Reconstruction algorithms: Transform methods
作者： R.M. Lewitt
关键词: Computation 、 Inversion (discrete mathematics) 、 Mathematics 、 Algebraic Reconstruction Technique 、 Line integral 、 Algorithm 、 Discretization 、 Frequency domain 、 Iterative reconstruction 、 Fourier transform 、 Electrical and Electronic Engineering
摘要: Transform methods for image reconstruction from projections are based on analytic inversion formulas. In this tutorial paper, the formula case of two-dimensional (2-D) line integrals is manipulated into a number different forms, each which may be discretized to obtain algorithms sampled data. For convolution-backprojection algorithm and direct Fourier emphasis placed understanding relationship between discrete operations specified by functional expressed formula. The performance improved, with negligible extra computation, interleaving two polar sampling grids in space. formulas adapted fan-beam geometry, other summarized, including rho-filtered layergram method, involving expansions angular harmonics. A standard mathematical process leads known iterative at finite angles. new obtained introducing one-dimensional (1-D) 2-D interpolating functions, applied images, respectively. These functions derived same approach aids development more conventional transform methods.
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