This talk is a tribute to the speaker's research stay in the group of Prof. Todd Quinto at Tufts University Meford (MA) during the years 2002 / 2003, that has been funded by the Alexander von Humboldt foundation. We present the inverse problem of reconstructing a function from its spherical means where the center set is located on a hyperplane. The underlying integral transform is linear and continuous between spaces of tempered distributions. The regularization theory in those days had to be extended to distribution spaces where we used the method of approximate inverse as starting point.