Proceedings ArticleDOI
Scalable regularized tomography without repeated projections
Jonas August,Takeo Kanade +1 more
- pp 232-239
TLDR
This work reviews the recent work in regularized tomography in which the smoothness constraint is analytically transformed from the image to the projection domain, before any computations begin, and demonstrates that this method provides linear speedup of regularization tomography for up to 20 compute nodes on a 100 Mb/s network using a Matlab MPI implementation.Abstract:
Summary form only given. X-ray computerized tomography (CT) and related imaging modalities (e.g., PET) are notorious for their excessive computational demands, especially when noise-resistant probabilistic methods such as regularized tomography are used. The basic idea of regularized tomography is to compute a smooth image whose simulated projections (line integrals) approximate the observed, noisy X-ray projections. The computational expense in previous methods stems from explicitly applying a large sparse projection matrix to enforce these smoothness and data fidelity constraints during each of many iterations of the algorithm. Here we review our recent work in regularized tomography in which the smoothness constraint is analytically transformed from the image to the projection domain, before any computations begin. As a result, iterations take place entirely in the projection domain, avoiding the repeated sparse matrix-vector products. A more surprising benefit is the decoupling of a large system of regularization equations into many small systems of simpler independent equations, whose solution requires an "embarassingly parallel" computation. Here, we demonstrate that this method provides linear speedup of regularized tomography for up to 20 compute nodes (Pentium 4, 1.5 GHz) on a 100 Mb/s network using a Matlab MPI implementation.read more
Citations
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Journal ArticleDOI
Penalized weighted least-squares approach to sinogram noise reduction and image reconstruction for low-dose X-ray computed tomography
TL;DR: This work investigated a penalized weighted least-squares (PWLS) approach to address this problem in two dimensions, where the WLS considers first- and second-order noise moments and the penalty models signal spatial correlations.
High Performance Computing
TL;DR: The key elements of the Core Program will be described including the construction of a UK e-Science Grid and the need to develop a data architecture for the Grid that will allow federated access to relational databases as well as flat files.
Book ChapterDOI
2.11 – Fundamentals of CT Reconstruction in 2D and 3D
TL;DR: This chapter describes the fundamentals of 2D and 3D image reconstruction algorithms, with the emphasis on x-ray CT imaging, though the general principles are also applicable to simplified versions of positron emission tomography and single-photon emission computed tomography, as well as some other imaging systems.
Computación científica paralela mediante uso de herramientas para paso de mensajes
TL;DR: Con base en la herramienta mas reciente, the Toolbox MPI para Octave, se describen brevemente sus caracteristicas principales, y se presenta un estudio de caso, el conjunto de Mandelbrot.
References
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Book
The Mathematics of Computerized Tomography
TL;DR: In this paper, the Radon transform and related transforms have been studied for stability, sampling, resolution, and accuracy, and quite a bit of attention is given to the derivation, analysis, and practical examination of reconstruction algorithm, for both standard problems and problems with incomplete data.
Journal ArticleDOI
Nonuniform fast Fourier transforms using min-max interpolation
TL;DR: This paper presents an interpolation method for the nonuniform FT that is optimal in the min-max sense of minimizing the worst-case approximation error over all signals of unit norm and indicates that the proposed method easily generalizes to multidimensional signals.
Book
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TL;DR: The first edition of this book has been out of print for some time and I have decided to follow the publisher's kind suggestion to prepare a new edition as mentioned in this paper, which is much more elementary.
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A local update strategy for iterative reconstruction from projections
TL;DR: It is shown that Bayesian segmentation using Gauss-Seidel iteration produces useful estimates at much lower signal-to-noise ratios than required for continuously valued reconstruction.
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High Performance Computing
TL;DR: This new edition of High Performance Computing gives a thorough overview of the latest workstation and PC architectures and the trends that will in?uence the next generation.
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