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Abstract The article suggests a new approach using the so-called consistency method for the inversion of the spherical mean Radon transform in 2D with detectors on a line. We present… Click to show full abstract
Abstract The article suggests a new approach using the so-called consistency method for the inversion of the spherical mean Radon transform in 2D with detectors on a line. We present a new iterative formula which gives an algorithm to recover an unknown function supported completely on one side of a line L from its spherical means over circles centered on the line L. Our reconstruction formula has the benefit of being local. Such an inversion is required in problems of thermo- and photo-acoustic tomography, ultrasound reflection tomography, radar imaging, and a few other.
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2019
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