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A new reconstruction method is given for the spherical mean transform withcenters on a plane in R3 which is also called the sonar transform. Standardinversion formulas require data over all spheres, but typically, the data arelimited in the sense that the centers and radii are in a compact set. Ourreconstruction operator is local because, to reconstruct at x, one needs onlyspheres that pass near ... read morex, and the operator reconstructs singularities, such asobject boundaries. The microlocal properties of the reconstruction operator,including its symbol as a pseudodifferential operator, are given. The methodis implemented using the approximate inverse, and reconstructions are given.They are evaluated in light of the microlocal properties of the reconstructionoperator.read less
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