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.

Tremor constitutes the most common motor disorder, and poses a functional problem to a large number of patients. Despite of the considerable experience in tremor management, current treatment based on drugs or surgery does not attain an effective attenuation in 25 % of patients, motivating the need for research in new therapeutic alternatives. In this context, this paper presents the concept design, development, and preliminary validation of a soft wearable robot for tremor assessment and suppression. The TREMOR neurorobot comprises a Brain Neural Computer Interface that monitors the whole neuromusculoskeletal system, aiming at characterizing both voluntary movement and tremor, and a Functional Electrical Stimulation system that compensates for tremulous movements without impeding the user perform functional tasks. First results demonstrate the performance of the TREMOR neurorobot as a novel means of assessing and attenuating pathological tremors.

This paper presents an effective blind statistical identification technique for nonstationary nonlinear systems based on an information theoretical algorithm. This technique firstly extracts, from the output signals, the multivariate relationships in the Hilbert spaces by exploiting the separability properties of the signal outputs transformed by the Karhunen-Loeve transform (KLT). Then, the algorithm methodologically clusters the stochastic surfaces in the Hilbert spaces using the self-organizing maps (SOMs) and further develops their best statistical model under the fixed-rank condition. The resulting blind identification of the statistical system model is based on marginal probability density functions (PDFs), whose convergence to the statistical system model based on Monte Carlo simulations has also been demonstrated by asymptotically vanishing the Kullback-Leibler divergences. A large number of simulations on both synthetic and real systems demonstrated the validity and the excellent performances of this technique that is irrespective of the system order, the stochastic surface topology, the true marginal PDFs, and the knowledge of the statistics of the noise superimposed to the output signals. Finally, this approach could also represent a suitable and promising technique for the noninvasive diagnosis of a large class of medical pathologies originated by unknown physiological factors (nonlinear compositions of unknown input signals) and/or when they are difficult or unpractical to measure.

This book presents the state of the art, the current best practices and the innovative techniques of the methods of information geometry. The first half of the book presents a comprehensive introduction to the mathematical foundation of information geometry, including preliminaries from differential geometry, the geometry of manifolds or probability distributions, and the general theory of dual affine connections. The second half describes many applications, such as statistics, linear systems, information theory, quantum mechanics, convex analysis, neural networks, and affine differential geometry. This is a well-written book, original and highly relevant from which to learn methods and results.

This paper addresses nonlinear nonstationary system identification from stimulus-response data, a problem concerning a large variety of applications, in dynamic control as well as in signal processing, communications, physiological system modelling and so on. Among the different methods suggested in the vast literature for nonlinear system modelling, the ones based on the Volterra series and the Neural Networks are the most commonly used. However, a strong limitation for the applicability of these methods lies in the necessary property of stationarity, an assumption that cannot be considered as valid in general and strongly affecting the validity of results. Another weakness of the approaches currently used is that they refer to differential systems, thus being unsuitable to model systems described by integral equations. A computational intelligence technique that exploits the potentialities of both the Karhunen-Loeve Transform (KLT) and Neural Networks (NNs) representation and without any of the limitations of the previous approaches is suggested in this paper. The technique is suitable for modelling the wide class of systems described by nonlinear nonstationary functionals, thus including both differential and integral systems. It takes advantage of the KLT separable kernel representation that is able to separate the dynamic and static behaviours of the system as two distinct components, and the approximation property of NNs for the identification of the nonlinear no-memory component. To validate the suggested technique comparisons with experimental results on both nonlinear nonstationary differential and integral systems are reported.

This book deals with the state-of-the-art current best practices and the innovative techniques of nonlinear dynamic modeling of physiological phenomena. The author beings together the theoretical and practical aspects of nonlinear system identification, nonstationary modeling, multiple-input-multiple-output system modeling, and closed-loop system modeling in a single volume, where all the content is enjoyable to read, well-written, highly relevant, original, and timely.

This purpose of this book is to bring to the attention of the scientific community the fact that an effective methodology for numerical solutions of applied mathematical problems and numerical schemes for particular problems or class of problems exists. The book presents many new results on high-order methods for strong sample path approximations and for weak functional approximation, including implicit, predictor corrector, extrapolation, and variance-reduction methods. Many simulation exercises are included throughout the book to assist the reader to develop hands on numerical skills and an intuitive understanding of the basis concepts and of the properties and the issues concerning implementation of the numerical schemes introduced.

This paper presents an exhaustive study on the classification capabilities of an efficient algorithm, which is able to accurately classify non-deterministic signals generated by chaotic dynamical systems, without estimating their probability density function (pdf). Experimental results were compared to other existing techniques such as hidden Markov model (HMM), vector quantization (VQ), and dynamic time warping (DTW). Classification performance is higher than current best practices for chaotic signals. A better noise rejection was also achieved, and a reduction of two orders of magnitude in training-times compared with HMM was obtained, thus making the proposed methodology one of the current best practices in this field. As an application example, the recognition of encrypted chaotic-signals in a secure-communication context, is reported and discussed.

This paper presents, on the basis of a rigorous mathematical formulation, a multicomponent sinusoidal model that allows an asymptotically exact reconstruction of nonstationary speech signals, regardless of their duration and without any limitation in the modeling of voiced, unvoiced, and transitional segments. The proposed approach is based on the application of the Hilbert transform to obtain an amplitude signal from which an AM component is extracted by filtering, so that the residue can then be iteratively processed in the same way. This technique permits a multicomponent AM-FM model to be derived in which the number of components (iterations) may be arbitrarily chosen. Additionally, the instantaneous frequencies of these components can be calculated with a given accuracy by segmentation of the phase signals. The validity of the proposed approach has been proven by some applications to both synthetic signals and natural speech. Several comparisons show how this approach almost always has a higher performance than that obtained by current best practices, and does not need the complex filter optimizations required by other techniques

The Karhunen-Loeve transform, being able to represent stochastic processes under appropriate conditions, is a powerful signal processing tool. But the high computational cost incurred in the modeling of long signals has limited its use in the recognition of speech segmented at the word level. In this paper, we present a novel algorithm that significantly reduces the computational cost when the number of signals to be treated is small in comparison to their samples.