RBF-Based Technique for Statistical Demodulation of Pathological Tremor

This paper presents an innovative technique based on the joint approximation capabilities of radial basis function (RBF) networks and the estimation capability of the multivariate iterated Hilbert transform (IHT) for the statistical demodulation of pathological tremor from electromyography (EMG) signals in patients with Parkinson's disease. We define a stochastic model of the multichannel high-density surface EMG by means of the RBF networks applied to the reconstruction of the stochastic process (characterizing the disease) modeled by the multivariate relationships generated by the Karhunen-Loéve transform in Hilbert spaces. Next, we perform a demodulation of the entire random field by means of the estimation capability of the multivariate IHT in a statistical setting. The proposed method is applied to both simulated signals and data recorded from three Parkinsonian patients and the results show that the amplitude modulation components of the tremor oscillation can be estimated with signal-to-noise ratio close to 30 dB with root-mean-square error for the estimates of the tremor instantaneous frequency. Additionally, the comparisons with a large number of techniques based on all the combinations of the RBF, extreme learning machine, backpropagation, support vector machine used in the first step of the algorithm; and IHT, empirical mode decomposition, multiband energy separation algorithm, periodic algebraic separation and energy demodulation used in the second step of the algorithm, clearly show the effectiveness of our technique. These results show that the proposed approach is a potential useful tool for advanced neurorehabilitation technologies that aim at tremor characterization and suppression.