BME210 Medical Imaging - Copy

BME210 Medical Imaging - Copy - BME 210 Spring 2009 Medical...

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BME 210 Spring 2009 Medical Imaging BME 210 Biomedical Computer Simulation Methods Medical Imaging Computerized Tomography I Introduction II. X-Ray Computed Tomography A. Introduction B. Data Collection for CT C. CT Numbers III. Solution of Linear Algebraic Equations by LU Decomposition A. LU Decomposition B. Crout’s Algorithm C. Example D. Forward/Backward Substitution E. Example Continued IV. MATLAB Solution A. Left Division B. Plotting – Image Function Study Problems Study Problem Solutions 1
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BME 210 Spring 2009 Medical Imaging Medical Imaging Computerized Tomography Note: The following material has been taken from: Kak and Slaney. Principles of Computerized Tomographic Imaging . IEEE Press, 1987; Jain. Fundamentals of Digital Image Processing . Prentice Hall, 1989; and from Harris and Kamel, "Iterative Reconstruction in Computerized Tomography”, UMAP Modules, 1990. I. Introduction Tomography refers to the cross-sectional imaging of an object from either transmission or reflection data collected by illuminating the object from many different directions. The impact of this technique in diagnostic medicine has been revolutionary, since it has enabled physicians to view internal organs with unprecedented precision and safety to the patient. The first medical application utilized x-rays for forming images of tissues based on their x-ray attenuation coefficient. More recently, however, medical imaging has also been successfully accomplished with radioisotopes, ultrasound, and magnetic resonance, the imaged properties being different in each case. There are numerous nonmedical imaging applications which lend themselves to the methods of computerized tomography. Researchers have applied this methodology to the mapping of underground resources via crossborehole imaging, some specialized cases of cross-sectional imaging for nondestructive testing, the determination of the brightness distribution over a celestial sphere, and three-dimensional imaging with electron microscopy. Fundamentally, tomographic imaging deals with reconstructing an image from its projections. In the strict sense of the word, a projection at a given angle is the integral of the image in the direction specified by that angle, as illustrated in Fig. 1. However, in a loose sense, projection means the information derived from the transmitted energies, when an object is illuminated from a particular angle; the phrase "diffracted projection" may be used when energy sources are diffracting, as is the case with ultrasound and microwaves. Although, from a purely mathematical standpoint, the solution to the problem of how to reconstruct a function from its projections dates back to the paper by Radon in 1917, the current excitement in tomographic imaging originated with Hounsfield's invention of the x-ray computed tomographic scanner for which he received a Nobel prize. He shared the prize with Allan Cormack who independently discovered some of the algorithms. His invention showed that it is possible to
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This note was uploaded on 09/09/2010 for the course BME 210 taught by Professor D'argenio during the Spring '07 term at USC.

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BME210 Medical Imaging - Copy - BME 210 Spring 2009 Medical...

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