The main purpose of in this chapter is to describe a robust approach for the simultaneous fusion and denoising of non-smooth multispectral images defined on grids with different resolution using for that a special extremal problem with nonstandard growth of the energy functional. In fact, we use the \(L^1\) -norm of the noise in the minimization function and a special form of anisotropic diffusion tensor for the regularization term. Following this approach, we increase the noise robustness of the proposed model albeit it makes such variational problem completely non-smooth, non-convex, and, hence, significantly more difficult from a minimization point of view. The principle characteristic feature of the proposed model is that we consider the energy functional with nonstandard growth for each spectral channel separately. The second point that should be emphasized is the fact that we do not predefine the variable exponents a priori using for that the original noisy images, but instead we associate these characteristics with each feasible solution.