The identification and separation of contributions associated with different sources or processes is a general problem in signal and image processing. Here, we focus on the decomposition of multiple linear relationships and introduce a non-negative formulation. The proposed models can be viewed as generalizations of latent class regression models and account for possibly varying magnitudes of the linear transfer functions. Along with these models, we present model calibration algorithms. We first demonstrate their performance on simulated data. We also report an application to the analysis of upper ocean dynamics from remote sensing data (namely, satellite-derived Sea Surface Height (SSH) and Sea Surface temperature (SST) image series). This application further stresses the proposed formulation's relevance compared to state-of-the-art regression models.