176 research outputs found
Faster PET reconstruction with non-smooth priors by randomization and preconditioning
Uncompressed clinical data from modern positron emission tomography (PET) scanners are very large, exceeding 350 million data points (projection bins). The last decades have seen tremendous advancements in mathematical imaging tools many of which lead to non-smooth (i.e. non-differentiable) optimization problems which are much harder to solve than smooth optimization problems. Most of these tools have not been translated to clinical PET data, as the state-of-the-art algorithms for non-smooth problems do not scale well to large data. In this work, inspired by big data machine learning applications, we use advanced randomized optimization algorithms to solve the PET reconstruction problem for a very large class of non-smooth priors which includes for example total variation, total generalized variation, directional total variation and various different physical constraints. The proposed algorithm randomly uses subsets of the data and only updates the variables associated with these. While this idea often leads to divergent algorithms, we show that the proposed algorithm does indeed converge for any proper subset selection. Numerically, we show on real PET data (FDG and florbetapir) from a Siemens Biograph mMR that about ten projections and backprojections are sufficient to solve the MAP optimisation problem related to many popular non-smooth priors; thus showing that the proposed algorithm is fast enough to bring these models into routine clinical practice
Joint Total Variation ESTATICS for Robust Multi-Parameter Mapping
Quantitative magnetic resonance imaging (qMRI) derives tissue-specific
parameters -- such as the apparent transverse relaxation rate R2*, the
longitudinal relaxation rate R1 and the magnetisation transfer saturation --
that can be compared across sites and scanners and carry important information
about the underlying microstructure. The multi-parameter mapping (MPM) protocol
takes advantage of multi-echo acquisitions with variable flip angles to extract
these parameters in a clinically acceptable scan time. In this context,
ESTATICS performs a joint loglinear fit of multiple echo series to extract R2*
and multiple extrapolated intercepts, thereby improving robustness to motion
and decreasing the variance of the estimators. In this paper, we extend this
model in two ways: (1) by introducing a joint total variation (JTV) prior on
the intercepts and decay, and (2) by deriving a nonlinear maximum \emph{a
posteriori} estimate. We evaluated the proposed algorithm by predicting
left-out echoes in a rich single-subject dataset. In this validation, we
outperformed other state-of-the-art methods and additionally showed that the
proposed approach greatly reduces the variance of the estimated maps, without
introducing bias.Comment: 11 pages, 2 figures, 1 table, conference paper, accepted at MICCAI
202
Aggregated motion estimation for real-time MRI reconstruction
Real-time magnetic resonance imaging (MRI) methods generally shorten the
measuring time by acquiring less data than needed according to the sampling
theorem. In order to obtain a proper image from such undersampled data, the
reconstruction is commonly defined as the solution of an inverse problem, which
is regularized by a priori assumptions about the object. While practical
realizations have hitherto been surprisingly successful, strong assumptions
about the continuity of image features may affect the temporal fidelity of the
estimated images. Here we propose a novel approach for the reconstruction of
serial real-time MRI data which integrates the deformations between nearby
frames into the data consistency term. The method is not required to be affine
or rigid and does not need additional measurements. Moreover, it handles
multi-channel MRI data by simultaneously determining the image and its coil
sensitivity profiles in a nonlinear formulation which also adapts to
non-Cartesian (e.g., radial) sampling schemes. Experimental results of a motion
phantom with controlled speed and in vivo measurements of rapid tongue
movements demonstrate image improvements in preserving temporal fidelity and
removing residual artifacts.Comment: This is a preliminary technical report. A polished version is
published by Magnetic Resonance in Medicine. Magnetic Resonance in Medicine
201
High-resolution myelin-water fraction and quantitative relaxation mapping using 3D ViSTa-MR fingerprinting
Purpose: This study aims to develop a high-resolution whole-brain
multi-parametric quantitative MRI approach for simultaneous mapping of
myelin-water fraction (MWF), T1, T2, and proton-density (PD), all within a
clinically feasible scan time.
Methods: We developed 3D ViSTa-MRF, which combined Visualization of Short
Transverse relaxation time component (ViSTa) technique with MR Fingerprinting
(MRF), to achieve high-fidelity whole-brain MWF and T1/T2/PD mapping on a
clinical 3T scanner. To achieve fast acquisition and memory-efficient
reconstruction, the ViSTa-MRF sequence leverages an optimized 3D
tiny-golden-angle-shuffling spiral-projection acquisition and joint
spatial-temporal subspace reconstruction with optimized preconditioning
algorithm. With the proposed ViSTa-MRF approach, high-fidelity direct MWF
mapping was achieved without a need for multi-compartment fitting that could
introduce bias and/or noise from additional assumptions or priors.
