This paper presents a methodology for automatically detecting mysticete calls. This methodology relies on sparse representations of these calls combined with a detection metric that explicitly takes into account the possible presence of interfering transient signals. Sparse representations can capture the possible variability observed for some vocalizations and can automatically be learned from the time series of the digitized acoustic signals, without requiring prior transforms such as spectrograms, wavelets or cepstrums. The proposed framework is general and applicable to any mysticete call lying in a linear subspace described by a dictionary-based representation. The potential of the detector is illustrated on North Pacific blue whale D calls extracted from the DCLDE 2015 low frequency database as well as on ``Madagascar'' pygmy blue whale calls extracted from the OHASISBIO 2015 database. Receiver operating characteristic curves (ROC) are calculated and performance is compared with three other methods used for automatic call detection: the XBAT bank of matched spectrograms, a bank of matched filters derived from a generalized likelihood ratio approach and a kernel-based spectrogram detector. On the test data, the ROC curves show that the proposed detector outperforms these three methods.