Reconstruction of channelized geological facies based on RIPless compressed sensing

• Published in: Computers & geosciences 2015-04, Vol.77, p.54-65
• Main Authors: Calderón, Hernán, Silva, Jorge F., Ortiz, Julián M., Egaña, Alvaro
• Format: Article
• Language: English
• Subjects: Algorithms; Basis selection; Compressed; Compressed sensing; Detection; Discrete cosine transform; Image reconstruction; Multichannel facies images; Reconstruction; Signal to noise ratio; Similarity; Training
• ISSN: 0098-3004; 1873-7803
• DOI: 10.1016/j.cageo.2015.01.006

This work proposes a new approach for multichannel facies image reconstruction based on compressed sensing where the image is recovered from pixel-based measurements without the use of prior information from a training image. An ℓ1-minimization reconstruction algorithm is proposed, and a performance guaranteed result is adopted to evaluate its reconstruction. From this analysis, we formulate the problem of basis selection, where it is shown that for unstructured pixel-based measurements the Discrete Cosine Transform is the best choice for the problem. In the experimental side, signal-to-noise ratios and similarity perceptual indicators are used to evaluate the quality of the reconstructions, and promising reconstruction results are obtained. The potential of this new approach is demonstrated in under-sampled scenario of 2–4% of direct data, which is known to be very challenging in the absence of prior knowledge from a training image. •The problem of facies reconstruction is formulated as a generalized sampling problem.•A image recovery algorithm is proposed based on a convex optimization algorithm that promotes sparsity.•From RIPless Compressed Sensing, DCT is shown to be the optimal basis to represent the facies images in this reconstruction problem.•Practical and theoretical aspects of this recovery problem are addressed.•Good facies reconstruction performances demonstrated even with 2–4% of direct data.