Image denoising using Euler-Lagrange equations for function-valued mappings

In this paper, we consider a new method for representing complex images, e.g., hyperspectral images and video sequences, in terms of function-valued mappings (FVMs), also known as Banach-valued functions. At each (pixel) location x, the FVM image u(x) is a function, as opposed to the traditional vector approach. We define the Fourier transform of an FVM as well as Euler-Lagrange conditions for functionals involving FVMs and then show how these results can be used to devise some FVM-based methods of denoising. We consider a very simple functional and present some numerical results.