Brain signals are nonlinear and nonstationary time series, which provide information about spatiotemporal patterns of electrical activity in the brain. CHMMs are suitable tools for modeling multi-channel time-series dependent on both time and space, but state-space parameters grow exponentially with the number of channels. To cope with this limitation, we consider the influence model as the interaction of hidden Markov chains called Latent Structure Influence Models (LSIMs). LSIMs are capable of detecting nonlinearity and nonstationarity, making them well suited for multi-channel brain signals. We apply LSIMs to capture the spatial and temporal dynamics in multi-channel EEG/ECoG signals. The current manuscript extends the scope of the re-estimation algorithm from HMMs to LSIMs. We prove that the re-estimation algorithm of LSIMs will converge to stationary points corresponding to Kullback-Leibler divergence. We prove convergence by developing a new auxiliary function using the influence model and a mixture of strictly log-concave or elliptically symmetric densities. The theories that support this proof are derived from previous studies by Baum, Liporace, Dempster, and Juang. We then develop a closed-form expression for re-estimation formulas using tractable marginal forward-backward parameters defined in our previous study. Simulated datasets and EEG/ECoG recordings confirm the practical convergence of the derived re-estimation formulas. We also study the use of LSIMs for modeling and classification on simulated and real EEG/ECoG datasets. Based on AIC and BIC, LSIMs perform better than HMMs and CHMMs in modeling embedded Lorenz systems and ECoG recordings. LSIMs are more reliable and better classifiers than HMMs, SVMs and CHMMs in 2-class simulated CHMMs. EEG biometric verification results indicate that the LSIM-based method improves the area under curve (AUC) values by about 6.8% and decreases the standard deviation of AUC values from 5.4% to 3.3% compared to the existing HMM-based method for all conditions on the BED dataset.

Sleep stage dynamics can be adequately represented using Markov chain models to improve classification accuracy. The present study proposes a new post-processing method based on channel fusion using Latent Structure Influence Models (LSIMs). The proposed method develops and examines two channel-fusion algorithms: the standard LSIM fusion and the integrated LSIM fusion, in which the latter is more efficient and performs better. The proposed LSIM-based method simultaneously incorporates the nonlinear interactions between channels and the sleep stage dynamics. In the first step, existing sleep staging systems process every data channel independently and produce stage score sequences for each channel. These single-channel scores are then projected into belief space using the marginal one-slice parameter of all channels by LSIM fusion algorithms. The logarithms of marginal one-slice parameters are concatenated to obtain log-scale belief state space (LBSS) features in the standard LSIM fusion. In the integrated LSIM fusion, integrated LBSS (ILBSS) features are formed by combining the LBSS features of several LSIMs. By utilizing four recently developed sleep staging systems, the proposed method is applied to the publicly available SleepEDF-20 database that contains five AASM sleep stages (N1, N2, N3, REM, and W). Compared to single-channel (Fpz-Cz, Pz-Oz, and EOG) results, integrated LSIM fusion results have a statistically significant improvement of 1.5% in 2-channel fusion (Fpz-Cz and Pz-Oz) and 2.5% in 3-channel fusion (Fpz-Cz, Pz-Oz, and EOG). With an overall accuracy of 87.3% for 3-channel post-processing, the integrated LSIM fusion system offers one of the highest overall accuracy rates among existing studies.

Many studies in the field of sleep have focused on connectivity and coherence. Still, the nonstationary nature of electroencephalography (EEG) makes many of the previous methods unsuitable for automatic sleep detection. Time-frequency representations and high-order spectra are applied to nonstationary signal analysis and nonlinearity investigation, respectively. Therefore, combining wavelet and bispectrum, wavelet-based bi-phase (Wbiph) was proposed and used as a novel feature for sleep-wake classification. The results of the statistical analysis with emphasis on the importance of the gamma rhythm in sleep detection show that the Wbiph is more potent than coherence in the wake-sleep classification. The Wbiph has not been used in sleep studies before. However, the results and inherent advantages, such as the use of wavelet and bispectrum in its definition, suggest it as an excellent alternative to coherence. In the next part of this paper, a convolutional neural network (CNN) classifier was applied for the sleep-wake classification by Wbiph. The classification accuracy was 97.17% in nonLOSO and 95.48% in LOSO cross-validation, which is the best among previous studies on sleep-wake classification.

