Due to the cost-efficiency of the ECG, the interest in noninvasive techniques to assess atrial fibrillation (AF) electrophysiological complexity is increasingly high. Still, ECG-based methods to measure AF complexity are limited in clinical practice and need estimation of the atrial activity (AA) signal from sufficiently long ECG recordings. Tensor-based techniques have been recently proven to be efficient and powerful AA extraction tools. The present work proposes a method called constrained alternating group lasso (CAGL), a tensor-based algorithm, as a noninvasive tool to quantify AF complexity. Experiments with a database of 30 ECG recordings from 10 patients suffering from persistent AF show that CAGL is able to both: extract the AA and quantify its complexity from very short ECG recordings (1.10 +/- 0.19 s). All the patients had undergone step-wise catheter ablation (CA) that ended in AF termination. CAGL is applied to the ECG recording after each step of the CA procedure, measuring the rank of the tensor that provides the AA signal. It is observed that such rank decreases at each step of the CA procedure, showing a less complex AA signal as the ablation is performed. In particular, ranks before the CA procedure range from 19-33, whereas after the procedure where AF is terminated, ranks range from 6-16. In addition, all patients that presented an AA rank between 19-23 before CA procedure, remained in sinus rhythm for over a year. The majority of other patients whose AA rank before CA procedure is at least 25, had AF recurrence after a few months. In conclusion, this rank parameter could improve clinical analysis and mainly support a real-time guided CA, improving its accuracy.