Soft morphological image prior

This paper presents an image prior based on soft morphological filters and its application to image recovery. In morphological image processing, a gray-scale image is represented as a subset in the three dimensional space, which is spanned by spatial and intensity axes. The image is approximated as an union of the structuring elements in this space. In this paper, this morphological image model is introduced to an image prior for image recovery problem. With the proposed image prior, the image is recovered as an image that has no noise component that is eliminated by the opening and closing, which are basic operations of the morphological image processing. In our study, the closing and opening are respectively approximated as soft closing and soft opening with relaxed max and min functions in order to improve the noise robustness. Several properties of the proposed prior with the soft morphology are shown. In recovery experiments, image denoising and deblurring with the proposed prior are demonstrated. The comparison of the proposed prior with the prior based on the intensity differences are also shown.