ECG processing by rational systems

One of the most effective methods in ECG processing is the so-called transformation technique. The most popular systems that are used frequently include the classical trigonometric Fourier, orthogonal polynomial, and spline systems. In recent applications the wavelet methods turned to be especially effective. Yet we propose another system that is built from basic rational functions. The rational orthogonal systems, i.e. the Malmquist-Takenaka systems, we use are determined by parameters called poles and multiplicities. This way we have infinitely many systems at hand. The main advantage of our approach is its flexibility. The parameters that control the system can be adjusted to the particular problem. It means that in ECG processing we may change them even from heartbeat to heartbeat. We have worked out the proper discretization of the original mathematical model [2-3] and designed optimization processes adapted to these systems [4]. The result is a special variable projection method. The algorithms we constructed turned to be very efficient. They outperform the existing ones in many respects [7]. Problems we considered so far include QRS modeling [4], R peak detection, ECG compression, heartbeat classification [1]. The tests were evaluated on the standard public MIT-BIH Arrhythmia Database available on PhysioNet [5]. We note that our algorithms are fast enough for real time applications, and also for big databases. one may use them as a tool for supporting cardiologists among others as a preprocessing long time records (Holter) or as a built in alert function. So far we have concentrated on ECG processing methods that work well in general circumstances. For instance in case of classification we constructed a mixed feature vector that consists of dynamic and morphological features. The morphological features, which can be divided into patient specific and heartbeat specific components, come from rational transforms. Then we used a so called Support Vector Machine classifier for them. The method can be performed for multiple leads independently or even together, and then we can combine the individual results to obtain an improved final result. Recently, we have been focusing on more specific situations where we take various aspects into consideration. In particular we have been working on a version designed for subject-based classification Moreover we have been refining the classification algorithm in order to reduce the rate of false negative results. In connection with it various evaluation and fusion techniques have been investigated. We note that our method can be efficient for medical signals other than ECG. An example for epileptic seizure detection in EEG signals can be found in [6].