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Statistical estimation applied to electrocardiographic imaging

Cardiovascular diseases are among the leading causes of death all over the world. Researchers have been extensively working on methods for early diagnosis and treatment of these diseases, with the goal of decreasing these death tolls. In Electrocardiographic Imaging (ECGI), the electrical activity of the heart is estimated from electrocardiographic measurements obtained from the body surface, using densely distributed electrodes, and a mathematical model of the body. This technique has advantages over classical electrocardiography (ECG) since it provides detailed information about the cardiac electrical activity without invasively recording measurements from the heart. From a mathematical point of view, this estimation problem is called the "inverse problem of ECG." However, this problem is ill-posed, and a priori information should be used to regularize the solutions. This paper presents an overview of several regularization methods with emphasis on statistical estimation methods such as Bayesian Estimation and Kalman Filtering. These techniques are advantageous over traditional methods due to their flexibility in incorporating the spatial and temporal information of the heart potentials for solving the inverse ECG problem, and yielding confidence intervals that help assess the accuracy of the solutions.