We introduce an exponential-based consistent approach to image scaling. Our model stems from Sobolev reproducing kernels, motivated by their role in continuous-domain stochastic autoregressive processes. The proposed approach imposes consistency and applies the minimum-norm criterion for determining the scaled image. We show by experimental results that the proposed approach provides images that are visually better than other consistent solutions. We also observe that the proposed exponential kernels yield better interpolation results than polynomial B-spline models. Our conclusion is that the proposed Sobolev-based image modeling could be instrumental and a preferred alternative in major image processing tasks.