Poisson Sinogram Resampling
The X-ray transform of a signal measures its integral along all possible lines. It is the mathematical foundation of several tomographic imaging modalities including X-ray CT, PET, and single particle cryo-EM. Each measurement follows a Poisson distribution, the rate of which is given by a known measurement functional applied to the X-ray transform. The goal of the project is to study the resampling of the set of available measurements to obtain an approximation of unknown measurements, using statistics and sampling theory. The procedure will eventually be used as a preprocessing step to accelerate the recovery of the signal from its measurements. Thus, the resampling itself must not depend on recovering the full signal. The student should have a solid understanding of functional analysis, convex optimization, and probability theory.
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