Kyle Champley :: Computed Tomography (CT)



    My current mathematical research interest is in computed tomography (CT). The most common uses for tomography lie in medical imaging e.g. CAT, SPECT, PET, MRI scans. In x-ray CT, the x-ray data can be modeled by line integrals of a function f which take on the values of tissue attenuation coefficients (one can think of these as tissue density values). We try to recover the function's point-wise values from this set of line integrals. Once this function is determined we display it as a colored image.

I am most interested with the mathematical aspects of CT, including modeling, inversion formulas (determination, stabilization, efficiencey), de-noiseing, sampling, etc. Currently I work on PET/CT imaging in the Imaging Research Laboratory at the University of Washington.

Below you will find links to some of my work and other CT references.


Selected Publications and Technical Papers
> Planogram Rebinning with the Frequency-Distance Relationship
    (to appear in the July 2008 issue of IEEE Transaction on Medical Imaging)
> SPECT Reconstruction Using the EM Algorithm and an Exact Inversion Formula
    (my math M.S. thesis)
> Theorems and Definitions of Mathematics
    (links to pdf files that contain over 100 pages of useful theorems and definitions)
> Katsvich Inversion formula, PI-Lines, and Kappa Planes
    (details behind the famous cone-beam inversion)



Tomography Links
> Tomography for Dummies
    (a naive explanation of tomography)
> Principles of Computerized Tomographic Imaging
    (classic tomography reference for engineers)
> Image Research Laboratory (IRL)
    (homepage for the research lab I work in)
> Paul Kinahan's Homepage
    (my Ph.D. advisor)
> Adel Faridani's Homepage
    (my math M.S. advisor)
> Gunther Ulhmann's Homepage
> Frederic Noo's Homepage
> Frank Natterer's Homepage
> Medical Physics at the University of Chicago
> Utah Center for Advanced Imaging Research (UCAIR)



Basic Definitions
> Tomography: Tomos is latin for slice
> CT: Computed Tomography
> CAT: Computer-Aided Tomography
> SPECT: Single Photon Emission Computed Tomography
> PET: Positron Emission Tomography
> MRI: Magnetic Resonance Imaging



MATLAB Code for 2D SPECT and X-Ray CT Reconstruction
> ExpectMax.m
> fbp.m
> phantom.m
> spect.m
> spectMain.m






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