Emission Discrete Tomography

A Pixel-based Discrete Tomographic Technique and Its Applications

“…The new pixel-based method (published by the author in [17,42]) essentially turns the reconstruction problem into an optimization task, and minimizes the objective functional 16) where P ϑ denotes the ϑ projection, f is the 2-dimensional image function that approximates the solution, [Rf ] (ϑ) denotes the projection of image f calculated at the angle ϑ, . is the Euclidean norm, φ(f ) is the so-called regularization (or penalty) term, and γ ≥ 0 is the regularization parameter.…”

“…It can contain three kinds of nodes, namely discrete images, projection sets, and some additional information. With this format one can store images and projections flexibly in different data type representations like integer, float, word, byte, β-representation [16], or in an external file of an arbitrary user defined format. In the latter case, the user has the freedom to implement and join custom file readers and writers.…”

Application of Discrete Tomographic Methods in Nondestructive Testing and Materials Science

“…While this problem is NP-complete or even NP-hard for most of the cases [12,54,57,67,68,97], there are also a few polynomial results [24,25,28,54,118,119].…”

“…A listing of a few sample uses follows: electron microscopy (EM) [91,102], medicine [28,32,47,89,100,117], radiography and nondestructive testing [23,49,111,143,172,180,187], reconstruction from limited view angles [62,100,111,191], electron tomography [11], materials science [14,15,31,126,136,148,155], geometric tomography [28,66,67,69,108], emission tomography [28,[118][119][120], geotomography [195]. Further examples for using DT in nondestructive testing and materials science are presented in Chapters 4-6 and Chapters 7-8 of the thesis, respectively.…”