Removal of achromatic reflections from a single color image

In this paper we consider the problem of removing achromatic reflections from a picture of a scene taken through a semi-transparent medium, assuming that the reflection pattern is due to a light source or another object located in front of the object of interest. While other works assume the availability of multiple observations, we consider the more challenging problem of having as data a single color image. We suppose a data model where the virtual reflected image combines additively with the real transmitted image of the object, through unknown coefficients. This highly underdetermined problem is handled by means of a blind estimation technique that exploits the strict dependence of the gradients of the three color channels of the ideal image, and their independence from the gradient of the grayscale reflected image. The model parameters are estimated through independent component analysis, and then the component images are estimated through a regularization technique. The whole algorithm is very fast, and its performance is quantitatively evaluated on numerically generated images, and qualitatively tested on real images.