NON-BLIND SOURCE SEPARATION AND FEATURE EXTRACTION: THEORY, APPROACH AND CASE STUDIES IN CARDIAC SIGNALS

Source separation (SS) and feature extraction (FE) are tools employed in digital signal processing. The former permits to estimate the values of some sources that have been mixed, and the latter extracts features from a set of measurements. SS and FE are widely applied on biomedical signals such as electrocardiogram (ECG), electroencephalogram, arterial blood pressure, etc., because these signals are collected in noisy environments. For instance, ECG recordings show the electrical activity generated by the whole heart at once. Yet, there are cardiac pathologies or arrhythmias related to only the atrial or ventricular chambers and thus, tools capable to separate them become fundamental for the diagnosis, prognosis and prediction of life-threatening events. Therefore, the quality of treatments depends on the reliability of the features extracted from the signals and then, the reduction of possible interferences becomes very relevant in this context. The study and the development of new SS technique play an important role in those application in which the components of a measurement cannot be splitted using classical temporal or frequency analysis. In addition, non-blind SS aims to employ further information and to develop mathematical and statistical model to make the estimates more reliable. Features extraction is fundamental for the classification task. In biomedical signals, features are used to characterize the status of the subjects in either healthy or pathological condition. For example, features to predict the risk of developing cardiac arrhythmias are continuously encouraged by regulatory agencies as the US Food and Drug Administration. The study of reliability and feasibility of features requires an extensive use of tests. These tests are necessary to evaluate some properties, e.g., the capability of the feature to be resilient to noise, variability of the estimate, classification power, etc. The aim of this thesis is to study, develop, validate and test new SS techniques and features applicable to different kind of signals. The new algorithms and features are extensively studied to characterize their properties from a methodological point of view. In addition, simulated and real data are considered as a test bench. Cardiac signals will be the specific field of application. First, a new algorithm for non-blind SS will be presented and discussed. In particular, this new methodology is an extension of a well-known algorithm, i.e., template, matching and subtraction (TMS), normally used to estimate transient sources, i.e., sources that are located only somewhere in the signals, in stationary conditions. TMS estimates the values of the source by averaging a set of measurements in which it is known to be constant over time. However, there are situations in which this assumption does not hold and the results obtained are not “good” estimates. In order to track changes over time, we proposed a method based on a multi-goal optimization problem to modulate the estimate provided by the classic TMS. The multi-goal optimization problem has been defined as a weighted sum of three subgoals measuring: i) difference in the power of the residue and that of the signal when the transient source is not present; ii) difference in the power of the first derivative of the residue and that of the signal when the transient source is not present; and iii) difference between the estimate provided by the classic TMS and its modulated version. A multi-particle swarm optimization algorithm was used to find the solution of a non-linear problem in a very high dimensional space (a vector in R^100). This technique employs a set of particles that moves in the search space with an heuristic rule and it has been shown to be highly robust to local optima. The algorithm was tested on synthetic and real data. First, a synthetic dataset was generated and the mean square error between the real source and the estimated one was determined. Second, a dataset collected from subjects undergoing ablation for the treatment of atrial fibrillation (AF) was employed. These signals contain both atrial and ventricular activity, but only the atrial one can be used by clinicians to perform the ablation. We tried to separate the atrial activity from the ventricular one. Two features, i.e., the amplitude reduction of the ventricular peak (VDR) and the percentage of residues in which their power was outside the 95th percentile of the atrial one (PP), were computed as measure of goodness of the separation. In both tests, the modulated TMS provided better performance than the classic TMS (p < 0.001), suggesting that a power-based modulation could be suitable to keep tracking the morphology of the ventricular activity. Second, three features have been study and tested. These three features can determine: i) the variability of times of occurrence of transient sources (V-index); ii) the organization of the propagation of wavefronts (OD); and iii) the average acceleration (AC) and deceleration capacities (DC) of a system. Briefly, the V-index is particularly suitable to be applied on signals in which: i) multiple measurements are available; ii) transient sources are linearly mixed; iii) the shape of each realization of the transient sources are similar between each other; and iv) the variability of the times of occurrence is relatively small. It is based on two models, a linear equivalent surface model and a statistical model, respectively. When applied on the T-wave of the ECG, it can provide an estimate of the spatial heterogeneity of the ventricular repolarization, measured as the standard deviation of the repolarization times of the myocytes. This index was tested on three scenario: i) before and after administration of sotalol; ii) before and after administration of moxifloxacin; and iii) on subjects affected by Chagas disease. In all the three cases, the V-index was sensitive to the known effects of the drugs on the ventricular repolarization as well as symptoms of the Chagas disease (p < 0.05). The second feature combines morphological, temporal and organization information to build a new index more suitable for the characterization of wave propagation. In several situations, sensors are not sensitive to the direction of the wave propagation because they can measure only scalar quantities: this is typical for electrodes. The use of multiple sensors permits to quantify/estimate the direction of the wave propagation. We proposed a new index, the organization degree (OD), to measure the degree of organization of a series of symbolic words. Each symbolic word is built labelling the electrical activity and the time of arrival of an electrical wave detected by a set of electrodes using a symbol for each signal. A sequence of words is then built for each wave detected and the Shannon entropy was used to determine the organization. OD was tested on a real dataset collected on subjects suffering from atrial fibrillation in four different situations: i) before and after the onset of AF; and ii) before and after the onset of AF after infusion of isoproterenol (ISO). Such drug stimulates the activation of the sympathetic branch of the autonomous nervous system and it is supposed to decrease the organization of the atrial activity (making it more “random”). OD was able to discriminate between all the cases (p < 0.05) and in particular between AF and AF+ISO, in which only the morphology was not. The last feature is related to the evaluation of the acceleration and deceleration capacities of a system. Both quantities have been introduced by Bauer et al. and depend on three free parameters, i.e., L, T and s. This index is built determining a list of anchor points that satisfy a specific rule (acceleration or deceleration rule) depending on the T value. Then, all the portions of signals of length 2L centered on each anchor point are aligned and then averaged. This series is called phase-rectified signal averaging (PRSA). Both capacities are computed subtracting the sum of s samples from the right side of the PRSA from the sum of s samples from the left one (divided by a normalization factor). In this study, we investigated the role of each parameter to better understand their significance when applied on stochastic signals, specifically on inter-time beat series (RR). These tests were performed on simulated data employing different strategies. All the parameters are somehow frequency related. s, more than T, plays a role of frequency band selector in which both AC and DC are maximally sensitive. While T, acting only on the anchor point list, less affects the value of the capacities. Since it acts as a lowpass filter, T equispaced zeros are placed in the frequency domain. Finally, L permits to select the lowest oscillation detectable. AC and DC were tested on an in-vivo model composed by 7 near-term pregnant sheep. The umbilical cord was occluded with three different level of strength. The main goal of this study was to determine whether AC and DC were sensitive to change in the autonomic regulation of the heart rate during lack of oxygen and if they were correlated with biomarkers such as pH, level of lactates and base deficit. Both capacities were maximally correlated with the biomarkers when using s = T within [2 - 5]. The range of s was coherent with the frequency band related to the autonomic regulation of the fetal RR series when a lack of oxygen occurs for a little period of time.