Kernel-based methods rely on a nonlinear transformation of available data. The so-called pre-image problem is the estimation of the inverse transformation. Solving this problem is of great interest in many fields, including pattern recognition and denoising problems. In this paper, we propose to overcome the pre-image problem by defining a novel model. This approach is illustrated on the nonnegative matrix factorization problem. The relevance of the proposed approach is illustrated on the unmixing problem in hyperspectral imagery.