Low-Rank Decomposition Based on Disjoint Component Analysis With Applications in Seismic Imaging

Abstract

Low-rank decomposition plays a fundamental role in signal processing and computational imaging, due to the possibility of decomposing a signal into semantic components. The classical singular value decomposition (SVD) separates globally correlated components from uncorrelated ones. Modified versions of SVD that have been recently proposed allow the separation between horizontal and vertical components of the image. These versions explore blind source separation techniques, specially the well-known independent component analysis (ICA). However, these existing techniques fail in separating horizontal or vertical signals that are linearly independent to each other. In this paper, we propose a new low-rank decomposition method based on disjoint component analysis (DCA), namely, SVD-DCA. In contrast with the SVD and the SVD-ICA techniques, this new method is able to separate horizontal from vertical events, as well as to separate horizontal or vertical components that are linearly independent to each other. The proposed method is evaluated in two relevant applications in seismic imaging, the attenuation of multiple reflections and the attenuation of ground-roll noise. The results involving these applications are obtained with real marine and land seismic data, respectively.