Image Recovery with Soft-Morphological Image Prior

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Abstract

In this paper, an image prior based on soft-morphological filters and its application to image recovery are presented. In morphological image processing, a gray-scale image is represented as a subset in a three-dimensional space, which is spanned by spatial and intensity axes. Morphological opening and closing, which are basic operations in morphological image processing, respectively approximate the image subset and its complementary images as the unions of structuring elements that are translated in the three-dimensional space. In this study, the opening and closing filters are applied to an image prior to resolve the regularization problem of image recovery. When the proposed image prior is applied, the image is recovered as an image that has no noise component, which is eliminated by the opening and closing. However, the closing and opening filters are less able to eliminate Gaussian noise. In order to improve the robustness against Gaussian noise, the closing and opening filters are respectively approximated as soft-closing and soft-opening with relaxed max and min functions. In image recovery experiments, image denoising and deblurring using the proposed prior are demonstrated. Comparisons of the proposed prior with the existing priors that impose a penalty on the gradient of the intensity are also shown.

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