Abstract:

To overcome the drawbacks of the existing image recovery method failing to separate the dense noise and sparse noise, a tri-decomposition model is proposed. This model decomposes the matrix into three component matrices. The first matrix represents clean data, assumed being low rank and measured by nuclear norm; second matrix represents noise data, assumed being sparse and measured by L1 norm; third matrix also represents noise data, but assumed being dense and measured by F norm. The observed data can be divided into clean data, sparse noise and dense noise by these three measurement functions. Furthermore, the algorithm for tri-decomposition model is designed, which is based on the multiplier alternate direction method and is suit for separable variable optimization. This algorithm is used to process image data corrupted by large sparse noise and small dense noise. Experimental results in face images and surveillance videos demonstrate the effectiveness of the proposed method.

Key words: robust principal component analysis, sparse, low-rank, mixed noise

摘要：

针对现有图像恢复方法无法同时分离出稠密噪声和稀疏噪声的不足，提出了一种三分解模型（tri-decomposition model，Tri-Decom）。该模型目的是将矩阵分解为三个分量矩阵，其中第一个矩阵表示干净数据，具有低秩性质，通过核范数刻画；第二个矩阵表示噪声数据，具有稀疏性质，通过L1范数刻画；第三个矩阵也表示噪声，但具有稠密性质，通过F范数刻画。通过不同的刻画函数可将观测数据分成干净数据、稀疏噪声和稠密噪声。为求解模型，设计了一种基于乘子交替方向法的求解算法，该算法可有效求解变量可分离的优化问题。该算法用于处理受到大稀疏噪声和小稠密噪声破坏的图像数据，在人脸图像和监控视频等领域的实验结果证明了所提方法的有效性。

关键词: 鲁棒主分量分析, 稀疏, 低秩, 混合噪声