Source separation via SVD-free rank minimization in the hierarchical semi-separable representation

Abstract

Recent developments in matrix rank optimization have allowed for new computational approaches in the field of source separation or deblending. In this paper, we propose a source separation algorithm for blended marine acquisition, where two sources are deployed at different depths (over/under acquisition). The separation method incorporates the Hierarchical Semi-Separable structure (HSS) inside rank-regularized leastsquares formulations. The proposed approach is suitable for large scale problems, since it avoids SVD computations and uses a low-rank factorized formulation instead. We illustrate the performance of the new HSS-based deblending approach by simulating an over/under blended acquisition, wherein uniformly random time delays (of < 1 second) are applied to the one of the sources.

Nonlinear Blind Compensation for Array Signal Processing Application

“…In References [ 25 , 26 , 27 , 28 , 29 ], some blind signal separation algorithms have been investigated; for instance, the singular value decomposition (SVD)-based and the eigenvalue decomposition (EVD)-based methods. The SVD-based algorithm is the standard due to its good performance and applicability, as confirmed in References [ 26 , 28 , 29 ].…”

“…In References [ 25 , 26 , 27 , 28 , 29 ], some blind signal separation algorithms have been investigated; for instance, the singular value decomposition (SVD)-based and the eigenvalue decomposition (EVD)-based methods. The SVD-based algorithm is the standard due to its good performance and applicability, as confirmed in References [ 26 , 28 , 29 ]. As learned from the References [ 26 , 28 , 29 ], the performance for large signal extraction is mainly determined by an adequate choice of the number of the largest singular values, .…”

Rank-reduction deblending for record length extension: The example of the Carnarvon basin

“…Several de-blending techniques have been developed over the past few years (Berkhout 2008, Mahdad et al 2011, Maraschini et al 2012, Wason et al 2014, Cheng and Sacchi 2015, Kumar et al 2015, but most of them are customized to separate almost simultaneous sources, aiming for signal preservation. In this paper we focus on the case where the blending noise amplitude is orders of magnitude higher than the signal, aiming to retrieve as much signal as possible whilst removing all of the blending noise.…”

Focal Deblending Using Smart Subsets of OBN 5D Data

“…Examples include coherency-based FK filtering (Mahdad et al, 2011), median-based filtering (Gan et al, 2015;Zhan et al, 2015), sparsity-based methods using Radon transforms (Ibrahim and Sacchi, 2013;Haacke et al, 2015), curvelets (Lin and Herrmann, 2009;Wason et al, 2011) and seislets (Chen, 2015). Another approach is to use rank-reduction techniques (Wason et al, 2014;Cheng and Sacchi, 2015).…”