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Limited Data Problems in Tomography

Todd Quinto
Department of Mathematics
Tufts University
March 23, 2001
 
Tomography is an exciting field that allows doctors to image the inside of the body using X-rays or other indirect data, and it provides engineers with an effective method for the nondestructive evaluation of industrial objects including rockets and turbines. In many problems in medicine and industry, some tomography data are impossible to acquire, and this gives rise to limited data problems. The speaker will give an introduction to limited data tomography and describe some of the industrial and medical problems that give rise to limited tomographic data. Reconstruction from limited data is more difficult than from complete data, and certain types of singularities (e.g., certain boundaries of regions in the object) are difficult to reconstruct from limited data. We will develop and then use Fourier analysis (microlocal analysis) to explain how different types of limited data detect singularities. Reconstructions from industrial data will be presented to illustrate these ideas.
 

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