Fractional differential and variational method for image fusion and super-resolution

This paper introduces a novel fractional differential and variational model that includes the terms of fusion and super-resolution, edge enhancement and noise suppression. In image fusion and super-resolution term, the structure tensor is employed to describe the geometry of all the input images. According to the fact that the fused image and the source inputs should have the same or similar structure tensor, the energy functional of the image fusion and super-resolution is established combining with the down-sampling operator. For edge enhancement, the bidirectional diffusion term is incorporated into the image fusion and super-resolution model to enhance the visualization of the fused image. In the noise suppression term, a new variational model is developed based on the fractional differential and fractional total variation. Thanks to the above three terms, the proposed model can realize the image fusion, super-resolution, and the edge information enhancement simultaneously. To search for the optimal solution, a gradient descent iteration scheme derived from the Euler–Lagrange equation of the proposed model is employed. The numerical results indicate that the proposed method is feasible and effective.