The Mathematics of Computerized Tomography
SIAM, 01.06.2001 - 240 Seiten
This book provides a unified view of tomographic techniques, a common mathematical framework, and an in-depth treatment of reconstruction algorithms. It focuses on the reconstruction of a function from line or plane integrals, with special emphasis on applications in radiology, science, and engineering. The Mathematics of Computerized Tomography covers the relevant mathematical theory of the Radon transform and related transforms and also studies more practical questions such as stability, sampling, resolution, and accuracy. Quite a bit of attention is given to the derivation, analysis, and practical examination of reconstruction algorithms, for both standard problems and problems with incomplete data.
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algorithm angle apply approximation assume called choose circle complete compute condition consider consistent constant contains continuous converges convolution coordinates defined depends derivatives determined directions discrete distributed equation error essentially estimate example fact filtered backprojection algorithm finite follows Fourier transform function function f geometry give given hence holds ill-posed inner integral interpolation inversion formula Lemma limited linear mathematical matrix means measured method minimal norm Note object obtain operator original orthogonal parallel plane polynomial of degree possible practical problem projection Proof Radon transform range reads reconstruction relation replaced respect rule sampling satisfies sense simply ſº solution solve sources spaces standard step Theorem Theorem 1.1 uniquely vanishes yields zero