Atrial fibrillation (AF) is the most common cardiac arrhythmia encountered in clinical practice and remains a major challenge in cardiology. The noninvasive analysis of AF usually requires the estimation of the atrial activity (AA) signal in surface electrocardiogram (ECG) recordings. The present contribution puts forward a tensor decomposition approach for noninvasive AA extraction in AF ECG recordings. As opposed to the matrix approach, tensor decompositions are generally unique under mild conditions and have the potential to perform source separation in scenarios with a limited number of electrodes. An experimental study on a synthethic signal model and a real AF ECG recording evaluates the performance of the so-called block term tensor decomposition approach as compared to matrix techniques such as principal component analysis and independent component analysis.