Monday, January 28, 2013

Tensor completion based on nuclear norm minimization for 5D seismic data reconstruction

Nadia Kreimer sent me the following:

Hello Igor,

I wanted to know if you could post this paper on your blog
It has been recently submitted to the Geophysics journal. It is about tensor completion using nuclear norm for the reconstruction of seismic data. It is the first time this technique is tried in seismic data, so we thought it would be interesting if it appeared on your Matrix Factorization group.
Me and the other authors belong to the SAIG Consortium at the University of Alberta (

Thanks, regards,
Nadia Kreimer
Thanks Nadia !

Nadia also tells me that they will probably release their code later. At which point, I will list it in the Matrix Factorization Jungle page. Here is the paper:

Prestack seismic data are multidimensional signals that can be described as a low-rank
fourth-order tensor in the frequency  space domain. Tensor completion strategies can be used to recover unrecorded observations and to improve the signal-to-noise ratio of prestack volumes. Additionally, tensor completion can be posed as an inverse problem and solved using convex optimization algorithms. The objective function for this problem contains a data mis t term and a term that serves to minimize the rank of the tensor. The alternating direction method of multipliers o ers automatic rank determination and it is used to obtain a reconstructed seismic volume. The proposed method converges to a good approximation of the rank of the tensor given the input data. We present synthetic examples to illustrate the behaviour of the algorithm in terms of trade-o parameters that control the quality of the reconstruction. We further illustrate the performance of the algorithm in a land data survey from Alberta, Canada.

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