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We develop a paradigm using microlocal analysis that allows one to characterize the visible and added singularities in a broad range of incomplete data tomography problems. We give precise characterizations for photo- and thermoacoustic tomography and Sonar, and provide artifact reduction strategies. In particular, our theorems show that it is better to arrange Sonar detectors so that the boundary of the set of detectors does not have corners and is smooth. To illustrate our results, we provide reconstructions from synthetic spherical mean data as well as from experimental photoacoustic data.
We analyze the mathematical model of multiwave tomography with a variable speed with integrating measurements on planes tangent to a sphere surrounding the source. We prove sharp uniqueness and stability estimates with full and partial data and propo
We present a paradigm for characterization of artifacts in limited data tomography problems. In particular, we use this paradigm to characterize artifacts that are generated in reconstructions from limited angle data with generalized Radon transforms
Quantitative image reconstruction in photoacoustic tomography requires the solution of a coupled physics inverse problem involvier light transport and acoustic wave propagation. In this paper we address this issue employing the radiative transfer equ
Photoacoustic computed tomography (PACT) is an emerging computed imaging modality that exploits optical contrast and ultrasonic detection principles to form images of the absorbed optical energy density within tissue. If the object possesses spatiall
Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by imperfect knowl