Mehdi Aharchaou and Alan Levander
Aharchaou, M., and A. Levander, 2016, A compressive sensing approach to the high-resolution linear Radon transform: Application on teleseismic wavefields, Geophysical Journal International, Express Letter, doi: 10.1093/gji/ggw307
Abstract: We propose a new approach to the linear Radon transform (LRT) based on compressive sensing (CS) theory. This method can be used to extract signals of interest embedded in teleseismic measurements recorded by regional seismic arrays. We pose the problem of enhancing the resolution of the LRT as an inverse problem formulated in the frequency domain and solved according to a CS framework. We show how irregularity in the measurements along with sparsity constraints can be used to reach very compact and meaningful representations in the Radon domain, offering a benefit for both signal isolation and spatial interpolation during data reconstruction. We demonstrate the effectiveness of our approach and its benefits on both synthetic and USArray seismograms. This CS-based version of the LRT presents a valuable tool relevant for both global and exploration seismic processing, and which can be used as a basis for signal enhancement techniques exploiting irregularly sampled data.