Context. The space-based gravitational wave observatory LISA will provide a wealth of information to analyze massive black hole binaries with high chirp masses, beyond 105 solar masses. The large number of expected MBHBs (one event a day on average) increases the risk of overlapping between events. As well, the data will be contaminated with non-stationary artifacts, such as glitches and data gaps, which are expected to strongly impact the MBHB analysis, which mandates the development of dedicated detection and retrieval methods on long time intervals.Aims. Building upon a methodological approach we introduced for galactic binaries, in this article we investigate an original non-parametric recovery of MBHB signals from measurements with instrumental noise typical of LISA in order to tackle detection and signal reconstruction tasks on long time intervals.Methods. We investigated different approaches based on sparse signal modeling and machine learning. In this framework, we focused on recovering MBHB waveforms on long time intervals, which is a building block to further tackling more general signal recovery problems, from gap mitigation to unmixing overlapped signals. To that end, we introduced a hybrid method called SCARF (sparse chirp adaptive representation in Fourier), which combines a deep learning modeling of the merger of the MBHB with a specific adaptive time-frequency representation of the inspiral.Results. Numerical experiments have been carried out on simulations of single MBHB events that account for the LISA response and with realistic realizations of noise. We checked the performances of the proposed hybrid method for the fast detection and recovery of the MBHB.