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27
Tensor-based formulation and nuclear norm regularization for multi-energy computed tomography
, 2014
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Splitting-based statistical X-ray CT image reconstruction with blind gain correction
- In Proc. SPIE 8668 Medical Imaging 2013: Phys. Med. Im
, 2013
"... ABSTRACT Variational methods are useful for solving ill-posed inverse imaging problems by minimizing a cost function with a data fidelity term and a regularization term. For statistical X-ray computed tomography (CT) image reconstruction, penalized weighted least-squares (PWLS) criteria with edge-p ..."
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Cited by 2 (1 self)
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ABSTRACT Variational methods are useful for solving ill-posed inverse imaging problems by minimizing a cost function with a data fidelity term and a regularization term. For statistical X-ray computed tomography (CT) image reconstruction, penalized weighted least-squares (PWLS) criteria with edge-preserving regularization can improve quality of the reconstructed image compared to traditional filtered back-projection (FBP) reconstruction. Nevertheless, the huge dynamic range of the statistical weights used in PWLS image reconstruction leads to a highly shift-variant local impulse response, making effective preconditioning difficult. To overcome this problem, iterative algorithms based on variable splitting were proposed recently. 1, 2 However, existing splitting-based iterative algorithms do not consider the (unknown) gain fluctuations that can occur between views. 3 This paper proposes a new variational formulation for splitting-based iterative algorithms where the unknown gain parameter vector and the image are estimated jointly with just simple changes to the original algorithms. Simulations show that the proposed algorithm greatly reduces the shading artifacts caused by gain fluctuations yet with almost unchanged computational complexity per iteration.
Combining ordered subsets and momentum for accelerated X-ray CT image reconstruction
- IEEE Trans. Med. Imag
, 2015
"... Abstract—Statistical X-ray computed tomography (CT) recon-struction can improve image quality from reduced dose scans, but requires very long computation time. Ordered subsets (OS) methods have been widely used for research in X-ray CT statistical image reconstruction (and are used in clinical PET a ..."
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Abstract—Statistical X-ray computed tomography (CT) recon-struction can improve image quality from reduced dose scans, but requires very long computation time. Ordered subsets (OS) methods have been widely used for research in X-ray CT statistical image reconstruction (and are used in clinical PET and SPECT reconstruction). In particular, OS methods based on separable quadratic surrogates (OS-SQS) are massively parallelizable and are well suited tomodern computing architectures, but the number of iterations required for convergence should be reduced for better practical use. This paper introduces OS-SQS-momentum algo-rithms that combine Nesterov’s momentum techniques with OS-SQS methods, greatly improving convergence speed in early iterations. If the number of subsets is too large, the OS-SQS-mo-mentum methods can be unstable, so we propose diminishing step sizes that stabilize the method while preserving the very fast con-vergence behavior. Experiments with simulated and real 3D CT scan data illustrate the performance of the proposed algorithms. Index Terms—Computed tomography (CT), momentum, or-dered subsets, parallelizable iterative algorithms, relaxation, separable quadratic surrogates, statistical image reconstruction, stochastic gradient. I.
Model-Based X-Ray CT Image and Light Field Reconstruction Using Variable Splitting Methods
, 2014
"... I could not finish this work without the help of many people. First of all, I would like to thank my advisor, Professor Jeffrey A. Fessler, for his careful guidance, constant encouragement, and the maximum freedom he gave me for developing inde-pendent thinking and research skills. Unlike most of my ..."
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I could not finish this work without the help of many people. First of all, I would like to thank my advisor, Professor Jeffrey A. Fessler, for his careful guidance, constant encouragement, and the maximum freedom he gave me for developing inde-pendent thinking and research skills. Unlike most of my colleagues, I knew nothing about medical imaging and worked on a totally different research topic when I first arrived at the University of Michigan. When I could not find a supervisor for taking the qualifying exams, it was Jeff who volunteeringly served as my directed research supervisor and gave me insightful advice on my preliminary research on light field reconstruction. When I had a hard and had to quit from the PhD program since I did not have a research advisor supporting my PhD research, it was Jeff who willingly served as my research advisor and supported my following doctoral study. Without Professor Jeff Fessler’s kindly help, this work would not have been possible, even from the very beginning. Furthermore, I would like to thank Professor Laura Balzano, Professor Anna C.
ASSEMBLIES
, 2015
"... Iterative CT reconstruction from few projections for the nondestructive post irradiation examination of nuclear fuel assemblies ..."
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Iterative CT reconstruction from few projections for the nondestructive post irradiation examination of nuclear fuel assemblies
LIST OF APPENDICES..................................
, 2013
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FRAME-BASED IMAGE DEBLURRING WITH UNKNOWN BOUNDARY CONDITIONS USING THE ALTERNATING DIRECTION METHOD OF MULTIPLIERS
"... The alternating direction method of multipliers (ADMM) is an efficient optimization tool that achieves state-of-the-art speed in several imaging inverse problems, by splitting the underlying problem into simpler, efficiently solvable sub-problems. In deconvolution, one of these sub-problems requires ..."
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The alternating direction method of multipliers (ADMM) is an efficient optimization tool that achieves state-of-the-art speed in several imaging inverse problems, by splitting the underlying problem into simpler, efficiently solvable sub-problems. In deconvolution, one of these sub-problems requires a matrix inversion, which has been shown to be efficiently computable (via the FFT), if the observation operator is circulant, i.e., under periodic boundary conditions. We extend ADMM-based image deconvolution to a more realistic scenario: unknown boundaries. The observation is modeled as the composition of a periodic convolution with a spatial mask that excludes the regions where the periodic convolution is invalid. We show that the resulting algorithms inherit the convergence guarantees of ADMM and illustrate its performance on non-periodic deblurring under frame-based regularization. Index Terms — Image deconvolution, alternating direction method of multipliers (ADMM), boundary conditions, non-periodic
Reconstruction
, 2013
"... Model-based reconstruction is a powerful framework for solving a variety of inverse problems in imaging. The method works by combining a forward model of the imaging system with a prior model of the image itself, and the reconstruction is then computed by minimizing a functional consisting of the su ..."
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Model-based reconstruction is a powerful framework for solving a variety of inverse problems in imaging. The method works by combining a forward model of the imaging system with a prior model of the image itself, and the reconstruction is then computed by minimizing a functional consisting of the sum of two terms corresponding to the forward and prior models. In recent years, enormous progress has been made in the problem of denoising, a special case of an inverse problem where the forward model is an identity operator. A wide range of methods including nonlocal means, dictionary-based methods, 3D block matching, TV minimization and kernel-based filtering have proven that it is possible to recover high fidelity images even after a great deal of noise has been added. Similarly, great progress has been made in improving model-based inversion when the forward model corresponds to complex physical measurements in applications such as X-ray CT, electronmicroscopy, MRI, and ultrasound, to name just a few. However, combining state-of-the-art denoising algorithms (i.e., prior models) with state-of-the-art inversion methods (i.e., forward models) has been a challenge for many reasons.
