Journal ArticleDOI
Development and Optimization of Regularized Tomographic Reconstruction Algorithms Utilizing Equally-Sloped Tomography
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TLDR
Two new algorithms for tomographic reconstruction which incorporate the technique of equally-sloped tomography (EST) and allow for the optimized and flexible implementation of regularization schemes, such as total variation constraints, and the incorporation of arbitrary physical constraints are developed.Abstract:
We develop two new algorithms for tomographic reconstruction which incorporate the technique of equally-sloped tomography (EST) and allow for the optimized and flexible implementation of regularization schemes, such as total variation constraints, and the incorporation of arbitrary physical constraints. The founding structure of the developed algorithms is EST, a technique of tomographic acquisition and reconstruction first proposed by Miao in 2005 for performing tomographic image reconstructions from a limited number of noisy projections in an accurate manner by avoiding direct interpolations. EST has recently been successfully applied to coherent diffraction microscopy, electron microscopy, and computed tomography for image enhancement and radiation dose reduction. However, the bottleneck of EST lies in its slow speed due to its higher computation requirements. In this paper, we formulate the EST approach as a constrained problem and subsequently transform it into a series of linear problems, which can be accurately solved by the operator splitting method. Based on these mathematical formulations, we develop two iterative algorithms for tomographic image reconstructions through EST, which incorporate Bregman and continuative regularization. Our numerical experiment results indicate that the new tomographic image reconstruction algorithms not only significantly reduce the computational time, but also improve the image quality. We anticipate that EST coupled with the novel iterative algorithms will find broad applications in X-ray tomography, electron microscopy, coherent diffraction microscopy, and other tomography fields.read more
Citations
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Journal ArticleDOI
Electron tomography at 2.4-ångström resolution
Mary Scott,Chien-Chun Chen,Matthew Mecklenburg,Chun Zhu,Rui Xu,Peter Ercius,Ulrich Dahmen,B. C. Regan,Jianwei Miao +8 more
TL;DR: The experimental demonstration of a general electron tomography method that achieves atomic-scale resolution without initial assumptions about the sample structure is reported, and it is anticipated that this general method can be applied not only to determine the 3D structure of nanomaterials at atomic- scale resolution, but also to improve the spatial resolution and image quality in other tomography fields.
Journal ArticleDOI
Compressed sensing electron tomography.
TL;DR: The CS-ET approach enables more reliable quantitative analysis of the reconstructions as well as novel 3D studies from extremely limited data, and robust reconstruction is shown to be possible from far fewer projections than are normally used.
Journal ArticleDOI
Atomic electron tomography: 3D structures without crystals
TL;DR: The combination of AET and atom-tracing algorithms has enabled the determination of the coordinates of individual atoms and point defects in materials with a 3D precision, allowing direct measurements of 3D atomic displacements and the full strain tensor.
Journal ArticleDOI
High-resolution, low-dose phase contrast X-ray tomography for 3D diagnosis of human breast cancers
Yunzhe Zhao,Emmanuel Brun,Emmanuel Brun,Paola Coan,Zhifeng Huang,A Sztrókay,Paul C. Diemoz,Susanne Liebhardt,Alberto Mittone,Sergei Gasilov,Jianwei Miao,Alberto Bravin +11 more
TL;DR: This work imaged a human breast in three dimensions and identified a malignant cancer with a pixel size of 92 μm and a radiation dose less than that of dual-view mammography, demonstrating that high-resolution 3D diagnostic imaging of human breast cancers can, in principle, be performed at clinical compatible doses.
Journal ArticleDOI
Three-dimensional coordinates of individual atoms in materials revealed by electron tomography
Rui Xu,Chien-Chun Chen,Chien-Chun Chen,Li Wu,Mary Scott,Wolfgang Theis,Colin Ophus,Matthias Bartels,Yongsoo Yang,Hadi Ramezani-Dakhel,Michael R. Sawaya,Hendrik Heinz,Laurence D. Marks,Peter Ercius,Jianwei Miao +14 more
TL;DR: The ability to precisely localize the 3D coordinates of individual atoms in materials without assuming crystallinity is expected to find important applications in materials science, nanoscience, physics, chemistry and biology.
References
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Book
Numerical Optimization
Jorge Nocedal,Stephen J. Wright +1 more
TL;DR: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization, responding to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.
Journal ArticleDOI
Nonlinear total variation based noise removal algorithms
TL;DR: In this article, a constrained optimization type of numerical algorithm for removing noise from images is presented, where the total variation of the image is minimized subject to constraints involving the statistics of the noise.
Journal ArticleDOI
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
TL;DR: In this paper, the authors considered the model problem of reconstructing an object from incomplete frequency samples and showed that with probability at least 1-O(N/sup -M/), f can be reconstructed exactly as the solution to the lscr/sub 1/ minimization problem.
Book
Principles of Computerized Tomographic Imaging
TL;DR: Properties of Computerized Tomographic Imaging provides a tutorial overview of topics in tomographic imaging covering mathematical principles and theory and how to apply the theory to problems in medical imaging and other fields.
Journal ArticleDOI
A Singular Value Thresholding Algorithm for Matrix Completion
TL;DR: This paper develops a simple first-order and easy-to-implement algorithm that is extremely efficient at addressing problems in which the optimal solution has low rank, and develops a framework in which one can understand these algorithms in terms of well-known Lagrange multiplier algorithms.