A New Total Variation Method for Multiplicative Noise Removal

Abstract

Image denoising plays a important role in the areas of image processing. A real recorded image may be distorted by many expected or unexpected random factors, of which random noise is a unavoidable one.Multiplicative noise is naturally dependent on the image data, the recorded image g is the multiplication of original image u and noise n: g = un.(1)Here u, g and n are n 2 -by-1 vector corresponding to n-by-n image. whereis the data fitting term, u T V is the total variation (TV) regularization term [1], λ is the regularization parameter which measures the trade off between a good fit and a regularized solution.The main aim of this paper is to propose and study a convex objective function for multiplicative noise removal in images. we consider an auxiliary variable z = log u in the multiplicative noise removal model.The proposed unconstrained TV denoising problem is given bywhere α 1 and α 2 are positive regularization parameters. The main advantage of using the new data fitting in the new minimization method. We can interpret the total variation minimization scheme to denoise the multiplicative noise removed image z. The main advantage of the proposed method is that an exact TV norm is used in the noise removal process. Therefore the new method has the ability to preserve edges very well in the denoised image.An alternating minimization algorithm was proposed to solve (3). Starting from an initial guess w (0) , this method computes a sequence of iteratesWe remark that T (·) = S(R(·)) is non-expansive and asymptotically regular. Since the objective function J is coercive, the set of minimizers of J is non-empty. Therefore, the set of fixed points of T is non-empty. According to the Opial theorem [2], the sequence z converges to a fixed point of J , i.e., a minimizer of J .We present numerical results to demonstrate the performance of our proposed algorithm. The results are compared with those obtained by "AA" method proposed by Aubert and Aujol [1]. Relative error of the 1

Removing Multiplicative Noise by Douglas-Rachford Splitting Methods

“…They applied a corresponding relaxed inverse scale space flow as denoising technique. The model of Shi and Osher was modified in [42] by adding a quadratic term to get a simpler alternating minimization algorithm. A variational model involving curvelet coefficients for cleaning multiplicative Gamma noise was considered in [24].…”

Double Reweighted Sparse Regression and Graph Regularization for Hyperspectral Unmixing

“…The symmetric alternating direction method with multipliers (symmetric ADMM) is an acceleration method of ADMM, which can be used to solve the constraint optimization formulation in image processing [34][35][36][37][38][39][40][41][42][43].…”

A Characterization of the Domain of Beta-Divergence and Its Connection to Bregman Variational Model

“…Although the domain B is nonnegative in real applications, through the dual formulation of the Bregman-divergence (17), the nonpositive domain is very common and sometimes is useful for convex reformulation of nonconvex variational models appearing in SAR image enhancement problems. See Theorem 7 for the negative domain of the conjugate function Φ * .…”

“…Actually, this model is highly nonconvex [15]. Therefore, various transforms are introduced to relax nonconvexity of the Gamma distribution related speckle reduction model [16][17][18][19][20][21]. Recently, we have shown that the β-divergence with β ∈ (0, 1) can be used as a transform-less convex relaxation model for SAR speckle reduction problem [12].…”

“…It is well known that it is not easy to find a global minimizer of (55), due to the severe nonconvexity of D Φ (b|u) in terms of u [15,21]. Therefore, various transform-based convex relaxation approaches are introduced [12,[16][17][18][19][20][21]42]. In this example, we are going to use dual Bregman-divergence to find a solution of (55).…”