Robust MPS-Based Modeling via Spectral Analysis

Spatially distributed phenomena typically do not exhibit Gaussian behavior, and consequently methods constrained to traditional two-point covariance statistics cannot correctly represent the spatial connectivity of such phenomena. This necessitates the development of multiple-point statistics (MPS)-based algorithms. However, due to the sparse data available to infer these MPS statistics, one needs to have a training image (TI) to accurately model higher-order statistics. Training images are usually inferred from outcrops and/or conceptual models and are subject to uncertainty that have to be accounted for in MPS algorithms.

[1]  B. Boashash,et al.  Pattern recognition using invariants defined from higher order spectra: 2-D image inputs , 1997, IEEE Trans. Image Process..

[2]  R. B. Bratvold,et al.  Parallel Nested Factorization Algorithms , 1993 .

[3]  D. Donoho,et al.  Basis pursuit , 1994, Proceedings of 1994 28th Asilomar Conference on Signals, Systems and Computers.

[4]  D. L. Donoho,et al.  Compressed sensing , 2006, IEEE Trans. Inf. Theory.

[5]  Junfeng Yang,et al.  A New Alternating Minimization Algorithm for Total Variation Image Reconstruction , 2008, SIAM J. Imaging Sci..

[6]  M.R. Raghuveer,et al.  Bispectrum estimation: A digital signal processing framework , 1987, Proceedings of the IEEE.

[7]  D. Brillinger An Introduction to Polyspectra , 1965 .

[8]  C. Deutsch,et al.  Teacher's Aide Variogram Interpretation and Modeling , 2001 .

[9]  J. Caers,et al.  Stochastic Simulation of Patterns Using Distance-Based Pattern Modeling , 2010 .

[10]  Snehamoy Chatterjee,et al.  Dimensional Reduction of Pattern-Based Simulation Using Wavelet Analysis , 2012, Mathematical Geosciences.

[11]  Julián M. Ortiz,et al.  Verifying the high-order consistency of training images with data for multiple-point geostatistics , 2014, Comput. Geosci..

[12]  Clayton V. Deutsch,et al.  Programs for kriging and sequential Gaussian simulation with locally varying anisotropy using non-Euclidean distances , 2011, Comput. Geosci..

[13]  A. Journel Nonparametric estimation of spatial distributions , 1983 .

[14]  Pejman Tahmasebi,et al.  Multiple-point geostatistical modeling based on the cross-correlation functions , 2012, Computational Geosciences.

[15]  Michael Edward Hohn,et al.  An Introduction to Applied Geostatistics: by Edward H. Isaaks and R. Mohan Srivastava, 1989, Oxford University Press, New York, 561 p., ISBN 0-19-505012-6, ISBN 0-19-505013-4 (paperback), $55.00 cloth, $35.00 paper (US) , 1991 .

[16]  Wenlong Xu,et al.  Conditional curvilinear stochastic simulation using pixel-based algorithms , 1996 .

[17]  G. Mariéthoz,et al.  Reconstruction of Incomplete Data Sets or Images Using Direct Sampling , 2010 .

[18]  Jeffrey A. Fessler,et al.  Nonuniform fast Fourier transforms using min-max interpolation , 2003, IEEE Trans. Signal Process..

[19]  Jef Caers,et al.  Stochastic Reservoir Simulation Using Neural Networks Trained on Outcrop Data , 1998 .

[20]  R. Dimitrakopoulos,et al.  High-order Stochastic Simulation of Complex Spatially Distributed Natural Phenomena , 2010 .

[21]  M. Rosenblatt Stationary sequences and random fields , 1985 .

[22]  Roussos G. Dimitrakopoulos,et al.  A new approach for geological pattern recognition using high-order spatial cumulants , 2010, Comput. Geosci..

[23]  Timothy C. Coburn,et al.  Geostatistics for Natural Resources Evaluation , 2000, Technometrics.

[24]  Roussos Dimitrakopoulos,et al.  High-order Statistics of Spatial Random Fields: Exploring Spatial Cumulants for Modeling Complex Non-Gaussian and Non-linear Phenomena , 2009 .

[25]  J. Chilès,et al.  Geostatistics: Modeling Spatial Uncertainty , 1999 .

[26]  Tinting Yao,et al.  Specsim: a Fortran-77 program for conditional spectral simulation in 3D , 1998 .

[27]  B. N. Chatterji,et al.  An FFT-based technique for translation, rotation, and scale-invariant image registration , 1996, IEEE Trans. Image Process..

[28]  Michael S. Sacks,et al.  Population-averaged geometric model of mitral valve from patient-specific imaging data , 2015 .

[29]  Emmanuel J. Candès,et al.  Near-Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? , 2004, IEEE Transactions on Information Theory.

[30]  Vivek K. Goyal,et al.  Transform-domain sparsity regularization for inverse problems in geosciences , 2009, GEOPHYSICS.

[31]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[32]  R. M. Srivastava Reservoir Characterization With Probability Field Simulation , 1992 .

[33]  Andrew Drach,et al.  A Comprehensive Framework for the Characterization of the Complete Mitral Valve Geometry for the Development of a Population-Averaged Model , 2015, FIMH.

[34]  Georgios B. Giannakis,et al.  Bispectral analysis and model validation of texture images , 1995, IEEE Trans. Image Process..

[35]  Omid Asghari,et al.  Multiple-point geostatistical simulation using the bunch-pasting direct sampling method , 2013, Comput. Geosci..

[36]  Vinod Chandran,et al.  Pattern Recognition Using Invariants Defined From Higher Order Spectra- One Dimensional Inputs , 1993, IEEE Trans. Signal Process..

[37]  M. Lustig,et al.  Compressed Sensing MRI , 2008, IEEE Signal Processing Magazine.

[38]  Stefan Kunis,et al.  Using NFFT 3---A Software Library for Various Nonequispaced Fast Fourier Transforms , 2009, TOMS.

[39]  K. Eskandari,et al.  Growthsim – A Multiple Point Framework for Pattern Simulation , 2007 .

[40]  Jerry M. Mendel,et al.  Identification of nonminimum phase systems using higher order statistics , 1989, IEEE Trans. Acoust. Speech Signal Process..

[41]  Lu Gan Block Compressed Sensing of Natural Images , 2007, 2007 15th International Conference on Digital Signal Processing.