced steady-state free precession (bSSFP) imaging sequence, since they have similar signal level and tissue contrast, but STFR has reduced banding artifacts. In this dissertation, an analytic equation of the steady-state signal for the unspoiled version of STFR is first derived. It is shown that unspoiled-STFR is less sensitive to the inaccuracy in excitation than the previous proposed spoiled-STFR. By combining unspoiled-STFR with jointly designed tip-down and tip-up pulses, a 3D STFR acquisition over 3-4 cm thick 3D ROI with single coil and short RF pulses (1.7 ms) is demonstrated. Then, it is demonstrated that STFR can reliably detect functional MRI signal and the contrast is driven mainly from intra-voxel dephasing, not diffusion, using Monte Carlo simulation, human experiments and test-retest reliability. Following that another version of STFR using a spectral pre-winding pulse instead of the spatially tailored pulse is investigated, leading to less T2* weighting, easier implementation. Multidimensional selective RF pulse is a key part for STFR and many other MRI applications. Two novel RF pulse optimization methods are proposed. First, a minimax formulation that directly controls the maximum excitation error, and an effective optimization algorithm using variable splitting and alternating direction method of multipliers (ADMM). The proposed method reduced the maximum excitation by more than half in all the testing cases. Second, a method that jointly optimizes the excitation k-space trajectory and RF pulse is proposed. The k-space trajectory is parametrized using 2nd-order B-splines, and an interior point algorithm is used to explicitly solve the constrained optimization. An effective initialization method is also suggested. The joint design reduced the NRMSE by more than 30 percent compared to existing methods in inner volume excitation and pre-phasing problem. Using the proposed joint design, rapid inner volume STFR imaging with a 4 ms excitation pulse with single transmit coil is demonstrated. Finally, a regularized Bloch-Siegert B1 map reconstruction method is presented that significantly reduces the noise in estimated B1 maps.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111514/1/sunhao_1.pd
Group-Sparse Signal Denoising: Non-Convex Regularization, Convex Optimization
Convex optimization with sparsity-promoting convex regularization is a
standard approach for estimating sparse signals in noise. In order to promote
sparsity more strongly than convex regularization, it is also standard practice
to employ non-convex optimization. In this paper, we take a third approach. We
utilize a non-convex regularization term chosen such that the total cost
function (consisting of data consistency and regularization terms) is convex.
Therefore, sparsity is more strongly promoted than in the standard convex
formulation, but without sacrificing the attractive aspects of convex
optimization (unique minimum, robust algorithms, etc.). We use this idea to
improve the recently developed 'overlapping group shrinkage' (OGS) algorithm
for the denoising of group-sparse signals. The algorithm is applied to the
problem of speech enhancement with favorable results in terms of both SNR and
perceptual quality.Comment: 14 pages, 11 figure
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