  Building on the well-known total-variation (TV), this paper develops a
general regularization technique based on nonlinear isotropic diffusion (NID)
for inverse problems with piecewise smooth solutions. The novelty of our
approach is to be adaptive (we speak of A-NID) i.e. the regularization varies
during the iterates in order to incorporate prior information on the edges,
deal with the evolution of the reconstruction and circumvent the limitations
due to the non-convexity of the proposed functionals. After a detailed analysis
of the convergence and well-posedness of the method, this latter is validated
by simulations perfomed on computerized tomography (CT).
