Modified singular value decomposition by means of independent component analysis

Abstract

In multisensor signal processing (underwater acoustics, geophysics, etc.), the initial dataset is usually separated into complementary subspaces called signal and noise subspaces in order to enhance the signal-to-noise ratio. The singular value decomposition (SVD) is a useful tool to achieve this separation. It provides two orthogonal matrices that convey information on normalized wavelets and propagation vectors. As signal and noise subspaces are on the whole well evaluated, usually the SVD procedure cannot correctly extract only the source waves with a high degree of sensor to sensor correlation. This is due to the constraint given by the orthogonality of the propagation vectors. To relax this condition, exploiting the concept of independent component analysis (ICA), we propose another orthogonal matrix made up of statistically independent normalized wavelets. By using this combined SVD–ICA procedure, we obtain a better separation of these source waves in the signal subspace. Efficiency of this new separation procedure is shown on synthetic and real datasets.