Reconstruction of channelized geological facies based on RIPless compressed sensing

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.