Sparsity promoting morphological decomposition for coherent noise suppression: Application to streamer vibration related noise

We address the signal and noise separation problem where the noise is coherent. We use a dictionary learning method to learn a dictionary of unit vectors called atoms; each one representing an elementary waveform redundant in the noisy data. In such a learned dictionary, some atoms represent signal waveforms while others represent noise waveforms. Using a multivariate Gaussian classifier trained on a noise recording, the atoms representing noise waveforms are discriminated and separated from the atoms representing seismic waveforms and two subdictionaries are created; one describing the morphology of the signal, the other describing the morphology of the noise. Using these sub-dictionaries, a morphological component analysis problem is set to separate the seismic signal and the coherent noise. In contrast to fixing transforms for representing the noise and the signal, our method is entirely adapting to the morphology of the signal and the noise. We present an application for removing streamer vibration related noise and show successful denoising results on synthetic and field data examples.