Analysis of the Wavelet Ginzburg--Landau Energy in Image Applications with Edges
Julia A. Dobrosotskaya, Andrea Louise Bertozzi · SIAM Journal on Imaging Sciences · 2013
A wavelet analogue of the Ginzburg--Landau energy was recently designed and integrated in variational methods for image processing. In this paper we prove global well-posedness of the gradient descent equation (in the weak sense) and convergence to an extremum. We also develop further uses for this energy completed with an additional edge-preserving forcing term. We present examples including inpainting, superresolution, segmentation, denoising, and contour detection. Combining the spatial and the edge-preserving forcing terms gives an amazing flexibility of the model that is not only applicable to various image processing tasks but is also highly tunable.