Specification of the observation model for regularized image up-sampling

Regularization is one of the most promising methods for image up-sampling, which is an ill-posed inverse problem. A key element of such a regularization approach is the observation model relating the observed lower resolution (LR) image to the desired higher resolution (HR) up-sampled image, used in the data-fidelity term of the regularization cost function. This paper presents an algorithm to determine this observation model based on a model of the physical acquisition process for the LR image, and the ideal acquisition process for the desired HR image, both from the same underlying continuous image. The method is illustrated with typical scenarios corresponding to LR and HR cameras modeled by either Gaussian or rectangular apertures. Experiments with some regularized image up-samplers demonstrate the importance of using the correct, adapted observation model as determined by our algorithm.