Geological Facies Recovery Based on Weighted ℓ1-Regularization
Published in Mathematical Geosciences, 2019
Recommended citation: Hernan Calderon, Felipe Santibañez, Jorge F. Silva, Julián M. Ortiz, and Alvaro Egaña. (2015). "Geological Facies Recovery Based on Weighted ℓ1-Regularization." Mathematical Geosciences. 52. pp 593 - 617. https://doi.org/10.1007/s11004-019-09825-5
A weighted compressed sensing (WCS) algorithm is proposed for the problem of channelized facies reconstruction from pixel-based measurements.
This strategy integrates information from:
- Image structure in a transform domain (the discrete cosine transform)
- A statistical model obtained from the use of multiple-point simulations (MPS) and a training image.
A method is developed to integrate multiple-point statistics within the context of WCS, using for that a collection of weight definitions. In the experimental validation, excellent results are reported showing that the WCS provides good reconstruction for geological facies models even in the range of 0.3–1.0% pixel-based measurements.
Experiments show that the proposed solution outperforms methods based on pure CS and MPS, when the performance is measured in terms of signal-to-noise ratio, and similarity perceptual indicators.