Image integration with learned dictionaries and application to seismic monitoring

Sparse coding can be applied to train an overcomplete dictionary on time-lapse seismic data or images. The learned dictionary generally consists of sparse representations of one or more images. We then use such sparse representations, along with L₁-regularization techniques, to predict missing values in seismic images by solving an inverse problem. The practical outcome of the proposed methodology can be a significant reduction in field operational costs by requiring only sparse instead of dense surveys, and by integrating in the seismic images the information captured by the learned dictionary from previous time-lapse and baseline images. A synthetic example is presented to test the method.