Minimax robust image fusion using an estimation theory approach

Image fusion is studied using a very basic and reasonable mathematical model for the observed images. The model attempts to characterize the statistical aspects of the problem, including the impact of random distortions, like noise. The image fusion problem is posed as an estimation problem where the best fusion algorithm minimizes the mean square error between the fused image and the true scene. The optimum image fusion approach is described for the case where all the parameters of the model are known. A robust image fusion approach is proposed for cases where various parameters of the model are unknown which may be the case in practice. It is shown that the robust image fusion approach will provide a mean square error which is always smaller than a given bound, thus limiting the loss from not knowing the exact model parameters. Further, our results imply that ignoring correlation between the noises from different sensors is a robust approach, a fact which has not been rigorously demonstrated elsewhere. Numerical results are presented which further verify the robustness of the proposed approach.