Regularization of multivalued images by means of a wavelet-based partial differential equation

In this work, a wavelet-based anisotropic diffusion partial differential equation (PDE) is developed. The new model makes use of a multiscale structure tensor as an extension of the single-scale structure tensor proposed by Di Zenzo. The multiscale structure tensor allows for accumulating multiscale gradient information of local regions. Thus, averaging properties are maintained while preserving edge structure. This structure tensor is used in an anisotropic diffusion process of multispectral images, namely, in the Perona-Malik model. Therefore, a more efficient and accurate formulation for edge-preserving diffusion is obtained.