Anisotropic Localized Wavelets for Image Processing

This paper proposes novel anisotropic localized wavelets (ALWs) for structure-preserving image analysis and processing. It is formulated as the negative first-order derivative of the fundamental solution of heat diffusion equation with respect to time, which is based on the rigorous mathematical derivation. Our ALW inherits powerful properties from Mexican hat wavelets in spirit. It also intrinsically conveys and encodes local and global structural properties. First, we construct anisotropic heat kernel by embedding the intrinsic structure into graph Laplacian, and on such basis, ALW is derived from the heat kernel difference of adjacent layers in image pyramid or adjacent time frequency in intralayer. We perform extensive experiments on image processing and conduct quantitative comparisons with other state-of-the-art methods. All the results demonstrate the superiority of our method in accuracy and versatility towards global salient structure and local detail preservation, noise compression and gradient reversion restraint.