By Jiang Hsieh

X-ray computed tomography (CT) keeps to event fast progress, either in uncomplicated expertise and new scientific purposes. Seven years after its first variation, Computed Tomography: ideas, layout, Artifacts, and up to date developments, moment version, offers an summary of the evolution of CT, the mathematical and actual elements of the know-how, and the basics of snapshot reconstruction algorithms. Image Read more...

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Six years after its first variation, Computed Tomography: ideas, layout, Artifacts, and up to date Advances, moment version presents and up-to-date assessment of the evolution of CT, the mathematical and Read more...

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Extra resources for Computed Tomography: Principles, Design, Artifacts, and Recent Advances, Second Edition

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Thus, the original signal is expanded to KN samples, as shown in Fig. 2. (4) Shift property: The Fourier transform of f(x–x0) is e  j 2 ux0 F (u ). This indicates that a shift of a function in the spatial domain is equivalent to a phase shift in the Fourier domain. This property is quite useful in data resampling or interpolation. It is often preferred over spatial domain interpolations. 2 sampling intervals. (5) Derivative: The Fourier transform of the derivative of f(x), df(x)/dx, is j 2uF (u ).

12. D. E. Kuhl and R. Q. Edwards, “Reorganizing data from transverse section scans of the brain using digital processing,” Radiology 91, 975–983 (1968). 13. R. N. Bracewell, “Strip integration in radiation astronomy,” Australian J. of Physics 9, 198–217 (1956). 14. S. I. Tetel’baum, “About the problem of improvement of images obtained with the help of optical and analog instruments,” Bull. Kiev Polytech. Inst. 21, 222 (1956) (in Russian). 15. S. I. Tetel’baum, “About a method of obtaining volume images with the help of x-rays,” Bull.

It can be shown that both the mean and the variance of the Poisson distribution equal m. 6 shows examples of the Poisson distribution for m = 10, 20, and 30. This section discusses only a few selected topics with a limited scope on statistics, so interested readers can refer to Refs. 4– 7 for more detailed treatments of the subject. 6 Poisson distributions for m = 10, 20, and 30. 3 Linear algebra An m × n matrix A is a rectangular array of numbers arranged in m rows and n columns:  a11 a A =  21     am1 a12 a22 am 2  a1n   a2 n  .

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