Atrial fibrillation (AF) is a common heart disorder. One of the most prominent hypothesis about its initiation and maintenance considers multiple uncoordinated activation foci inside the atrium. However, the implicit assumption behind all the signal processing techniques used for AF, such as dominant frequency and organization analysis, is the existence of a single regular component in the observed signals. In this paper we take into account the existence of multiple foci, performing a spectral analysis to detect their number and frequencies. In order to obtain a cleaner signal on which the spectral analysis can be performed, we introduce sparsity-aware learning techniques to infer the spike trains corresponding to the activations. The good performance of the proposed algorithm is demonstrated both on synthetic and real data.

Assume that we observe a large number of signals, all of them with identical, although unknown, shape, but with a different random shift. The objective is to estimate the individual time shifts and their distribution. Such an objective appears in several biological applications like neuroscience or ECG signal processing, in which the estimation of the distribution of the elapsed time between repetitive pulses with a possibly low signal-noise ratio, and without a knowledge of the pulse shape is of interest. We suggest an M-estimator leading to a three-stage algorithm: we first split our data set in blocks, then the shift estimation in each block is done by minimizing a cost function based on the periodogram; the estimated shifts are eventually plugged into a standard density estimator.We show that under mild regularity assumptions the density estimate converges weakly to the true shift distribution. The theory is applied both to simulations and to alignment of real ECG signals.The proposed approach outperforms the standard methods for curve alignment and shift density estimation, even in the case of low signal-to-noise ratio, and is robust to numerous perturbations common in ECG signals. Index Termssemiparametric methods, density estimation, shift estimation, ECG data processing, nonlinear inverse problems.

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The problem of blind sparse analysis of electrogram (EGM) signals under atrial fibrillation (AF) conditions is considered in this paper. A mathematical model for the observed signals that takes into account the multiple foci typically appearing inside the heart during AF is firstly introduced. Then, a reconstruction model based on a fixed dictionary is developed and several alternatives for choosing the dictionary are discussed. In order to obtain a sparse solution, which takes into account the biological restrictions of the problem at the same time, the paper proposes using a Least Absolute Shrinkage and Selection Operator (LASSO) regularization followed by a post-processing stage that removes low amplitude coefficients violating the refractory period characteristic of cardiac cells. Finally, spectral analysis is performed on the clean activation sequence obtained from the sparse learning stage in order to estimate the number of latent foci and their frequencies. Simulations on synthetic signals and applications on real data are provided to validate the proposed approach.

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