4 research outputs found
Robust Depth Linear Error Decomposition with Double Total Variation and Nuclear Norm for Dynamic MRI Reconstruction
Compressed Sensing (CS) significantly speeds up Magnetic Resonance Image
(MRI) processing and achieves accurate MRI reconstruction from under-sampled
k-space data. According to the current research, there are still several
problems with dynamic MRI k-space reconstruction based on CS. 1) There are
differences between the Fourier domain and the Image domain, and the
differences between MRI processing of different domains need to be considered.
2) As three-dimensional data, dynamic MRI has its spatial-temporal
characteristics, which need to calculate the difference and consistency of
surface textures while preserving structural integrity and uniqueness. 3)
Dynamic MRI reconstruction is time-consuming and computationally
resource-dependent. In this paper, we propose a novel robust low-rank dynamic
MRI reconstruction optimization model via highly under-sampled and Discrete
Fourier Transform (DFT) called the Robust Depth Linear Error Decomposition
Model (RDLEDM). Our method mainly includes linear decomposition, double Total
Variation (TV), and double Nuclear Norm (NN) regularizations. By adding linear
image domain error analysis, the noise is reduced after under-sampled and DFT
processing, and the anti-interference ability of the algorithm is enhanced.
Double TV and NN regularizations can utilize both spatial-temporal
characteristics and explore the complementary relationship between different
dimensions in dynamic MRI sequences. In addition, Due to the non-smoothness and
non-convexity of TV and NN terms, it is difficult to optimize the unified
objective model. To address this issue, we utilize a fast algorithm by solving
a primal-dual form of the original problem. Compared with five state-of-the-art
methods, extensive experiments on dynamic MRI data demonstrate the superior
performance of the proposed method in terms of both reconstruction accuracy and
time complexity
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