Microlocal analysis in tomography

Abstract

Several limited data problems in tomography will be presented in this chapter, including ones for X-ray tomography, electron microscopy, and radar imaging. First, reconstructions from limited data will be evaluated to observe their strengths and weaknesses. Then, the basic analytic properties of the transforms will be presented. The concept of microlocal analysis will be introduced to make the notion of singularity precise. Finally, the microlocal properties of the tomographic transforms are given and then used to explain the observed strengths and limitations of the reconstructions. This will show that these limitations are intrinsic to these limited data problems themselves.