Download Computed Tomography: Principles, Design, Artifacts, and by Jiang Hsieh PDF

By Jiang Hsieh

X-ray computed tomography (CT) maintains to event quick progress, either in simple expertise and new scientific functions. Seven years after its first variation, Computed Tomography: rules, layout, Artifacts, and up to date developments, moment version, offers an summary of the evolution of CT, the mathematical and actual elements of the expertise, and the basics of photograph reconstruction algorithms. Image Read more...

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

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Additional info for Computed Tomography: Principles, Design, Artifacts, and Recent Advances, Second Edition

Example text

One basic assumption of Eq. 44) is the monoenergetic nature of the input x-ray beam. This assumption requires all of the x-ray photons emitting from an xray source to have the same energy. In “real world” clinical CT, this condition is rarely satisfied. The output energy spectrum of an x-ray tube is quite broad. For example, when we select 120 kVp on a CT scanner, the output x-ray photon energies vary between 10 kVp and 120 kVp, as shown in Fig. 14. For the majority of the materials, the  value varies significantly with the x-ray energy, as previously illustrated in Fig.

4 Illustration of the convolution process between functions f1(x) and f2(x). f2(x) is first flipped and shifted with respect to its x axis. The resulting convolution represents the area under the product of the two functions. The inverse Fourier transform can be defined in a similar manner: f ( x, y )        F (u, v)e j 2  ( ux  vy ) dudv . 8) All properties presented for the 1D Fourier transform can be extended to the two dimensional case. 2 Random variables For a random variable x′, its cumulative distribution function P(x) is defined as a function whose value at each point x is the probability that a random observation of x′ will be less than or equal to x.

Because of the inherent advantages of the third-generation technology, nearly all of the state-of-the-art scanners on the market today are third generation. Several technology challenges in the design of the third-generation CT, including detector stability and aliasing, led to investigations of the fourthgeneration concept depicted in Fig. 17. In this design, the detector forms an enclosed ring and remains stationary during the entire scan, while the x-ray tube rotates about the patient. Unlike the third-generation scanner, a projection is formed with signals measured on a single detector as the x-ray beam sweeps across the object.

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