When our sources are graph signals, a more efficient algorithm for Blind Source Separation (BSS) can be provided by using structural graph information along with statistical independence and/or non-Gaussianity. To the best of our knowledge, the GraphJADE and GraDe algorithms are the only BSS methods addressing this issue in the case of known underlying graphs. However, in many real-world applications, these graphs are not necessarily a priori known. In this paper, we propose a method called GraphJADE-GL (GraphJADE with Graph Learning) that jointly separates the graph signal sources and learns the graphs related to them accurately, in an alternating style.

The joint analysis of multiple data sets to extract their interdependency information has wide applications in biomedical and health informatics. In this paper, we propose an algorithm to extract joint and individual sources of multisubject data sets by using a deflation-based procedure, which is referred to as joint/individual thin independent component analysis (JI-ThICA). The proposed algorithm is based on two cost functions utilizing higher order cumulants to extract joint and individual sources. Joint sources are discriminated by fusing signals of all subjects, whereas individual sources are extracted separately for each subject. Furthermore, JI-ThICA algorithm estimates the number of joint sources by applying a simple and efficient strategy to determine the type of sources (joint or individual). The algorithm also categorizes similar sources automatically across data sets through an optimization process. The proposed algorithm is evaluated by analyzing simulated functional magnetic resonance imaging (fMRI) multisubject data sets, and its performance is compared with existing alternatives. We investigate clean and noisy fMRI signals and consider two source models. Our results reveal that the proposed algorithm outperforms its alternatives in terms of the mean joint signal to interference ratio. We also apply the proposed algorithm on a public-available real fMRI multisubject data set, which was acquired during naturalistic auditory experience. The extracted results are in accordance with the previous studies on naturalistic audio listening and results of a recent study investigated this data set, which demonstrates that the JI-ThICA algorithm can be applied to extract reliable and meaningful information from multisubject fMRI data.

In this paper, we present a novel framework for the coupled hidden Markov model (CHMM), based on the forward and backward recursions and conditional probabilities, given a multidimensional observation. In the proposed framework, the interdependencies of states networks are modeled with Markovian-like transition laws that influence the evolution of hidden states in all channels. Moreover, an offline inference approach by maximum likelihood estimation is proposed for the learning procedure of model parameters. To evaluate its performance, we first apply the CHMM model to classify and detect disturbances using synthetic data generated by the FitzHugh-Nagumo model. The average sensitivity and specificity of the classification are above 93.98% and 95.38% and those of the detection reach 94.49% and 99.34%, respectively. The method is also evaluated using a clinical database composed of annotated physiological signal recordings of neonates suffering from apnea-bradycardia. Different combinations of beat-to-beat features extracted from electrocardiographic signals constitute the multidimensional observations for which the proposed CHMM model is applied, to detect each apnea bradycardia episode. The proposed approach is finally compared to other previously proposed HMM-based detection methods. Our CHMM provides the best performance on this clinical database, presenting an average sensitivity of 95.74% and specificity of 91.88% while it reduces the detection delay by -0.59 s.

In this paper, we propose a Jacobi-like Deflationary ICA algorithm, named JDICA. More particularly, while a projection-based deflation scheme inspired by Delfosse and Loubaton's ICA technique ( DelL\BBR) is used, a Jacobi-like optimization strategy is proposed in order to maximize a fourth order cumulant-based contrast built from whitened observations. Experimental results obtained from simulated epileptic EEG data mixed with a real muscular activity and from the comparison in terms of performance and numerical complexity with the FastICA, RobustICA and DelL\BBRalgorithms, show that the proposed algorithm offers the best trade-off between performance and numerical complexity when a low number ( ~ 12) of electrodes is available.

