基于可分离全变差模型的图像去噪

Image Denoising Based on Seperable Total Variation Model

在传统离散全变差模型的基础上,利用低维投影思想,建立了元素可分离的全变差模型;结合Frobenius范数,根据图像的凸性,提出利用凸优化方法求解元素可分离的离散全变差问题,并将其应用于图像去噪.仿真表明:对于添加方差为0.1的随机噪音的256×256图像,去噪后峰值信噪比可达到28.5dB左右,并且能有效地保持轮廓和细节,说明该方法对随机噪音具有良好的去除能力;通过改变迭代次数可灵活平衡计算速度和准确度以适应不同的去噪要求.

Based on traditional discrete total variation model, we established the separable total variation model exploiting low-dimensional projection; Combining with Frobenius norm and the convexity of image, we proposed a method that rooted in convex optimization to solve the separable discrete total variation problem, which can be applied into image denoising. Simulation results show that, with the ability of effectively keeping profile and details, the peak signal to noise ratio of 256 × 256 size image after denoising can reach 28.5 dB while the variance of random noise is 0.1, thus illustrating the good performance at the removal of random noise. By revising the numbers of iterations , the relationship between speed and accuracy can be balanced with considerable flexibility, thus adjusting to different denoising requirements.