The research 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. There, he presents 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. The proposed 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.
The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions.