为了达到全变差噪声消除的图像去噪目的, 将去噪问题转换为优化问题。采用了结合广义最小残差法的半光滑牛顿法来解决相关优化问题, 求解非对称线性方程组, 进行了理论分析和实验验证, 取得了将该方法与其它方法应用于1维信号、2维图像去噪实验的大量可行数据。结果表明, 结合广义最小残差法的半光滑牛顿法的收敛速度比结合预处理共轭梯度法的半光滑牛顿法和交替方向乘子法更快, 而且能够有效地消除噪声。

In order to remove the noise of image based on total variation, the denoising problem was converted to optimization problem. Semi-smooth Newton method incorporated by generalized minimum residual method was used to solve the associated optimization problem and non-symmetric linear equations. After theoretical analysis and experimental verification, a great deal of feasible data of removal noise experiment for 1-D signal and 2-D image were obtained by different methods. The results show that semi-smooth Newton method incorporated by generalized minimum residual method converges faster than that incorporated by preconditioned conjugate gradients method and alternating direction method of multipliers algorithm. The proposed method can remove the noise of image effectively.