Radon Transform: Beyond Aliasing With Irregular Sampling

Aliasing imposes a strict limitation on the maximum frequency allowed in a data set, or the maximum<br>possible sampling interval that can be used in the sampling of a time series. In the Fourier transform<br>this is completely justi ed, as regular sampling is almost always used and FFT algorithms based on<br>regular sampling are much more faster than any other technique to estimate the transformed data.<br>However, in other elds, the advantages of regular sampling may be less clear. That could be the case<br>in seismic processing where sometimes irregular sampling is imposed by practical considerations. Even<br>when further processing usually requires regular sampling in o set, modeling in the Radon domain<br>allows the re-sampling to a regular grid. Furthermore, High Resolution RT allows us to interpolate<br>and extrapolate the nal grid, with an increase in aperture. Here we show some simple examples of<br>information beyond Nyquist in the context of the Radon transform.