Abstract:

In order to avoid staircasing effect and preserve small
scale texture information for the classical total variation regularization,
a new minimization energy functional model for image
decomposition is proposed. Firstly, an adaptive regularization
based on the local feature of images is introduced to substitute total
variational regularization. The oscillatory component containing
texture and/or noise is modeled in generalized function space div
(BMO). And then, the existence and uniqueness of the minimizer
for proposed model are proved. Finally, the gradient descent flow
of the Euler-Lagrange equations for the new model is numerically
implemented by using a finite difference method. Experiments
show that the proposed model is very robust to noise, and the
staircasing effect is avoided efficiently, while edges and textures
are well remained.