Quaternion Adaptive Line Enhancer based on Singular Spectrum Analysis

Quaternion adaptive line enhancer (QALE) has been proposed recently for the recovery of two-(2-D) or three-dimensional (3-D) periodic signals from their noisy mixtures [1] with the help of quaternion-valued adaptive filtering theory. Similar to the traditional 1-D [2] version, QALE, relies mainly on the second order similarity between the signal and its delayed version and is more effective when the signal is narrowband. Here, quaternion-valued singular spectrum analysis (QSSA) [3] is used to develop a robust 3-D ALE system where in the reconstruction stage of QSSA the eigentriples are adaptively selected (filtered) using the delayed version of the data. Unlike the QALE where (second) order statistics are taken into account, in the proposed QSSA-QALE the full eigen-spectrum of the embedding matrix is exploited. Consequently, the system works for non-Gaussian noise and wideband 3-D periodic signals. The two systems have been implemented and their results compared. It is shown that the QSSA-QALE significantly outperformed QALE when the noise is not Gaussian.