基于加权Lp范数和总变分范数的图像去噪算法

Image denoising algorithm based on weighted Lp norm and total variational norm

为了获得更好的图像结构平滑度,并显著提高恢复图像的质量,本文将总变分范数和Lp范数引入已有的重加权低秩矩阵恢复算法,提出一种新的低秩矩阵恢复算法,并将其应用在图像去噪中。结合总变分范数和Lp范数,从而能够利用自然图像的低秩特性,增强结构平滑性,并消除大的稀疏噪声以及各种混合噪声。利用迭代交替方向和快速梯度投影算法,顺利求解具有挑战性的非凸优化问题。图像去噪的实验结果表明:所提的方法优于最先进的低秩矩阵恢复方法,特别是对于大的随机噪声。当随机稀疏噪声密度为30%和40%时,图像经本文算法去噪后的峰值信噪比数据和现有方法相比提高多达3. 61 d B和7. 13 d B。

In order to obtain better image structure smoothness and significantly improve the quality of restored images,total variational norm and Lp norm are introduced into the existing reweighted low rank matrix restoration algorithm,and a new low rank matrix recovery algorithm is proposed and applied in image denoising. Combining the total variational norm and the Lp norm,it is possible to utilize the low rank property of natural images,enhance structural smoothness,and eliminate large sparse noise and various mixed noises. The iterative alternating direction and fast gradient projection algorithm are used to solve the challenging non-convex optimization problem smoothly.Experimental results of image denoising show that the proposed method is superior to the most advanced low rank matrix recovery method,especially for large random noise. When the random sparse noise density is 30 % and40 %,the peak signal-to-noise ratio of the image after denoising by the proposed algorithm is increased by 3. 61 d B and 7. 13 d B,compared with the existing methods.