Abstract
We explore the effect of sampling rates when measuring data given by Mf for special operators M arising in Thermoacoustic Tomography. We start with sampling requirements on Mf given f satisfying certain conditions. After this we discuss the resolution limit on f posed by the sampling rate of Mf without assuming any conditions on these sampling rates. Next we discuss aliasing artifacts when Mf is known to be under sampled in one or more of its variables. Finally, we discuss averaging of measurement data and resulting aliasing and artifacts, along with a scheme for anti-aliasing.
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1600327
Funding statement: The author was partly supported by NSF Grant DMS-1600327.
Acknowledgements
The author would like to thank Dr. Plamen Stefanov for suggesting this problem and for his guidance in the analysis of this problem.
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