Image regularization with multiple morphological gradient priors

In this paper, we propose an image prior based on morphological gradients for image recovery. The morphological gradient is defined as the difference between dilation and erosion of an image and approximates the image gradient. This prior provides regularization with an L1-L∞ norm. The regularization problem with the proposed prior is reduced to a constrained minimization problem and is solved by an augmented Lagrangian method with proximal operators. We apply the proposed prior to image denoising and demonstrate an image decomposition along with the size of the structuring element of the morphological gradients. Comparing with the total variation (TV) norm, which is an L1-L2 norm, the proposed prior is superior in recovery of fine details by choice of the structuring element.

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