Nonlinear analysis of the performance and reliability of wavelet singularity detection based denoising for Doppler ultrasound fetal heart rate signals

Many studies on the physiology of the cardiovascular system revealed that nonlinear chaotic dynamics govern the generation of the heart rate signal. This is also valid for the fetal heart rate (FHR) variability, where however the variability is affected by many more factors and is significantly more complicated than for the adult case. Recently an adaptive wavelet denoising method for the Doppler ultrasound FHR recordings has been introduced. In this paper the performance and reliability of that method is confirmed by the observation that for the wavelet denoised FHR signal, a deterministic nonlinear structure, which was concealed by the noise, becomes apparent. It provides strong evidence that the denoising process removes actual noise components and can therefore be utilized for the improvement of the signal quality. Hence by observing after denoising a significant improvement of the 'chaoticity' of the FHR signal we obtain strong evidence for the reliability and efficiency of the wavelet based denoising method. The estimation of the chaoticity of the FHR signal before and after the denoising is approached with three nonlinear analysis methods. First, the rescaled scale analysis (RSA) technique reveals that the denoising process increases the Hurst exponent parameter as happens when additive noise is removed from a chaotic signal. Second, the nonlinear prediction error evaluated with radial basis function (RBF) prediction networks is significantly lower at the denoised signal. The significant gain in predictability can be attributed to the drastic reduction of the additive noise from the signal by the denoising algorithm. Moreover, the evaluation of the correlation coefficient between actual and neural network predicted values as a function of the prediction time displays characteristics of chaos only for the denoised signal. Third, a chaotic attractor, reconstructed with the embedding dimension technique, becomes evident for the denoised signal, while it is completely obscured for the original signals. The correlation dimension of the reconstructed attractor for the denoised signal tends to reach a value independent of the embedding dimension, a sign of deterministic chaotic signal. In contrast for the original signal the correlation dimension increases steadily with the embedding dimension, a fact that indicates strong contribution of noise.