Nicoletta Saulig

Estimating the number of components of a multicomponent nonstationary signal using the short-term time-frequency Rényi entropy

The time-frequency Rényi entropy provides a measure of complexity of a nonstationary multicomponent signal in the time-frequency plane. When the complexity of a signal corresponds to the number of its components, then this information is measured as the Rényi entropy of the time-frequency distribution (TFD) of the signal. This article presents a solution to the problem of detecting the number of components that are present in short-time interval of the signal TFD, using the short-term Rényi entropy. The method is automatic and it does not require a prior information about the signal. The algorithm is applied on both synthetic and real data, using a quadratic separable kernel TFD. The results confirm that the short-term Rényi entropy can be an effective tool for estimating the local number of components present in the signal. The key aspect of selecting a suitable TFD is also discussed.

Analysis of local time-frequency entropy features for nonstationary signal components time supports detection

Identification of different specific signal components, produced by one or more sources, is a problem encountered in many signal processing applications. This can be done by applying the local time-frequency-based Renyi entropy for estimation of the instantaneous number of components in a signal. Using the spectrogram, one of the most simple quadratic time-frequency distributions, the paper proves the local applicability of the counting property of the Renyi entropy. The paper also studies the influence of the entropy order and spectrogram parameters on the estimation results. Numerical simulations are provided to quantify the observed behavior of the local entropy in the case of intersecting components. The causes of decrements in the local number of time supports in the time-frequency plane are also studied. Finally, results are provided to illustrate the findings of the study and its potential use as a key step in multicomponent instantaneous frequency estimation.

Algorithm Based on the Short-Term Rényi Entropy And IF Estimation for Noisy EEG Signals Analysis

Stochastic electroencephalogram (EEG) signals are known to be nonstationary and often multicomponential. Detecting and extracting their components may help clinicians to localize brain neurological dysfunctionalities for patients with motor control disorders due to the fact that movement-related cortical activities are reflected in spectral EEG changes. A new algorithm for EEG signal components detection from its time-frequency distribution (TFD) has been proposed in this paper. The algorithm utilizes the modification of the Rényi entropy-based technique for number of components estimation, called short-term Rényi entropy (STRE), and upgraded by an iterative algorithm which was shown to enhance existing approaches. Combined with instantaneous frequency (IF) estimation, the proposed method was applied to EEG signal analysis both in noise-free and noisy environments for limb movements EEG signals, and was shown to be an efficient technique providing spectral description of brain activities at each electrode location up to moderate additive noise levels. Furthermore, the obtained information concerning the number of EEG signal components and their IFs show potentials to enhance diagnostics and treatment of neurological disorders for patients with motor control illnesses.

An automatic time-frequency procedure for interference suppression by exploiting their geometrical features

This paper presents an adaptive method for interference suppression in the Wigner-Ville distribution. The structure of the artifacts in the Wigner-Ville distribution has been analyzed to optimally mask the signal Wigner-Ville distribution by the Pseudo Wigner-Ville distribution. The resulting time-frequency distribution outperforms in terms of representation quality the Wigner-Ville distribution, the Pseudo Wigner-Ville distribution with fixed smoothing windows, as well as the Modified B distribution.

Optimization of quadratic time-frequency distributions using the local Rényi entropy information

This paper presents two TFD optimization schemes, extending an optimization method so far limited to the spectrogram. The first method is focused on the enhancement of the spectrogram concentration, by an adaptive realization of the S-method TFD which prevents cross-terms generation. The second approach, a generalization of the first one to the Quadratic class of TFDs, operates on a set of TFDs with different kernel parameters, selecting for each time instant the best performing one. Both methods use an entropy-based criterion for concentration enhancement, and a here-proposed method for the detection of cross-terms. The combination of the two criteria allows us to generate optimal TFDs, i.e. TFDs with highly concentrated components, but at the same time avoiding the appearance of undesirable cross-terms in the resulting TFD. HighlightsTwo TFD adaptive optimization schemes are proposed.An entropy criterion and a method for detection of cross-terms are combined.TFDs with highly concentrated components and no cross-terms are obtained.

TFD thresholding in estimating the number of EEG components and the dominant if using the short-term rényi entropy.

Time-frequency (TF) based EEG signal analysis using the local or short-term Rényi entropy often requires low-energy cross-terms and noise suppression prior to the estimation of the local number of components and the dominant component instantaneous frequency (IF). This can be easily accomplished by thresholding in the TF domain with the preset TF threshold value, often chosen empirically. The paper investigates the sensitivity of the method based on the local Rényi entropy to the chosen threshold value. The study was performed on real-life left and right hand movements EEG signals. As shown in the paper, the number of the EEG components extracted using the short-term Rényi entropy is highly sensitive to the chosen TF threshold value, unlike the dominant IF which was shown to be highly robust to TF thresholding. Hence, characterization of the EEG signals using the short-term Rényi entropy should include both detecting the number of EEG components and the dominant component IF estimation.

A local entropy-based algorithm for information content extraction from time–frequency distributions of noisy signals

Abstract In this paper, an automatic adaptive method for identification and separation of the useful information content, from the background noise of time–frequency distributions (TFD) of multicomponent nonstationary signals, is presented. The method is based on an initial segmentation of the TFD information content by the K-means clustering algorithm, that partitions the initial data set in order to obtain K classes containing elements with similar amplitudes. It is shown that the local Renyi entropy (LRE) can accurately distinguish classes containing noise from classes with the useful information content, as a consequence of their basic structural differences in the time–frequency plane. Simulations are run to compare the performance of the proposed adaptive algorithm for blind separation of useful information from background noise (i.e. blind amplitude threshold) and non-adaptive (hard) amplitude TFD threshold procedures. Simulation results indicate that the proposed method performs better or closely to the best of five blindly chosen hard thresholds. The limitation of efficient hard-thresholding is the need of previous knowledge of the signals structure and SNR or visual evaluation.

Rényi entropy based failure detection of medical electrodes

Medical electrodes used for measuring low amplitude signals, such as EEG electrodes, have to be robust and guarantee a high level of reliability. Corkscrew electrodes, considered in this paper, can become faulty due to cold solder that can appear immediately after the manufacturing process or due to mechanical stress after a few months of use. This problem is hard to detect and is usually manifested as noisy output signal. Commonly used method for monitoring the reliability of materials or circuit interconnects is the resistance measurement. Although very easy to implement, this method does not provide a reliable failure detection. Motivated by these facts, in this paper we propose a computer model based on resistance measurements, for predicting and detecting failure in EEG electrodes supported by laboratory measurements. Level and type of noise is obtained from the comparison of resistance fluctuations of the electrodes tip recorded under stress, and simulated signals. Time-frequency analysis has been applied to real and simulated reference and faulty electrode signals and results compared in order to establish a failure detection measure. Since the energy spectrum of the signal is shown to be an unreliable indicator of the failure appearance, the Rényi entropy is used to determine the difference between reference and faulty electrodes. This measure is applied to measured and simulated spectrograms, denoised using the K-means algorithm. It is shown that the difference between global entropies of the reference and faulty electrode spectrograms is significant when K-means based denoising is applied, thus providing a method for reliable failure detection.