International Journal of Computer Applications (0975 – 8887) Volume 98– No.17, July 2014 24 Image Denoising by Two-Pass of Total Variation Filter Dao Nam Anh Electric Power University 235 Hoang Quoc Viet road, Hanoi, Vietnam a. b. c. Fig. 1. Denoise keeping edges by TV denoising and TV inpainting. ABSTRACT Total variation based methods are widely applied for image enhancement and particularly for de-noising. The majority of these is designed for a specific noise model. The alternative total variation based approach proposed here can deal with multiple noise models via two-pass iterative algorithm basing on total variation. The first pass is designed for draft denoising and to detect noise region. The second pass restores the noise region by total variation based inpainting. Experiments on Salt & Pepper, Gaussian, Speckle, Poisson, and Impulse noise models demonstrate the effectiveness of the proposed method. General Terms Image Processing Keywords denoising, inpainting, restoration, keeping edge, filtering, total variation 1. INTRODUCTION Images are viewed as realization of optical and digital processes where noise from transmission errors or external factors can be added. Most widely used noise models are Salt & Pepper, Gaussian, Speckle, Poisson, Impulse. Removing these different noises is necessary to achieve quality for still images and videos. Image denoising methods have been improved recently in accuracy and performance for noise variance. However limitations and effects are found in some denoising methods: blurring fine image structure or introducing artifacts. Total variation (TV) concept of Rudin, Osher and Fatemi (ROF) [1] presented an effective algorithm for denoising image but keeping edges. Success of TV concept is confirmed by its further studies for deblurring [2, 3, 4], inpainting [5, 6, 7], interpolation [8], super-resolution [9], cartoon/texture decomposition [10]. This paper studies TV in recent works for image denoising and introduces a new way of its application with performance improvement. This is illustrated in fig.1, where 1a is input image with Poisson noise, 1b is denoised by the first pass of TV method and 1c is final denoised result after second pass with TV method in term of inpainting. 2. OUTLINE OF PAPER The rest of the paper is organized as follows: in the next section - a brief review of related work and contributions. Major development of total variation will be presented. This is followed by description of two-pass algorithm of total variation for denoising gray image in section 4. Section 5 describes algorithm for color image. In section 6, experiments on a variety of image data set are discussed with conclusion. 3. CONTRIBUTIONS AND RELATED WORK Let’s denote image as a M-dimension function of space. )) ( ),.. ( ( : ) ( , : 1 x u x u x u u M N     , 2     x (1) M i u i ,.., 1 , :     (2) Suppose input image u includes pure signal v and additive noise n : ) ( ) ( ) ( x n x v x u   (3) Reconstruction objective is to recover v from u . Total variation regularization method by ROF for denoising consists of two terms [1]:        dx x v x u dx x v v F ROF 2 2 | ) ( ) ( | ) ( ) (  (4) The first is a regularization term, the second is data-fidelity term in L2 norm. The model regards as the solution to a variation problem, to minimize ) (v F ROF (4). The solution attends to diminish variation of v and keep v close to the input u . The selection of noise model can have significant influence on outcomes, so the denoise algorithm should agree with the actual noise model in the image. Some previous denoising methods were addressed to specific noise models. TV denoising TV inpainting