New and not-so-new applications of low-rank matrix and tensor completion to seismic data processing

In recent years, the development of recommendation systems has become an important area of research for data scientists. A recommendation system (or recommender system) is an algorithm that attempts to predict the rating that a user or costumer will give to an item. Recommendation systems are becoming quite popular in the field of e-commerce for predicting ratings of movies, books, news, research articles etc. Research in the area of data analytics and recommendation systems has lead to important efforts toward solving the so-called matrix completion problem. The latter entails estimating the missing elements of a matrix containing customer ratings. The aforementioned problem can be extended to the recovery of the missing elements of a multilinear array or tensor. Prestack seismic data in midpoint-offset domain can be represented by a 5th order tensor. Therefore, tensor completion methods can be applied to the recovery of unrecorded traces. Furthermore, tensor completion methodologies can also be applied to multidimensional signal-to-noise-ratio enhancement, simultaneous source separation, interpretative attribute analysis etc. In this presentation, I will review matrix and tensor completion methods and discuss their implementation to reconstruct, process and enhance seismic volumes. I will also discuss the successful application of tensor completion techniques to the reconstruction of industrial data sets.