Dictionary Learning and Sparse Representations for Denoising and Reconstruction of Marine Seismic Data
AbstractSeismic signals are generally spread across many data samples of the recorded data. Applying a mathematical transformation to the data can however concentrate them on few samples only of the transform domain. Such representations are called sparse and have gained high interest in seismic processing because they build the necessary requirement to better compress or analyze the signal in the data. This thesis first assesses the effectiveness of building sparse representations for three critical seismic processing tasks, i.e., random noise attenuation, signal separation, and data reconstruction. The presented theory and the numerical experiments reveal that sparse representations can be used to achieve the aforementioned processing tasks under the condition that the signal has a high level of sparsity in the transform domain. It then follows an investigation of the transforms that can lead to sparse representations of the seismic data. A particular focus is placed on dictionary learning (DL) methods. These methods are applied to a data set to find a dictionary that can be used for sparse representation of the data set. The dictionary is a set of signals, called atoms, that represent elementary patterns of the data, and the sparse representation is found by reconstruction of the data with linear combinations of few dictionary atoms. The conventional DL methods are examined, and various modifications are implemented to develop three DL-based methods that are better adapted to each of the seismic processing tasks of interest. (1) A DL method is developed to attenuate the random noise in the seismic data. This method learns a dictionary and finds a sparse approximation of the data based on a statistical measure of the coherence in the residuals. Due to this particularity, the method is released from the need of the a priori knowledge of the noise energy. This is attractive for seismic data applications because the noise in seismic data has an intensity that is often unknown and that is varying across the data set. (2) A DL-based method is developed to separate the coherent noise from the seismic data. Some types of noise that contaminate seismic data cannot be removed with random noise attenuation methods because they appear with spatial or temporal coherency in the data. To tackle such noise, DL is combined with a statistical classification. First, DL is applied to the noise-contaminated data, which results in a dictionary of atoms representing either signal patterns or noise patterns. Using a statistical classification, the noise atoms are separated from the signal atoms, which divides the dictionary into a subdictionary of noise atoms and a subdictionary of signal atoms. Then, by finding a sparse representation of the data in the two subdictionary domains, the signal and the noise contributions in the data are identified and separated. This DL-based method has compelling advantages compared to the traditional coherent noise removal methods based on sparse representation; it does not require someone to search for adequate transforms that may sparsify the signal and the noise, and it adapts to the signal and noise in the data for an optimal separation. (3) a DL method is developed to interpolate and regularize the seismic data. In this method, each learned atom is constrained to represent an elementary waveform that has a constant amplitude along a parabolic traveltime moveout characterized by kinematic wavefield parameters. Such a parabolic structure is consistent with the physics of the seismic wavefield propagation and it can be used to easily interpolate and extrapolate the atoms. Using this advantage, the method can interpolate and regularize the seismic data. The process consists in learning a parabolic dictionary, interpolating the atoms, and computing a sparse representation of the data in the interpolated dictionary domain. Benefiting from the parabolic structure, the sparsity promotion, and the data adaptation, this method is able to interpolate severely aliased data. The three proposed DL methods are validated with synthetic and field seismic data examples. The effectiveness of the denoising methods are also assessed in comparison to industry-standard and state-of-the-art methods. Each method is demonstrated to be valuable for seismic processing.
List of papers
|I Turquais, P., E. G. Asgedom, and W. Söllner, 2017c, A method of combining coherence-constrained sparse coding and dictionary learning for denoising: Geophysics, 82, V137–V148 The published version is available in DUO: http://hdl.handle.net/10852/61245|
|II Turquais, P., E. G. Asgedom, and W. Söllner, 2017a, Coherent noise suppression by learning and analyzing the morphology of the data: Geophysics, 82, V397–V411 The published version is available in DUO: http://hdl.handle.net/10852/61247|
|III Turquais, P., E. G. Asgedom, W. Söllner, and L.-J. Gelius, 2017f, Parabolic dictionary learning for seismic wavefield reconstruction across the streamers: Submitted to Geophysics To be published. The paper is removed from the thesis in DUO awaiting publishing.|