Geological Facies Recovery Based on Weighted $$ell _1$$ ℓ 1 -Regularization

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.