This paper was recently accepted for publication in Mathematical Geosciences. It presents an approach to reconstruct categorical facies models based on Weighted Compressed Sensing.

The work is part of ongoing collaboration with Prof. Jorge Silva at the Department of Electrical Engineering, at Universidad de Chile.

The paper can be accessed here.

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Geological Facies Recovery Based on Weighted ℓ1 -Regularization

Hernan Calderon (Information and Decision System Group (IDS), Department of Electrical Engineering, Universidad de Chile), Felipe Santibañez (Information and Decision System Group (IDS), Department of Electrical Engineering, Universidad de Chile), Jorge F. Silva (Information and Decision System Group (IDS), Department of Electrical Engineering, Universidad de Chile), Julian M. Ortiz (The Robert M. Buchan Department of Mining, Queen’s University), Alvaro Egaña (Advanced Mining Technology Center, Universidad de Chile)

Abstract A weighted compressed sensing (WCS) algorithm is proposed for the problem of channelized facies reconstruction from pixel-based measurements. This strategy integrates information from: (i) image structure in a transform domain (the discrete cosine transform); and (ii) 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%] 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.