Analysis of the Compatibility Conditions for the Radon Projections, with an Application to Seismology

摘要

In the context of the Radon approach to tomographic imaging, we face the problem of ascertaining whether or not a set of functions can be considered a set of reliable projections of an unknown function. We first review some results about the singular system of the Radon operator. Then, we define a set of parameters that allows us to evaluate the degree of compatibility of a set of projections. We apply our analysis to the seismic source imaging problem. In particular, we show that the compatibility conditions can be used for the empirical Green function retrieval.