Combining observation models in dual exposure problems using the Kullback-Leibler divergence

Photographs acquired under low-lighting conditions require long exposure times and therefore exhibit significant blurring due to the shaking of the camera. Using shorter exposure times results in sharper images but with a very high level of noise. By taking a pair of blurred/noisy images it is possible to reconstruct a sharp image without noise. This paper is devoted to the combination of observation models in the blurred/noisy image pair reconstruction problem. By examining the difference between the blurred image and the blurred version of the noisy image a third observation model is obtained. Based on the minimization of a linear convex combination of Kullback-Leibler divergences between posterior distributions, a procedure to combine the three observation models is proposed in the paper. The estimated images are compared with images provided by other reconstruction methods.