Image regularization with higher-order morphological gradients

In this paper, we propose an image prior based on morphological image features for image recovery. The proposed prior is obtained as the sum of morphological gradient and its higher-order extensions. The morphological gradient is defined as the difference between dilation and erosion of an image and obtains a discretized modulus of gradient. In order to suppress artifacts appear in the recovered image, we introduce higherorder morphological gradients. The regularization problem with the proposed prior is reduced to a constrained minimization problem. In order to apply the subgradient method to this problem, we derive the subgradient of the proposed priors. We apply the proposed prior to image denoising and demonstrate that the proposed higher-order morphological gradient prior is capable to suppress staircase artifacts. Comparison with the total variation image prior is also demonstrated.