A new image reconstruction algorithm is proposed based on weighted compressed sensing (WCS) for the problem of channelized facies recovery from pixel-based measurements. This algorithm integrates information from: (1) signal structure dependencies in a transform domain (the discrete cosine transform); and (2) multiple-point statistics obtained from a training image. In the experimental side, excellent results are reported showing that the WCS scheme provides good reconstruction for geological facies models even in the [0.3%-1%] range of data. Experiments show that the proposed solution outperforms methods based on CS and MPS, when reconstruction performance is measured in terms of similarity perceptual indicators (MSSIM).