By Peter W. Hawkes
Advances in Imaging and Electron Physics merges long-running serials-Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. This sequence beneficial properties prolonged articles at the physics of electron units (especially semiconductor devices), particle optics at low and high energies, microlithography, snapshot technological know-how and electronic picture processing, electromagnetic wave propagation, electron microscopy, and the computing equipment utilized in most of these domain names.
An vital characteristic of those Advances is that the topics are written in this type of means that they are often understood by means of readers from different specialities.
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Extra resources for Advances in Imaging and Electron Physics, Vol. 151
Parameter v0 corresponds to the vP coordinate of the κ-line at uP = 0. It is given by v0 = vP (γ0 ), tan γ0 = − b·u , e·u (66) where γ0 is defined by the condition uP (γ0 ) = 0. So far we have considered the case that vectors b and e define the filtering plane. Based on this, we have computed the parameters in Eq. (59). For completeness, we now follow the opposite approach: we assume that the κline is given by Eq. (59) and compute vectors b and e. Since Eq. (14) gives points in world coordinates, vector b associated with coordinate uP and the filter line under consideration can be computed via b(uP ) = uP u(s) + (vP (uP ) + yz (s))v(s) − y(s) .
In other words, 1- and 3-planes get the desired weights from all source positions, such that the proof is finished. 4. Reconstruction Results For the evaluation of the CLT reconstruction algorithm we simulated a CT scanner with 256 detector rows. Table 1 summarizes the simulation parameters of the circle part. 5)3 degrees mm mm2 mm mm mm3 41 RECONSTRUCTION ALGORITHMS (a) (b) (c) F IGURE 32. Reconstruction results for the CLT. The three images show (a) the result of the complete CLT, (b) the contribution of the circle, and (c) the contribution of the line, respectively.
With these conventions the Radon transform of object 1 Johann Radon, Austrian mathematician, 1887–1956. 16 BONTUS AND KÖHLER F IGURE 12. An exemplary Radon plane with normal vector ω. The dashed line has the length ρ, which is the shortest distance from the origin to the plane. Points x on the plane fulfill the relation ω · x = ρ. function μ(x) is given by ∞ Rμ(ρ, ω) = d3 x μ(x)δ(ρ − ω · x). (34) −∞ 1. Inverse Radon Transform The inverse of the Radon transform can be obtained via the following formula (Natterer, 1986) π −1 μ(x) = 8π 2 2π dα sin α R μ(ω · x, ω), dϑ 0 (35) 0 where ω = (cos α sin ϑ, sin α sin ϑ, cos ϑ) (36) and R μ(ρ, ω) = ∂ 2 Rμ(ρ, ω) ∂ρ 2 (37) is the second derivative of the Radon transform with respect to ρ.