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

In this talk, we study a fast total variation minimization method for image restoration. In the proposed method, we use the exact total variation minimization scheme to denoise the deblurred image. An alternating minimization algorithm is employed to solve the proposed total variation minimization problem. Our experimental results show that the quality of restored images by the proposed method is competitive with those restored by the existing total variation restoration methods. We show the convergence of the alternating minimization algorithm and demonstrate that the algorithm is very efficient.

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In this paper, we propose iterative algorithms for solving image restoration problems. The iterative algorithms are based on decoupling of deblurring and denoising steps in the restoration process. In the deblurring step, an efficient deblurring method using fast transforms can be employed. In the denoising step, effective methods such as the wavelet shrinkage denoising method or the total variation denoising method can be used. The main advantage of this proposal is that the resulting algorithms can be very efficient and can produce better restored images in visual quality and signalto-noise ratio than those by the restoration methods using the combination of a data-fitting term and a regularization term. The convergence of the proposed algorithms is shown in the paper. Numerical examples are also given to demonstrate the effectiveness of these algorithms.