DFT-based fast superresolution image reconstruction using INLA approximation

Recently, we have successfully exploited and applied the new and powerful non-parametric Integrated Nested Laplace Approximation (INLA) Bayesian inference method to the problem of Superresolution (SR) image reconstruction, generating the INLA SR algorithm. Such approach achieved superior image reconstruction results in comparison to other state-of-the-art methods. In this paper we propose a modification in the mathematical model of the INLA SR, generating the new DFT INLA SR algorithm. It is shown that the new approach reduces the computation cost of the INLA SR algorithm (from O(n⁴) to O(n log(n))), as well as the dimension of the matrices handled (from n² × n² to n × n, the size of the HR image), at the cost of a slight reduction of the HR image quality.