Developing a variational model that is capable of restoring both smooth (no edges) and non-smooth (with edges) images is still a valid challenge in the image processing. In this
paper, we present two methods for image denoising problems based on the use of the LLT model
(see ) and iterated total variation refinement. The idea of our methods is, first make use of
the LLT model to get a smooth primal sketch, and then get some meaningful signal by iterated
total variation refinement from the removed noise image. Numerical experiments show that our
method is able to maintain some important information such as small details in the image, and
at the same time to get a better visualization.