Removing muscle activity from ictal ElectroEncephaloGram (EEG) data is an essential preprocessing step in diagnosis and study of epileptic disorders. Indeed, at the very beginning of seizures, ictal EEG has a low amplitude and its morphology in the time domain is quite similar to muscular activity. Contrary to the time domain, ictal signals have specific characteristics in the time-frequency domain. In this paper, we use the time-frequency signature of ictal discharges as a priori information on the sources of interest. To extract the time-frequency signature of ictal sources, we use the Canonical Correlation Analysis (CCA) method. Then, we propose two time-frequency based semi-blind source separation approaches, namely the Time-Frequency-Generalized EigenValue Decomposition (TF-GEVD) and the Time-Frequency-Denoising Source Separation (TF-DSS), for the denoising of ictal signals based on these time-frequency signatures. The performance of the proposed methods is compared with that of CCA and Independent Component Analysis (ICA) approaches for the denoising of simulated ictal EEGs and of real ictal data. The results show the superiority of the proposed methods in comparison with CCA and ICA.

The automatic detection of Electrocardiogram (ECG) waves is important to cardiac disease diagnosis. A good performance of an automatic ECG analyzing system depends heavily upon the accurate and reliable detection of QRS complex, as well as P and T waves. In this paper, we propose an efficient method for extraction of characteristic points of ECG signal. The method is based on a nonlinear dynamic model, previously introduced for generation of synthetic ECG signals. For estimating the parameters of model, we use an Extendend Kalman Filter (EKF). By introducing a simple AR model for each of the dynamic parameters of Gaussian functions in model and considering separate states for ECG waves, the new EKF structure was constructed. Quantitative and qualitative evaluations of the proposed method have been done on Physionet QT database (QTDB). This method is also compared with another EKF approach (EKF17). Results show that the proposed method can detect fiducial points of ECG precisely and mean and standard deviation of estimation error do not exceed two samples (8 msec).

In this paper, we propose a new semi-algebraic algorithm to compute the Canonical Polyadic (CP) decomposition of complex-valued multi-way arrays. The proposed algorithm is based on the Simultaneous Schur Decomposition (SSD) of particular matrices derived from the array to process. This CP algorithm solves some convergence problems of classical iterative techniques and its identifiability assumptions are less restrictive than those of other semi-algebraic methods. We also propose a new Jacobi-like algorithm to calculate the SSD of several complex-valued matrices. Finally the usefulness of the proposed method is illustrated in the context of fluorescence spectroscopy and epileptic source localization.

We have recently proposed a correlated model to provide a Gaussian mixture representation of the cardiovascular signals, with promising results in identifying rhythm disturbances. The approach provides a transformation of the data into a set of integrable Gaussians distributed over time. Looking into the model from a new joint modeling perspective, it is capable of assembling a filtered estimation, and can be used to derive temporal information of the waveforms. In this paper, we present a step-by-step derivation of the joint model putting correlation assumptions together to conclude a minimal joint description for a pair of ECG-ABP signals. We then probe novel applications of this model, including Kalman filter based denoising and fiducial point detection. In particular, we use the joint model for denoising and employ the denoised signals for pulse transit time (PTT) estimation. We analyzed more than 70 h of data from 76 patients from the MIMIC database to illustrate the accuracy of the algorithm. We have found that this method can be effectively used for robust joint ECG-ABP noise suppression, with mean signal-to-noise ratio (SNR) improvement up to 23.2 (12.0) dB and weighted diagnostic distortion measures as low as 2.1 (3.3)% for artificial (real) noises, respectively. In addition, we have estimated the error distributions for QT interval, systolic and diastolic blood pressure before and after filtering to demonstrate the maximal preservation of morphological features (ΔQT: mean ± std = 2.2 ± 6.1 ms; ΔSBP: mean ± std = 2.3 ± 1.9 mmHg; ΔDBP: mean ± std = 1.9 ± 1.4 mmHg). Finally, we have been able to present a systematic approach for robust PTT estimation (r = 0.98, p <; 0.001, mean ± std of error = -0.26 ± 2.93 ms). These findings may have important implications for reliable monitoring and estimation of clinically important features in clinical settings. In conclusion, the proposed framework opens the door to the possibility of deploying a hybrid system that integrates these algorithmic approaches for index estimation and filtering scenarios with high output SNRs and low distortion.

