A Bidirectional Flow Joint Sobolev Gradient for Image Interpolation

An energy functional with bidirectional flow is presented to sharpen image by reducing its edge width, which performs a forward diffusion in brighter lateral on edge ramp and backward diffusion that proceeds in darker lateral. We first consider the diffusion equations as gradient flows on integral functionals and then modify the inner product from to a Sobolev inner product. The experimental results demonstrate that our model efficiently reconstructs the real image, leading to a natural interpolation with reduced blurring, staircase artifacts and preserving better the texture features of image.