Results: The in-vivo results demonstrate the effectiveness of the proposed
acquisition and reconstruction framework to provide fast multi-parametric
mapping with high SNR and good quality. The in-vivo results of 1mm- and
0.66mm-iso datasets indicate that the MWF values measured by the proposed
method are consistent with standard ViSTa results that are 30x slower with
lower SNR. Furthermore, we applied the proposed method to enable 5-minute
whole-brain 1mm-iso assessment of MWF and T1/T2/PD mappings for infant brain
development and for post-mortem brain samples.
Conclusions: In this work, we have developed a 3D ViSTa-MRF technique that
enables the acquisition of whole-brain MWF, quantitative T1, T2, and PD maps at
1mm and 0.66mm isotropic resolution in 5 and 15 minutes, respectively. This
advancement allows for quantitative investigations of myelination changes in
the brain.Comment: 38 pages, 12 figures and 1 tabl
Enhancing Compressed Sensing 4D Photoacoustic Tomography by Simultaneous Motion Estimation
A crucial limitation of current high-resolution 3D photoacoustic tomography
(PAT) devices that employ sequential scanning is their long acquisition time.
In previous work, we demonstrated how to use compressed sensing techniques to
improve upon this: images with good spatial resolution and contrast can be
obtained from suitably sub-sampled PAT data acquired by novel acoustic scanning
systems if sparsity-constrained image reconstruction techniques such as total
variation regularization are used. Now, we show how a further increase of image
quality can be achieved for imaging dynamic processes in living tissue (4D
PAT). The key idea is to exploit the additional temporal redundancy of the data
by coupling the previously used spatial image reconstruction models with
sparsity-constrained motion estimation models. While simulated data from a
two-dimensional numerical phantom will be used to illustrate the main
properties of this recently developed
joint-image-reconstruction-and-motion-estimation framework, measured data from
a dynamic experimental phantom will also be used to demonstrate their potential
for challenging, large-scale, real-world, three-dimensional scenarios. The
latter only becomes feasible if a carefully designed combination of tailored
optimization schemes is employed, which we describe and examine in more detail
Efficient Model-Based Reconstruction for Dynamic MRI
Dynamic magnetic resonance imaging (MRI) has important clinical and neuro- science applications (e.g., cardiac disease diagnosis, neurological behavior studies). It captures an object in motion by acquiring data across time, then reconstructing a sequence of images from them. This dissertation considers efficient dynamic MRI reconstruction using handcrafted models, to achieve fast imaging with high spatial and temporal resolution. Our modeling framework considers data acquisition process, image properties, and artifact correction. The reconstruction model expressed as a large-scale inverse problem requires optimization algorithms to solve, and we consider efficient implementations that make use of underlying problem structures.
In the context of dynamic MRI reconstruction, we investigate efficient updates in two frameworks of algorithms for solving a nonsmooth composite convex optimization problem for the low-rank plus sparse (L+S) model. In the proximal gradient framework, current algorithms for the L+S model involve the classical iterative soft thresholding algorithm (ISTA); we consider two accelerated alternatives, one based on the fast iterative shrinkage-thresholding algorithm (FISTA), and the other with the recent proximal optimized gradient method (POGM). In the augmented Lagrangian (AL) framework, we propose an efficient variable splitting scheme based on the form of the data acquisition operator, leading to simpler computation than the conjugate gradient (CG) approach required by existing AL methods. Numerical results suggest faster convergence of our efficient implementations in both frameworks, with POGM providing the fastest convergence overall and the practical benefit of being free of algorithm tuning parameters.
In the context of magnetic field inhomogeneity correction, we present an efficient algorithm for a regularized field inhomogeneity estimation problem. Most existing minimization techniques are computationally or memory intensive for 3D datasets, and are designed for single-coil MRI. We consider 3D MRI with optional consideration of coil sensitivity and a generalized expression that addresses both multi-echo field map estimation and water-fat imaging. Our efficient algorithm uses a preconditioned nonlinear conjugate gradient method based on an incomplete Cholesky factorization of the Hessian of the cost function, along with a monotonic line search. Numerical experiments show the computational advantage of the proposed algorithm over state- of-the-art methods with similar memory requirements.
In the context of task-based functional MRI (fMRI) reconstruction, we introduce a space-time model that represents an fMRI timeseries as a sum of task-correlated signal and non-task background. Our model consists of a spatiotemporal decomposition based on assumptions of the activation waveform shape, with spatial and temporal smoothness regularization on the magnitude and phase of the timeseries. Compared with two contemporary task fMRI decomposition models, our proposed model yields better timeseries and activation maps on simulated and human subject fMRI datasets with multiple tasks.
The above examples are part of a larger framework for model-based dynamic MRI reconstruction. This dissertation concludes by presenting a general framework with flexibility on model assumptions and artifact compensation options (e.g., field inhomogeneity, head motion), and proposing future work ideas on both the framework and its connection to data acquisition.PHDApplied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/168081/1/yilinlin_1.pd
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