The Mathematics of Computerized TomographySIAM, 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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a₁ Abramowitz and Stegun apply approximation artefacts assume band-limited functions C₁ compute constant converges convolution defined derivatives discrete Fourier transform eigenvalues error essentially b-band-limited estimate exterior problem fan-beam filtered backprojection algorithm finite follows Fourier algorithm Fourier reconstruction function ƒ Gegenbauer polynomials H₁ hence ill-posed problems incomplete data problems inner integral interpolation inversion formula iteration Kaczmarz's method L₂ Lemma limited angle line integrals linear m-resolving mathematical matrix norm obtain operator parallel geometry plane polynomial of degree Proof Radon transform range S₁ sampling scanning geometry Section singular value decomposition Sobolev spaces solution solve spherical harmonics step Theorem 1.1 Theorem II.1.1 Toeplitz matrix transform of length Tuy's uniquely vanishes zero Σ Σ