Exploiting transformation-domain sparsity for fast query in multiple-point geostatistics
Multiple-point geostatistics has recently attracted significant attention for characterization of environmental variables. Such methods proceed by searching a large database of patterns obtained from a training image to find a match for a given data-event. The template-matching phase is usually the most time-consuming part of a MPS method. Linear transformations like discrete cosine transform or wavelet transform are capable of representing the image patches with a few nonzero coefficients. This sparsifying capability can be employed to speed up the template-matching problem up to hundreds of times by multiplying only nonzero coefficients. This method is only applicable to rectangular data-events because it is impossible to represent an odd-shaped data-event in a transformation domain. In this paper, the method is applied to speed up the image quilting (IQ) method. The experiments show that the proposed method is capable of accelerating the IQ method tens of times without sensible degradation in simulation results. The method has the potential to be employed for accelerating optimization-based and raster-scan patch-based MPS algorithms.
KeywordsDiscrete cosine transform Image quilting Template matching Transformation domain
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- 3.Ronayne, MJ, Gorelick, SM, Caers, J: Identifying discrete geologic structures that produce anomalous hydraulic response: An inverse modeling approach. Water Resour. Res. 44(8) (2008)Google Scholar
- 6.dellArciprete, D, Bersezio, R, Felletti, F, Giudici, M, Comunian, A, Renard, P: Comparison of three geostatistical methods for hydrofacies simulation: a test on alluvial sediments. J. Hydrol. 20(2), 299–311 (2012)Google Scholar
- 11.de Almeida, JA: Stochastic simulation methods for characterization of lithoclasses in carbonate reservoirs. Earth Sci. Rev. 101(3), 250–270 (2010)Google Scholar
- 20.Mariethoz, G, Renard, P, Straubhaar, J: The direct sampling method to perform multiple-point geostatistical simulations. Water Resour. Res. 46(11) (2010)Google Scholar
- 21.Rezaee, H, Mariethoz, G, Koneshloo, M, Asghari, O: Multiple-point geostatistical simulation using the bunch-pasting direct sampling method. Comput. Geosci., 293–308 (2013)Google Scholar
- 22.Abdollahifard, MJ, Faez, K: Fast direct sampling for multiple-point stochastic simulation. Arab. J. Geosci., 1–13 (2013)Google Scholar
- 29.Gonzalez, RC, Woods, RE: Digital image processing (2002)Google Scholar
- 31.Mariethoz, G, Caers, J: Multiple-point geostatistics: stochastic modeling with training images. Wiely-Blackwell (2014)Google Scholar
- 32.Efros, AA, Freeman, WT: Image quilting for texture synthesis and transfer. In: Proceedings of the 28th annual conference on Computer graphics and interactive techniques, pp 341–346. ACM (2001)Google Scholar