Image Restoration Based On Convex Optimization Methods

Digital image denoising is an important branch of image processing. It aims to denoise the observed image so that recover the original information in the true image. However, noise removal and original information preservation are usually a dilemma. In this paper, we take advantage of total variation regularization method to tackle this kind of problem. Due to the different imaging system, the image may degraded by different kind of noise, such as the two most common noise type: additive and multiplicative. We mainly focus on multiplicative noise in this work. The work is outlined as following three parts:Firstly, consider the degradation model uvf ?, where f is the observed noisy image, u is the true image and v is the multiplicative noise. Since the degradation model includes multiplication, the classic recovery model is not convex. And the solution could be negative which breaks the nonnegative of the image pixel values. In this work, we proposed a revised denoising model based on the previous classic model. The main contribution of proposed model is the improvement of regularization term which makes the new model convex and the solution will keep the nonnegative of image pixel values.Secondly, we solve the proposed model by introducing auxiliary variables. The unconstrained extreme value problem can be reformulated as the constrained problem. Then we use alternating direction of multipliers method to solve the corresponding augmented Lagrangian function of the constrained problem. This method is to solve several variables separately so as to reduce the solving difficulty. In the process of iteration, the functions in sub-problems are different and solving methods are also different. In this work, we utilize Newton method and shrinkage algorithm to solve the sub-problems. Note that we cannot obtain the exact solution with Newton method, but the approximate solution instead. However, The Newton method yields a faster(and very accurate) solution by running just a few iterations.Finally, we carry out a lot of numerical experiments, including parameter selection, the noise level, different test images and so on. Compared with the classic denoisng model, our results show that the proposed model in the paper behaves much better not only in visual quality but SNR of denoised images.