Reconstruction from circular and spherical mean data

Abstract Circular and spherical mean data arise in various models of thermoacoustic and photoacoustic tomography which are rapidly developing modalities for in vivo imaging. We describe variants of a summability type reconstruction method adapted to this type of data. Among the highlights of the resulting algorithms, suggested by the results of numerical experiments, is the feature that the detectors need not lie on a regular curve or surface, such as a circle or a sphere. Several such numerical examples are included here.