Reconstruction of signals from highly aliased multichannel samples by Generalized Matching Pursuit

In this paper we consider the problem of reconstructing a bandlimited signal from severely aliased multichannel samples. Multichannel sampling in this context means that the samples are available after the signal has been filtered by various linear operators. We propose the method of Generalized Matching Pursuit to solve the reconstruction problem. We illustrate the potential of the method using synthetic data computed for multimeasurement towed-streamer seismic data acquisition. A remarkable observation is that high-fidelity reconstruction is possible even when the data are uniformly and coarsely sampled, with the order of aliasing significantly exceeding the number of channels.