Tensor Factorization and its Application to Multidimensional Seismic Data Recovery
- Mauricio D. Sacchi (University of Alberta) | Jianjun Gao (China University of Geosciences) | Aaron Stanton (University of Alberta) | Jinkun Cheng (University of Alberta)
- Document ID
- Society of Exploration Geophysicists
- 2015 SEG Annual Meeting, 18-23 October, New Orleans, Louisiana
- Publication Date
- Document Type
- Conference Paper
- 2015. Society of Exploration Geophysicists
- high-resolution, imaging, interpolation, processing
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- 25 since 2007
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Research in the area of data analytics and recommendation systems have lead to important efforts toward solving the problem of matrix completion. The latter entails estimating the missing elements of a matrix by assuming a low-rank matrix representation. 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 for multidimensional signal-tonoise- ratio enhancement. We discuss the implementation of the Parallel Matrix Factorization (PMF) algorithm, an SVD free tensor completion method that we applied to 5D seismic data reconstruction. The Parallel Matrix Factorization (PMF) algorithm expands our first generation of 5D tensor completion codes based on High Order SVD and Nuclear norm minimization. We review the PMF method and explore its applicability to processing industrial data sets via tests with synthetic and field data.
In recent years, the development of recommendation systems has become an important area of research for data scientists (Koren et al., 2009). 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 have become quite popular in e-commerce for predicting ratings of movies, books, news, research articles etc. In Figure 1, we provide a simplified example of a data matrix with ratings of a series of movies. It is clear that recommendation systems use thousands of users to rate thousands of items and that our figure is merely for illustrative purposes. A rating of 5 means that the user liked the movie, a rating of 1 means that he/she did not like the movie. Question marks are used to indicate that the movie has not been rated by the user. This is a table (matrix) where one can immediately infer that the data could be predicted by simple examination of patterns or relationships between users and movies. For instance, users who liked romantic movies appear not to like action movies. The main task for the recommendation algorithm is to extract patterns that might exist in the data and use them to predict the rating a user would have given to an item he/she did not rate. The unknown ratings can be found by solving the so called Matrix Completion problem (Recht, 2011). A similar problem is also present in seismic data processing (Kreimer and Sacchi, 2011).
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