Multi-frame image super-resolution (SR) is an image processing technology applicable to any digital, pixilated camera that is limited, by construction, to a certain number of pixels. The objective of SR is to utilize signal processing to overcome the physical limitation and emulate the 'capabilities' of a camera with a higher-density pixel array. SR is well known to be an ill-posed problem and, consequently, state-of-the-art solutions approach it statistically, typically making use of Bayesian inference. Unfortunately, direct marginalization of the posterior distribution resulting from the Bayesian modeling is not analytically tractable. An approximation method, such as Variational Bayesian Inference (VBI), is a powerful tool that retains the advantages of statistical modeling. However, its derivation is tedious and model specific. In this paper, we propose an alternative approximate inference methodology, based upon the well-established, Gaussian Information Filter, which offers a much simpler mathematical derivation while retaining the statistical advantages of VBI.