去除稀疏和结构化噪声的交替方向增强拉格朗日算法

An Alternating Direction Augmented Lagrange Multiplier Algorithm for Removing Sparse and Structured Noise

图像和视频去噪是数字图像处理的必要环节之一.为了去除图像和视频中广泛存在的稀疏噪声和结构化噪声,提出了一种分离低秩矩阵、稀疏矩阵和结构化矩阵的优化模型一主成分离群点追求.在交替方向最小化思想的基础上,利用增强拉格朗日乘子法求解主成分离群点追求模型,设计了求解模型的交替方向增强拉格朗日(ADAL)算法,加入了一种连续技术以提高算法的收敛速率.仿真实验结果表明,提出的模型和算法能够有效去除不同尺寸矩阵的不同比例的稀疏噪声和结构化噪声.

The image and video denoising is one of the necessary steps in digital image pro- cessing. In order to remove sparse noise and structured noise existing extensively in images and videos, this paper proposes an optimization model for the separation of a low-rank matrix, a sparse matrix and a structured matrix ----Principal Component Outlier Pursuit. On the basis of the idea of the alternating direction minimization, we use the augmented Lagrange multiplier method to solve Principal Component Outlier Pursuit model, design an algorithm ----Alternating Direction Augmented Lagrange （ADAL） for solving the model, and add a continuous technology to improve the convergence rate of the algorithm. The results of the simulation experiments show that the proposed model and algorithm in this paper can effectively denoise different proportional sparse noise and structured noise of different matrix sizes.