Remotely sensed data are essential for understanding environmental dynamics, for their forecasting, and for early detection of disasters. Microwave remote sensing sensors complement the information provided by observations in the optical spectrum, with the advantage of being less sensitive to adverse atmospherical conditions and of carrying their own source of illumination. On the one hand, new generations and constellations of Synthetic Aperture Radar (SAR) sensors provide images with high spatial and temporal resolution and excellent coverage. On the other hand, SAR images suffer from speckle noise and need specific models and information extraction techniques. In this sense, the ${\mathcal{G}}^0$ family of distributions is a suitable model for SAR intensity data because it describes well areas with different degrees of texture. Information theory has gained a place in signal and image processing for parameter estimation and feature extraction. Entropy stands out as one of the most expressive features in this realm. We evaluate the performance of several parametric and non-parametric Shannon entropy estimators as input for supervised and unsupervised classification algorithms. We also propose a methodology for fine-tuning non-parametric entropy estimators. Finally, we apply these techniques to actual data.

The aim of this study is to formulate a new methodology based upon informational tools to detect patients with cardiac arrhythmias. As it is known, sudden death is the consequence of a final arrhythmia, and here lies the relevance of the efforts aimed at the early detection of arrhythmias. The information content in the time series from an electrocardiogram (ECG) signal is conveyed in the form of a probability distribution function, to compute the permutation entropy proposed by Bandt and Pompe. This selection was made seeking its remarkable conceptual simplicity, computational speed, and robustness to noise. In this work, two well-known databases were used, one containing normal sinus rhythms and another one containing arrhythmias, both from the MIT medical databank. For different values of embedding time delay $\tau$ , normalized permutation entropy and statistical complexity measure are computed to finally represent them on the horizontal and vertical axes, respectively, which define the causal plane $H\times C$ . To improve the results obtained in previous works, a feature set composed by these two magnitudes is built to train the following supervised machine learning algorithms: random forest (RF), support vector machine (SVM), and $k$ nearest neighbors (kNN). To evaluate the performance of each classification technique, a 10-fold cross-validation scheme repeated 10 times was implemented. Finally, to select the best model, three quality parameters were computed, namely, accuracy, the area under the receiver operative characteristic (ROC) curve (AUC), and the F1-score. The results obtained show that the best classification model to detect the ECG coming from arrhythmic patients is RF. The values of the quality parameters were at the same levels reported in the available literature using a larger data set, thus supporting this proposal that uses a very small-sized feature space to train the model later used to classify. Summarizing, the attained results show the possibility to discriminate both groups of patients, with normal sinus rhythm or arrhythmic ECG, showing a promising efficiency in the definition of new markers for the detection of cardiovascular pathologies.

We obtain expressions for the asymptotic distributions of the Rényi and Tsallis of order q entropies and Fisher information when computed on the maximum likelihood estimator of probabilities from multinomial random samples. We verify that these asymptotic models, two of which (Tsallis and Fisher) are normal, describe well a variety of simulated data. In addition, we obtain test statistics for comparing (possibly different types of) entropies from two samples without requiring the same number of categories. Finally, we apply these tests to social survey data and verify that the results are consistent but more general than those obtained with a ${\chi }^2$ test.

In the present work a method for the detection of the cardiac pathology known as atrial fibrillation is proposed by calculating different information, statistics and other nonlinear measures over ECG signals. The original database contains records corresponding to patients who are diagnosed with this disease as well as healthy subjects. To formulate the dataset the Rényi permutation entropy, Fisher information measure, statistical complexity, Lyapunov exponent and fractal dimension were calculated, in order to determine how to combine this features to optimize the identification of the signals coming from ECG with the above mentioned cardiac pathology. With the aim to improve the results obtained in previous studies, a classification method based upon decision trees algorithms is implemented. Later a Montecarlo simulation of one thousand trials is performed with a seventy percent randomly selected from the dataset dedicated to train the classifier and the remaining thirty percent reserved to test in every trial. The quality of the classification is assessed through the computation of the area under the receiver operation characteristic curve (ROC), the F1-score and other classical performance metrics, such as the balanced accuracy, sensitivity, specificity, positive and negative predicted values. The results show that the incorporation of all these features to the dataset when are employed to train the classifier in the training task produces the best classification, in such a way that the largest quality parameter is achieved.