A sparse representation-based classification algorithm with rejection option dedicated to baleen whale calls is proposed. Sparse representations express a given signal as a linear combination of base elements called atoms belonging to a dictionary. Such representations can capture the variability observed for some calls that can be learned from given signals in the time domain, without requiring prior transforms such as spectrograms, wavelets or cepstrums. This approach is applicable to all baleen whales’ calls lying in a linear subspace described by a dictionary-based representation. The rejection option accounts for noise or “unknown classes” by not assigning a received signal to a class if it does not belong to the linear subspace spanned by the dictionary atoms. This noise rejection is achieved without feature learning and it is relevant to manage false-alarms. The potential of the method is shown on a passive acoustic monitoring data set collected in the Cape Cod Bay in 2011 that contains low frequency calls produced by North Atlantic Right Whale (Eubalaena glacialis), Humpback Whale (Megaptera novaeangliae), Sei Whale (Balaenoptera borealis). First, the classification results are presented. More than 1000 calls were considered and the method obtained an average recall of 92% for good classification. Then, the rejection option is considered and used to manage the false alarm of the output of a detector. Finally, the proof of concept of a general method to detect and classify baleen whale calls is introduced.