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In this paper, we study the connections between generalized mean operators and entropies, where the mean value operators are related to the strictly monotone logical operators of fuzzy theory. Here, we propose a new entropy measure based on the family of generalized Dombi operators. Namely, this measure is obtained by using the Dombi operator as a generator function in the general solution of the bisymmetric functional equation. We show how the proposed entropy can be used in a fuzzy system where the performance is consistent in choosing the best alternative in the Multiple Attribute Decision-Making Problem. This newly defined entropy was also applied to the problem of extracting useful information from time-frequency representations of noisy, nonstationary, and multicomponent signals. The denoising results were compared to Shannon and Rényi entropies. The proposed entropy measure is shown to significantly outperform the competing ones in terms of denoising classification accuracy and the F1-score due to its sensitivity to small changes in the probability distribution. [ABSTRACT FROM AUTHOR]

The brain dynamics in the electroencephalogram (EEG) data are often challenging to interpret, specially when the signal is a combination of desired brain dynamics and noise. Thus, in an EEG signal, anything other than the desired electrical activity, which is produced due to coordinated electrochemical process, can be considered as unwanted or noise. To make brain dynamics more analyzable, it is necessary to remove noise in the temporal location of interest, as well as to denoise data from a specific spatial location. In this paper, we propose a novel method for noisy EEG analysis with accompanying toolbox which includes adaptive, data-driven noise removal technique based on the improved intersection of confidence interval (ICI)-based algorithm. Next, a local entropy-based method for EEG data analysis was designed and included in the toolbox. As shown in the paper, the relative intersection of confidence interval (RICI) procedure retains the dominant dipole activity projected on electrodes, while the local (short-term) Rényi entropy-based analysis of the EEG representation in the time-frequency domain is efficient in detecting the presence of P300 event-related potential (ERP) at specific electrodes. Namely, the P300 are detected as sharp drop of entropy in the temporal domain that enabled accurate calculation of the index of the noise class for the EEG signals. [ABSTRACT FROM AUTHOR]

This paper proposes an automatic method for extraction of useful information content from time-frequency distributions of nonstationary signals heavily corrupted by additive noise. The proposed method, which does not require prior knowledge of the signal, initially performs a one-dimensional clustering of the time-frequency distribution aimed at segmenting it into a fixed number of classes. This procedure points out basic structural differences of noise and signal components (i.e., useful information) in the time-frequency plane. In fact, noise presents a flat spectrum with large time-frequency supports, while signal components are narrow energy ridges. The time-frequency supports are estimated for each of the obtained classes and used as input for an algorithm aimed at discriminating “noise” affine classes, containing mainly non-zero coefficients located outside the components time-frequency supports, from “useful information” affine classes, containing mainly coefficients inside time-frequency supports of the signal components. Simulations show the superiority of the proposed algorithm, mainly in terms of error rate reduction of classified time-frequency coefficients, compared to hard amplitude thresholding methods, as well as to a recently proposed method for information content extraction based on adaptive thresholding, which is also outperformed in terms of computational complexity and execution time (by up to 43 and 28 times, respectively). [ABSTRACT FROM AUTHOR]

The paper presents an analysis and overview of vertex–frequency analysis, an emerging area in graph signal processing. A strong formal link of this area to classical time–frequency analysis is provided. Vertex–frequency localization-based approaches to analyzing signals on the graph emerged as a response to challenges of analysis of big data on irregular domains. Graph signals are either localized in the vertex domain before the spectral analysis is performed or are localized in the spectral domain prior to the inverse graph Fourier transform is applied. The latter approach is the spectral form of the vertex–frequency analysis, and it will be considered in this paper since the spectral domain for signal localization is well ordered and thus simpler for application to the graph signals. The localized graph Fourier transform is defined based on its counterpart, the short-time Fourier transform, in classical signal analysis. We consider various spectral window forms based on which these transforms can tackle the localized signal behavior. Conditions for the signal reconstruction, known as the overlap-and-add (OLA) and weighted overlap-and-add (WOLA) methods, are also considered. Since the graphs can be very large, the realizations of vertex–frequency representations using polynomial form localization have a particular significance. These forms use only very localized vertex domains, and do not require either the graph Fourier transform or the inverse graph Fourier transform, are computationally efficient. These kinds of implementations are then applied to classical time–frequency analysis since their simplicity can be very attractive for the implementation in the case of large time-domain signals. Spectral varying forms of the localization functions are presented as well. These spectral varying forms are related to the wavelet transform. For completeness, the inversion and signal reconstruction are discussed as well. The presented theory is illustrated and demonstrated on numerical examples. [ABSTRACT FROM AUTHOR]

Electroencephalogram (EEG) signals are known to contain signatures of stimuli that induce brain activities. However, detecting these signatures to classify captured EEG waveforms is one of the most challenging tasks of EEG analysis. This paper proposes a novel time–frequency-based method for EEG analysis and characterization implemented in a computer-aided decision-support system that can be used to assist medical experts in interpreting EEG patterns. The computerized method utilizes EEG spectral non-stationarity, which is clearly revealed in the time–frequency distributions (TFDs) of multicomponent signals. The proposed algorithm, which is based on the modification of the Rényi entropy, called local or short-term Rényi entropy (STRE), was upgraded with a blind component separation procedure and instantaneous frequency (IF) estimation. The method was applied to EEGs of both forward and backward movements of the left and right hands, as well as to EEGs of imagined hand movements, which were captured by a 19-channel EEG recording system. The obtained results show that in a given virtual instrument, the proposed methods efficiently distinguish between real and imagined limb movements by considering their signatures in terms of the dominant EEG component's IFs at the specified subset of EEG channels (namely, F3, F4, F7, F8, T3, and T4). Furthermore, computing the number of EEG signal components, their extraction, and IF estimation provide important information that shows potential to enhance existing clinical diagnostic techniques for detecting the intensity, location, and type of brain function abnormalities in patients with neurological motor control disorders. [ABSTRACT FROM AUTHOR]