Journal ArticleDOI
An Iterative Image Space Reconstruction Algorthm Suitable for Volume ECT
TLDR
The method, the iterative image space reconstruction algorithm (ISRA), is able to reconstruct data from a scanner with a spatially variant point spread function in less time than other proposed algorithms.Abstract:
The trend in the design of scanners for positron emission computed tomography has traditionally been to improve the transverse spatial resolution to several millimeters while maintaining relatively coarse axial resolution (1-2 cm). Several scanners are being built with fine sampling in the axial as well as transverse directions, leading to the possibility of the true volume imaging. The number of possible coincidence pairs in these scanners is quite large. The usual methods of image reconstruction cannot handle these data without making approximations. It is computationally most efficient to reduce the size of this large, sparsely populated array by back-projecting the coincidence data prior to reconstruction. While analytic reconstruction techniques exist for back-projected data, an iterative algorithm may be necessary for those cases where the point spread function is spatially variant. A modification of the maximum likelihood algorithm is proposed to reconstruct these back-projected data. The method, the iterative image space reconstruction algorithm (ISRA), is able to reconstruct data from a scanner with a spatially variant point spread function in less time than other proposed algorithms. Results are presented for single-slice data, simulated and actual, from the PENN-PET scanner.read more
Citations
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Book
Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation
TL;DR: This book provides a broad survey of models and efficient algorithms for Nonnegative Matrix Factorization (NMF), including NMFs various extensions and modifications, especially Nonnegative Tensor Factorizations (NTF) and Nonnegative Tucker Decompositions (NTD).
MonographDOI
Nonnegative Matrix and Tensor Factorizations
TL;DR: A broad survey of models and efficient algorithms for nonnegative matrix factorization (NMF) can be found in this paper, where the authors focus on the algorithms that are most useful in practice, looking at the fastest, most robust, and suitable for large-scale models.
Journal ArticleDOI
Algorithms for nonnegative matrix factorization with the β-divergence
Cédric Févotte,Jérôme Idier +1 more
TL;DR: This letter describes algorithms for nonnegative matrix factorization (NMF) with the β-divergence, a family of cost functions parameterized by a single shape parameter β that takes the Euclidean distance, the Kullback-Leibler divergence, and the Itakura-Saito divergence as special cases.
Journal Article
Treatment of Axial Data in Three-Dimensional PET
TL;DR: Two methods of treating the axial information from a volume PET scanner are presented and Qualitative and quantitative errors introduced by the approximations are examined for simulated objects with sharp boundaries and for a more anatomically realistic distribution with smooth activity gradients.
Posted Content
The Why and How of Nonnegative Matrix Factorization.
TL;DR: A recent subclass of NMF problems is presented, referred to as near-separable NMF, that can be solved efficiently (that is, in polynomial time), even in the presence of noise.
References
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Journal ArticleDOI
Maximum Likelihood Reconstruction for Emission Tomography
L. A. Shepp,Y. Vardi +1 more
TL;DR: In this paper, the authors proposed a more accurate general mathematical model for ET where an unknown emission density generates, and is to be reconstructed from, the number of counts n*(d) in each of D detector units d. Within the model, they gave an algorithm for determining an estimate? of? which maximizes the probability p(n*|?) of observing the actual detector count data n* over all possible densities?.
Journal Article
EM reconstruction algorithms for emission and transmission tomography.
Kenneth Lange,Richard E. Carson +1 more
TL;DR: The general principles behind all EM algorithms are discussed and in detail the specific algorithms for emission and transmission tomography are derived and the specification of necessary physical features such as source and detector geometries are discussed.
Journal ArticleDOI
A Statistical Model for Positron Emission Tomography
TL;DR: In this article, a mathematical model tailored to the physics of positron emissions is presented, and the model is used to describe the image reconstruction problem of PET as a standard problem in statistical estimation from incomplete data.
Journal ArticleDOI
Finite series-expansion reconstruction methods
TL;DR: These methods are based on the discretization of the image domain prior to any mathematical analysis and thus are rooted in a completely different branch of mathematics than the transform methods which are discussed in this issue.
Journal ArticleDOI
Reconstruction algorithms: Transform methods
TL;DR: In this paper, the inversion formula for the case of 2D reconstruction from line integrals is manipulated into a number of different forms, each of which may be discretized to obtain different algorithms for reconstruction from sampled data.