Basic Methods of Tomography and Inverse Problems: A Set of Lectures |
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Image Reconstruction from Projections An Approach from | 5 |
Background from Mathematical Analysis | 21 |
The Radon Transform in the Space of Distributions with Compac | 69 |
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algorithm applied backprojection backpropagation chapter compact support compare fig components computed continuous linear continuous linear form convergence convex convolution corresponding cose cross-section defined denoted derive differential distribution of compact eigenvalues Ewald-sphere example far-field far-field image filtered backpropagation finite formula Fourier space Fourier transform function f Green's function Hence Hilbert space holographic holographic image image of rigid integrable function integral equation inverse problem K-space kernel Lemma linear operator locally integrable function mapping mathematical measurement surface method norm obtain orthogonal projection parameters physical optics planar plane wave Porter-Bojarski propagation Radon transform range of views Rayleigh-Sommerfeld reconstruction result rigid scatterer scalar scattered field scattering problem secondary sources sequence solution spatial Fourier spectrum subspace tempered distribution threedimensional tion twodimensional vector wave equation wavefields weak scatterer yields zero