Coherent noise suppression by learning and analyzing the morphology of the data

ABSTRACTWe have developed a method for suppressing coherent noise from seismic data by using the morphological differences between the noise and the signal. This method consists of three steps: First, we applied a dictionary learning method on the data to extract a redundant dictionary in which the morphological diversity of the data is stored. Such a dictionary is a set of unit vectors called atoms that represent elementary patterns that are redundant in the data. Because the dictionary is learned on data contaminated by coherent noise, it is a mix of atoms representing signal patterns and atoms representing noise patterns. In the second step, we separate the noise atoms from the signal atoms using a statistical classification. Hence, the learned dictionary is divided into two subdictionaries: one describing the morphology of the noise and the other one describing the morphology of the signal. Finally, we separate the seismic signal and the coherent noise via morphological component analysis (MCA); it us...

[1]  Wei Wang,et al.  Ground-roll Separation By Sparsity And Morphological Diversity Promotion , 2010 .

[2]  Mirko van der Baan,et al.  High-amplitude noise detection by the expectation-maximization algorithm with application to swell-noise attenuation , 2010 .

[3]  Jian-Feng Cai,et al.  Data-driven tight frame construction and image denoising , 2014 .

[4]  Nasser Kazemi,et al.  Attenuation of swell noise in marine streamer data via nonnegative matrix factorization , 2016 .

[5]  James H. McClellan,et al.  Seismic data denoising through multiscale and sparsity-promoting dictionary learning , 2015 .

[6]  Mauricio D. Sacchi,et al.  FX Singular Spectrum Analysis , 2009 .

[7]  A. Day,et al.  Wavefield-separation methods for dual-sensor towed-streamer data , 2013 .

[8]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[9]  Jianwei Ma,et al.  Simultaneous dictionary learning and denoising for seismic data , 2014 .

[10]  B. P. West,et al.  Interactive seismic facies classification using textural attributes and neural networks , 2002 .

[11]  Mauricio D. Sacchi,et al.  Interpolation and denoising of high-dimensional seismic data by learning a tight frame , 2015 .

[12]  Klaus Mosegaard,et al.  Seismic Texture Classification: A Computer-aided Approach to Stratigraphic Analysis , 1995 .

[13]  Don R. Hush,et al.  Network constraints and multi-objective optimization for one-class classification , 1996, Neural Networks.

[14]  Stéphane Mallat,et al.  A Wavelet Tour of Signal Processing - The Sparse Way, 3rd Edition , 2008 .

[15]  Vicente Oropeza,et al.  The Singular Spectrum Analysis method and its application to seismic data denoising and reconstruction , 2010 .

[16]  M. Elad,et al.  $rm K$-SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation , 2006, IEEE Transactions on Signal Processing.

[17]  Felix J. Herrmann,et al.  Seismic denoising with nonuniformly sampled curvelets , 2006, Computing in Science & Engineering.

[18]  Necati Gulunay,et al.  FXDECON and complex wiener prediction filter , 1986 .

[19]  Stanley Osher,et al.  Monte Carlo data-driven tight frame for seismic data recovery , 2016 .

[20]  Michael Elad,et al.  Efficient Implementation of the K-SVD Algorithm using Batch Orthogonal Matching Pursuit , 2008 .

[21]  E. Candès,et al.  The curvelet representation of wave propagators is optimally sparse , 2004, math/0407210.

[22]  Yang Liu,et al.  Seislet transform and seislet frame , 2010 .

[23]  Y. C. Pati,et al.  Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[24]  Sergey Fomel,et al.  OC-seislet: Seislet transform construction with differential offset continuation , 2010 .

[25]  J. MacQueen Some methods for classification and analysis of multivariate observations , 1967 .

[26]  Michael Elad,et al.  Double Sparsity: Learning Sparse Dictionaries for Sparse Signal Approximation , 2010, IEEE Transactions on Signal Processing.

[27]  D. Donoho,et al.  Redundant Multiscale Transforms and Their Application for Morphological Component Separation , 2004 .

[28]  Dengliang Gao,et al.  Volume texture extraction for 3D seismic visualization and interpretation , 2003 .

[29]  Yangkang Chen,et al.  Double Sparsity Dictionary for Seismic Noise Attenuation , 2016 .

[30]  R. Neelamani,et al.  Coherent and random noise attenuation using the curvelet transform , 2008 .

[31]  Stewart Trickett,et al.  F-xy Cadzow Noise Suppression , 2008 .

[32]  Jianwei Ma,et al.  Seismic data restoration via data-driven tight frame , 2014 .

[33]  Michael Elad,et al.  From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images , 2009, SIAM Rev..

[34]  Walter Söllner,et al.  Sparsity promoting morphological decomposition for coherent noise suppression: Application to streamer vibration related noise , 2016 .

[35]  J. Bobin,et al.  Morphological component analysis , 2005, SPIE Optics + Photonics.

[36]  Kjersti Engan,et al.  Method of optimal directions for frame design , 1999, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258).

[37]  Charles C. Mosher,et al.  Wavelet Transform Methods For Geophysical Applications , 1994 .

[38]  T. W. Anderson,et al.  Classification into two Multivariate Normal Distributions with Different Covariance Matrices , 1962 .

[39]  Mauricio D. Sacchi,et al.  Robust reduced-rank filtering for erratic seismic noise attenuation , 2015 .

[40]  Walter Söllner,et al.  A method of combining coherence-constrained sparse coding and dictionary learning for denoising , 2017 .

[41]  Cássio Fraga Dantas,et al.  Learning Dictionaries as a Sum of Kronecker Products , 2017, IEEE Signal Processing Letters.

[42]  Margaret Yu Seismic interference noise elimination - a multidomain 3D filtering approach , 2011 .

[43]  Robert M. Haralick,et al.  Textural Features for Image Classification , 1973, IEEE Trans. Syst. Man Cybern..