Recently, a new set of dyadic wavelet frames based on oversampled filter banks is introduced that provides a higher sampling in both time and frequency, compared to the usual dyadic wavelets. This transform (called HDDWT) is not shift-invariant; a feature which is desirable particularly for signal denoising. In this paper we propose a new transform, referred to as nonsubsampled HDDWT (NS-HDDWT), which is the shift-invariant version of HDDWT. The NS-HDDWT filter bank is built upon iterated nonsubsampled filter banks which are derived from the HDDWT filter bank in a way that is similar to the a trous algorithm. We employ HDDWT and NS-HDDWT for decomposition of images by performing the separable filtering. The performance of both HDDWT and NS-HDDWT is assessed in image denoising. Experimental results show that the performance of NS-HDDWT is superior to that of HDDWT, and in some cases NS-HDDWT outperforms powerful wavelet-based image denoising methods.

In this paper, we study the nonsubsampled higher-density discrete wavelet transform (NS-HDDWT) and its application in image enhancement. In contrast to the HDDWT, the NS-HDDWT transform is shift-invariant, which is a desirable feature in many applications. We address the filter design problem and provide a solution based on the spectral factorization. Our proposed solution enables constructing new filter sets, in addition to the ones originally offered for the HDDWT filter bank. We use the NS-HDDWT transform for image enhancement by applying a locally adaptive nonlinear operator. Experimental results show that the NS-HDDWT transform yields better enhancement results compared to the undecimated DWT (UDWT) transform.

Estimating the depth of anesthesia (DOA) is still a challenging area in anesthesia research. The objective of this study was to design a fuzzy rule based system which integrates electroencephalogram (EEG) features to quantitatively estimate the DOA. The proposed method is based on the analysis of single-channel EEG using frequency and time domain features as well as Shannon entropy measure. The fuzzy classifier is trained with features obtained from four subsets of data comprising well-defined anesthesia states: awake, moderate, general anesthesia, and isoelectric. The classifier extracts efficient fuzzy if-then rules and the DOA index is derived between 100 (full awake) to 0 (isoelectric) using fuzzy inference engine. To validate the proposed method, a clinical study has conducted on 22 patients to construct 4 subsets of reference states and also to compare the results with CSM monitor (Danmeter, Denmark), which has revealed satisfactory correlation with clinical assessments

Feature vector extraction, based on local image texture, is a primitive algorithm for many other applications, like segmentation, clustering and identification. If these feature vectors are a good match to the human visual system (HVS), we can expect to get the appropriate results by using them. Gabor filters have been used for this purpose successfully. In this paper we introduce a novel refinement, with the use of matching pursuits (MP) to improve the Gabor based texture feature extractor. With this improvement, we show that the separability of different textures increases. Another consideration in this work is computation complexity. Therefore, we limit the basis function set to reduce MP computation time.

The ARMA filtered fractionally differenced Gaussian noise (FdGn) model and a new AR filtered FdGn added up model are applied to a speech signal and performance of their parameters on speech unvoiced/voiced/mixed/silence classification is evaluated against the zero crossing rate (ZCR) feature. For parameter estimation of AR filtered FdGn model two methods were applied: the iterative maximum likelihood (ML) method of Tewfik (1993) and a new computationally efficient linear minimum square error (LMSE) algorithm. Also for parameter estimation of the new added up model two approaches were implemented: an expectation-maximization (EM) based approach and an iterative MSE approach. The described models and methods were applied to a speech signal and also its real cepstrum. The performance of the described models on V/U/M/S speech classification was obtained based on the J/sub 1/ parameter in this order: added up model on real cepstrum of speech, filtered FdGn model on real cepstrum of speech (LMSE method), filtered FdGn model on speech (LMSE method), ZCR, and filtered FdGn model on speech (Tewfik method).