Standard recordings of electrocardiograhic signals are contaminated by a large variety of noises and interferences, which impair their analysis and the further related diagnosis. In this article, we propose a method, based on compressive sensing techniques, to remove the main noise artifacts and to locate the main features of the pulses in the electrocardiogram (ECG). The motivation is to use trend filtering with a varying proximal parameter, in order to sequentially capture the peaks of the ECG, which have different functional regularities. The practical implementation is based on an adaptive version of the alternating direction method of multiplier (ADMM) algorithm. We present results obtained on simulated signals and on real data illustrating the validity of this approach, showing that results in peak localization are very good in both cases and comparable to state of the art approaches.