Sampling Functions and Sparse Reconstruction Methods

In this paper we investigate the effects of different sampling operators on the performance of sparse reconstruction methods. The common paradigm in seismic data processing is to favor regular sampling. We will show, however, that regular sampling often hampers our data recovery efforts. Random sampling, on the other hand, can lead to algorithms where the reconstruction is almost perfect when the underlying spectrum of the signal can be assumed sparse. Also, simple 1D, 2D and 3D synthetic examples are provided to test the sparse reconstruction of signals sampled by various sampling functions.