No description available.

Conventional electrocardiography (ECG) is an essential tool for investigating cardiac disorders such as arrhythmias or myocardial infarction. It consists of interpretation of potentials recorded at the body surface that occur due to the electrical activity of the heart. However, electrical signals originated at the heart suffer from attenuation and smoothing within the thorax, therefore ECG signal measured on the body surface lacks some important details. The goal of forward and inverse ECG problems is to recover these lost details by estimating the heart&amp / #8217 / s electrical activity non-invasively from body surface potential measurements. In the forward problem, one calculates the body surface potential distribution (i.e. torso potentials) using an appropriate source model for the equivalent cardiac sources. In the inverse problem of ECG, one estimates cardiac electrical activity based on measured torso potentials and a geometric model of the torso. Due to attenuation and spatial smoothing that occur within the thorax, inverse ECG problem is ill-posed and the forward model matrix is badly conditioned. Thus, small disturbances in the measurements lead to amplified errors in inverse solutions. It is difficult to solve this problem for effective cardiac imaging due to the ill-posed nature and high dimensionality of the problem. Tikhonov regularization, Truncated Singular Value Decomposition (TSVD) and Bayesian MAP estimation are some of the methods proposed in literature to cope with the ill-posedness of the problem. The most common approach in these methods is to ignore temporal relations of epicardial potentials and to solve the inverse problem at every time instant independently (column sequential approach). This is the fastest and the easiest approach / however, it does not include temporal correlations. The goal of this thesis is to include temporal constraints as well as spatial constraints in solving the inverse ECG problem. For this purpose, two methods are used. In the first method, we solved the augmented problem directly. Alternatively, we solve the problem with column sequential approach after applying temporal whitening. The performance of each method is evaluated.

The main goal in inverse and forward problems of electrocardiography (ECG) is to better understand the electrical activity of the heart. In the forward problem of ECG, one obtains the body surface potential (BSP) distribution (i.e., the measurements) when the electrical sources in the heart are assumed to be known. The result is a mathematical model that relates the sources to the measurements. In the inverse problem of ECG, the unknown cardiac electrical sources are estimated from the BSP measurements and the mathematical model of the torso. Inverse problem of ECG is an ill-posed problem, and regularization should be applied in order to obtain a good solution. Tikhonov regularization is a well-known method, which introduces a trade-off between how well the solution fits the measurements and how well the constraints on the solution are satisfied. This trade-off is controlled by a regularization parameter, which can be easily calculated by the L-curve method. It is theoretically possible to include more than one constraint in the cost function / however finding more than one regularization parameter to use with each constraint is a challenging problem. It is the aim of this thesis to use genetic algorithm (GA) optimization method to obtain regularization parameters to solve the inverse ECG problem when multiple constraints are used for regularization. The results are presented when there are two spatial constraints, when there is one spatial, one temporal constraint, and when there are two spatial one temporal constraints / the performances of these three applications are compared to Tikhonov regularization results and to each other. As a conlcusion, it is possible to obtain correct regularization parameters using the GA method, and using more than one constraints yields improvements in the results.