  We study a generalization of a cross-diffusion problem deduced from a
nonlinear complex-variable diffusion model for signal and image denoising.
  We prove the existence of weak solutions of the time-independent problem with
fidelity terms under mild conditions on the data problem. Then, we show that
this translates on the well-posedness of a quasi-steady state approximation of
the evolution problem, and also prove the existence of weak solutions of the
latter under more restrictive hypothesis.
  We finally perform some numerical simulations for image denoising, comparing
the performance of the cross-diffusion model and its corresponding scalar
Perona-Malik equation.
