Denoising Dolphin Click Series in the Presence of Tonals, using Singular Spectrum Analysis and Higher Order Statistics

We examine the use of Singular Spectrum Analysis (SSA) technique as an alternative technique to using standard wavelet shrinkage schemes for the purpose of de-noising mixtures of tonals, transients and Gaussian noise. Wavelet schemes require a calculation of a threshold to determine which components are taken to be signal and noise. If the noise component is Gaussian, then threshold can be determined by using an appropriate estimator. However, in the presence of strong tonal content the Gaussian threshold estimators do not give optimal performance. One method is to iteratively shift the threshold until some performance criterion has been maximized. However this frequently leads to over de-noising this time series. Since the wavelet basis is chosen to best represent the signal of interest, over de-noising can cause artifacts to appear similar to the signal of interest. In most applications this can not be tolerated. SSA has advantages in that the basis of decomposition is derived from the time series itself. So-called Empirical Orthogonal Functions (EOFs) are derived from a lag matrix created from the time series. Singular Value Decomposition (SVD) is then used to decompose a time series into a number of time series components. In the case of signal separation or de-noising the time series components can be combined by using their statistical properties. We examine the use of higher order statistics, to group components into tonals, transient, and Gaussian noise. By using the properties of the kurtosis for these three types of signal, the grouping of components can be done in a more formal manner, than the thresholding technique found in wavelet schemes. The technique is demonstrated on test data consisting of dolphin clicks in the presence of tonal and Gaussian noise. Results are also shown for real data of a dolphin click series while echo-locating on a target. It is critical for future work that after de-noising, the shape of the dolphin clicks is preserved, and t- he recorded reflections from the target are adequately de-noised, without introducing artifacts which could be mistaken for reflections. We discuss the results of the SSA and evaluate its potential for de-noising applications.