Wavelet-promoted sparsity for non-invasive reconstruction of electrical activity of the heart

Cluitmans, Matthijs; Karel, Joël; Bonizzi, Pietro; Volders, Paul G.A.; Westra, Ronald L.; Peeters, Ronald

doi:10.1007/s11517-018-1831-2

Cited by 11 publications

(13 citation statements)

References 34 publications

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“…However, the most common approach to model temporal behavior is to use deterministic restrictions of the solution space. This is done via projection of the data and solutions onto a feasible set [4,21–25] or through explicit constraints in the optimization [26]. These temporal restrictions correspond to setting probability zero to the unfeasible space and creating truncated probability distributions.…”

Section: Modeling Approachesmentioning

confidence: 99%

A Common-Ground Review of the Potential for Machine Learning Approaches in Electrocardiographic Imaging Based on Probabilistic Graphical Models

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Wang

Brooks

2018

2018 Computing in Cardiology Conference (CinC)

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Machine learning (ML) methods have seen an explosion in their development and application. They are increasingly being used in many different fields with considerable success. However, although the interest is growing, their impact in the field of electrocardiographic imaging (ECGI) remains limited. One of the main reasons that ML has yet to become more prevalent in ECGI is that the published literature is scattered and there is no common ground description and comparison of these methods in an ML framework. Here we address this limitation with a review of ECGI methods from the perspective of ML. We will use probabilistic modeling to provide a common ground framework to compare different methods and well known approaches. Finally, we will discuss which approaches have been used to do inference on these models and which alternatives could be utilized as the methods in ML become more mature.

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Section: Modeling Approachesmentioning

confidence: 99%

A Common-Ground Review of the Potential for Machine Learning Approaches in Electrocardiographic Imaging Based on Probabilistic Graphical Models

Coll‐Font

Wang

Brooks

2018

2018 Computing in Cardiology Conference (CinC)

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“…To formulate the ECGI inverse problem, we start from the forward model of electrocardiology, which assumes an instantaneous and linear relationship between the heart surface potentials

and the corresponding body surface potentials

, at any given moment in time t [ 3 ]:

…”

Section: Introductionmentioning

confidence: 99%

Influence of the Tikhonov Regularization Parameter on the Accuracy of the Inverse Problem in Electrocardiography

Wang

Karel

Bonizzi

et al. 2023

Sensors

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The electrocardiogram (ECG) is the standard method in clinical practice to non-invasively analyze the electrical activity of the heart, from electrodes placed on the body’s surface. The ECG can provide a cardiologist with relevant information to assess the condition of the heart and the possible presence of cardiac pathology. Nonetheless, the global view of the heart’s electrical activity given by the ECG cannot provide fully detailed and localized information about abnormal electrical propagation patterns and corresponding substrates on the surface of the heart. Electrocardiographic imaging, also known as the inverse problem in electrocardiography, tries to overcome these limitations by non-invasively reconstructing the heart surface potentials, starting from the corresponding body surface potentials, and the geometry of the torso and the heart. This problem is ill-posed, and regularization techniques are needed to achieve a stable and accurate solution. The standard approach is to use zero-order Tikhonov regularization and the L-curve approach to choose the optimal value for the regularization parameter. However, different methods have been proposed for computing the optimal value of the regularization parameter. Moreover, regardless of the estimation method used, this may still lead to over-regularization or under-regularization. In order to gain a better understanding of the effects of the choice of regularization parameter value, in this study, we first focused on the regularization parameter itself, and investigated its influence on the accuracy of the reconstruction of heart surface potentials, by assessing the reconstruction accuracy with high-precision simultaneous heart and torso recordings from four dogs. For this, we analyzed a sufficiently large range of parameter values. Secondly, we evaluated the performance of five different methods for the estimation of the regularization parameter, also in view of the results of the first analysis. Thirdly, we investigated the effect of using a fixed value of the regularization parameter across all reconstructed beats. Accuracy was measured in terms of the quality of reconstruction of the heart surface potentials and estimation of the activation and recovery times, when compared with ground truth recordings from the experimental dog data. Results show that values of the regularization parameter in the range (0.01–0.03) provide the best accuracy, and that the three best-performing estimation methods (L-Curve, Zero-Crossing, and CRESO) give values in this range. Moreover, a fixed value of the regularization parameter could achieve very similar performance to the beat-specific parameter values calculated by the different estimation methods. These findings are relevant as they suggest that regularization parameter estimation methods may provide the accurate reconstruction of heart surface potentials only for specific ranges of regularization parameter values, and that using a fixed value of the regularization parameter may represent a valid alternative, especially when computational efficiency or consistency across time is required.

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“…Both norms and mixtures of them are broadly used in convex optimisation, for example, elastic-net [18], group lasso [19] and sparse group lasso [20]. Except for [21], these methods have rarely been applied to ECGI.…”

Section: Introductionmentioning

confidence: 99%

A fast algorithm for spatiotemporal signals recovery using arbitrary dictionaries with application to electrocardiographic imaging

Caracciolo¹,

Caiafa²,

Pería³

et al. 2022

Biomed. Phys. Eng. Express

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This paper presents a method to solve a linear regression problem subject to group lasso and ridge penalisation when the model has a Kronecker structure. This model was developed to solve the inverse problem of electrocardiography using sparse signal representation over a redundant dictionary or frame. The optimisation algorithm was performed using the block coordinate descent and proximal gradient descent methods. The explicit computation of the underlying Kronecker structure in the regression was avoided, reducing space and temporal complexity. We developed an algorithm that supports the use of arbitrary dictionaries to obtain solutions and allows a flexible group distribution.

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Wavelet-promoted sparsity for non-invasive reconstruction of electrical activity of the heart

Cited by 11 publications

References 34 publications

A Common-Ground Review of the Potential for Machine Learning Approaches in Electrocardiographic Imaging Based on Probabilistic Graphical Models

A Common-Ground Review of the Potential for Machine Learning Approaches in Electrocardiographic Imaging Based on Probabilistic Graphical Models

Influence of the Tikhonov Regularization Parameter on the Accuracy of the Inverse Problem in Electrocardiography

A fast algorithm for spatiotemporal signals recovery using arbitrary dictionaries with application to electrocardiographic imaging

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