Multiplicative noise removal combining a total variation regularizer and a nonconvex regularizer

Abstract

A novel variational model for removing multiplicative noise is proposed in this paper. In the model, a novel regularization term is elaborately designed which is inherently equivalent to a combination of the classical total variation regularizer and a nonconvex regularizer. The proposed regularization term, on the one hand, can better remove the noise in homogeneous regions of a noisy image and, on the other hand, can preserve edge details of the image during the denoising process. In order to solve the model efficiently, we design an alternating iteration process in which two coupling minimization problems are solved. For each of the two minimization problems, the existence and uniqueness of their solutions are proved under some necessary assumptions. Numerical results are reported to demonstrate the effectiveness of the proposed regularization term for multiplicative noise removal.

Euler’s elastica and curvature based model for image restoration

“…Y. Han et. al proposed a new variational model (in 2014) [ 60 ] and hence some good restoration results have been obtained. The minimization functional for this model is given as follow: where the second term is called the weighted total variation term, function ϵ is the positive parameter such that 0 < ϵ < 1.…”

“…According to the authors, due to the nonconvex nature of minimization problem ( 69 ) it is hard to prove the global convergence about the whole algorithm in Algorithm 2. For, further details, see [ 60 ].…”

A Robust Functional Minimization Technique to Protect Image Details from Disturbances

“…where div z is the divergence (div) of the vector respectively. The controlling parameter  is equivalent to the noise level and  is selected from a fixed range   0, 0.6 as in [27,30], however we choose  for any values from the range   0, 1 . In experiment, the parameters  and  are for the role of controlling the smoothness.…”

“…Moreover, the solution of the models can ensure image smoothness and details preservation abilities, those abilities are also reported as in the PDE-based methods [20,22]. Similarly, energy minimization or variationalbased approaches such as [23][24][25][27][28][29] using in image enhancement problems. The nonconvexbased smoothing approaches such as [30][31][32][33] can also preserve image details.…”

“…However, the high isotropic polishing phenomena hamper some important image details. To defeat this problem, a nonconvex way of enhancement is proposed in [27,30] which ensure the ability of details protection and noise elimination. However, it is much slower method and cannot guarantee unique solution.…”