Spectral Vector-valued Image Restoration using a Hyperbolic Partial Differential Equation-based Filter

Aneffective denoising and restoration framework that removes successfully theadditive white Gaussian noise (AWGN) from the spectral images is introduced inthis paper. Since the multispectral images can be described as vector-valuedfunctions, the proposed technique uses a novel partial differential equation(PDE)-based model created for this type of image functions. So, we consider anonlinear vector-valued hyperbolic PDE filtering model for the restorationtask. It is equivalent to a system of second-order hyperbolic equationsevolving simultaneously and sharing some coupling terms that model theinter-channel correlation. A finite difference-based fast-convergingdiscretization algorithm which solves numerically the PDE-based model ispresented next. It has been applied successfully in the MSI restorationexperiments that are also described here.