Thermoacoustic Tomography with Circular Integrating Detectors and Variable Wave Speed
Abstract: We explore Thermoacoustic Tomography with circular integrating detectors assuming variable, smooth wave speed. We show that the measurement operator in this case is a Fourier Integral Operator and examine how the singularities in initial data and measured data are related through the canonical relation of this operator. We prove which of those singularities in the initial data are visible from a fixed open subset of the set on which measurements are taken. In addition, numerical results are shown for both full and partial data.
arXiv
Submitted
to Inverse
Problems and Imaging
Sampling in Thermoacoustic Tomography
Abstract: We explore the effect of sampling rates of
Fourier Integral Operators on reconstructed images in Thermoacoustic
Tomography. We start with sampling requirements on $M f$ given $f$
satisfying certain conditions. After this we discuss the resolution
limit on $f$ posed by the sampling rate of $M f$ without assuming
any conditions on these sampling rates. Next we discuss aliasing
artifacts when $M f$ is known to be under sampled in one or more of
its variables, and finally, we discuss averaging of measurement data
and resulting aliasing and artifacts.
arXiv
Submitted to Journal of Inverse and Ill-posed Problems