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.

中文翻译：

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基于加权$$ \ ell _1 $$ℓ1-正则化的地质相恢复

针对基于像素测量的信道化相重构问题，提出了一种加权压缩感知（WCS）算法。该策略整合了来自以下方面的信息：（i）变换域中的图像结构（离散余弦变换）；（ii）通过使用多点模拟（MPS）和训练图像获得的统计模型。开发了一种在WCS上下文中集成多点统计信息的方法，为此使用了权重定义的集合。在实验验证中，报告的优异结果表明，即使在[0.3–1 \（\％\）的范围内，WCS也能为地质相模型提供良好的重建。基于像素的测量。实验表明，以信噪比和相似感知指标衡量性能时，所提出的解决方案优于基于纯CS和MPS的方法。