Nonlinear Image Reconstruction from Projections of Ultrasonic Travel Times and Electric Current Densities

Image reconstruction from projections may be tried with ultrasound or electric current as projecting phenomena. For both these phenomena we outline an experiment supplying the projections and derive a mathematical model describing the experiment. These models are nonlinear variations of the Radon transform. We present practical algorithms for their numerical inversion and report on numerical tests carried out with simulated and real projection data. Our starting-point is the linear case.

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