Eric Todd Quinto

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These notes represent an extended version of the contents of the third lecture delivered at the AMS Short Course “Radon Transform and Applications to Inverse Problems” in Atlanta in January 2005. They contain a brief description of properties of some generalized Radon transforms arising in inverse problems. Here by generalized Radon transforms we mean(More)
We consider the reconstruction problem for limited angle tomography using filtered backprojection (FBP) and Lambda tomography. We use microlocal analysis to explain why the well-known streak artifacts are present at the end of the limited angular range. We explain how to mitigate the streaks and prove that our modified FBP and Lambda operators are standard(More)
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 photoacoustic and thermoacoustic tomography and sonar, and provide artifact reduction strategies. In particular, our theorems show that it is better(More)
Filtered back-projection and weighted back-projection have long been the methods of choice within the electron microscopy community for reconstructing the structure of macromolecular assemblies from electron tomography data. Here, we describe electron lambda-tomography, a reconstruction method that enjoys the benefits of the above mentioned methods, namely(More)
Exterior tomographic data are taken over lines outside a central region, and such data occur in the industrial nondestructive evaluation of large objects such as rockets. We explain, using microlocal analysis, which singularities are well reconstructed from exterior data, and we explain how this phenomenon is reflected in the singular value decomposition(More)