L_0 Norm Based Sparse Regularization for Non-invasive Infarct Detection Using ECG Signal

Abstract

Non-invasive reconstruction of infarcts inside the heart from ECG signals is an important and difficult problem due to the need to solve a severely ill-posed inverse problem. To overcome this ill-posedness, various sparse regularization techniques have been proposed and evaluated for detecting epicardial and transmural infarcts. However, the performance of sparse methods in detecting non-transmural, especially endocardial infarcts, is not fully explored. In this paper, we first show that the detection of non-transmural endocardial infarcts poses severe difficulty to the prevalent algorithms. Subsequently, we propose a novel sparse regularization technique based on a variational approximation of L0 norm. In a set of simulation experiments considering transmural and endocardial infarcts, we compare the presented method with total variation minimization and L1 norm based regularization techniques. Experiment results demonstrated that the presented method outperformed prevalent algorithms by a large margin, particularly when infarction is entirely on the endocardium. IntroductionInverse electrocardiography (ECG) refers to the noninvasive reconstruction of electrical activity inside the heart from ECG signals. It has been shown that inverse ECG can be used to detect or quantify myocardial infarcts [1,2]. The main challenge in inverse ECG is the need to solve a severely ill-posed problem. To address this problem, various regularization techniques have been used in the literature. For the purpose of infarct detection, sparse regularization in the spatial gradient domain of the action potential has been shown to be effective [2]. It is based on the idea that between depolarization and repolarization (i.e. ST segment of ECG), the gradient of action potential is expected to be close to zero everywhere except along the border of an infarct in between viable active tissue and necrotic inactive tissue. L1 norm penalty was used to enforce sparsity to the gradient of action potential and epicardial potential was obtained as inverse solution in [3,4]. In [1, 2], total-variation minimization was used to enforce sparsity and the inverse solution obtained was applied to quantify transmural infarcts at different locations of the heart. However, the performance of sparse regularization based inverse ECG methods in the presence of nontransmural infarcts, especially endocardial infarcts, remains largely unexplored.In this paper, we first examine the performance of prevalent sparse inverse ECG methods in detecting transmural versus endocardial infarcts and show that they perform poorly in the endocardial case. We then present a novel L0-norm based sparse regularization method and compare its performance against prevalent algorithms regarding detection of infarcts in both transmural and endocardial cases. L0-norm based sparse regularization is realized in a Bayesian setting where a sparse prior based on a generalized normal distribution is used. To obtain a closed form for the posterior distribution, we derive a variational lowe...

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

“…Total Variation uses this same distribution —with a covariance matrix equal to the inverse gradient operator— to allow for a small number of large gradients on the heart potentials [11–15]. Other groups have extended this idea to induce sparsity with generalized Gaussian distributions —equivalent to the Lp norm in classical optimization [16,17].…”