Abstract:

Low rank and sparse decomposition （LRSD） is a data representation technology and has been widely used in the field of computer vision and many other fields. The LRSD method is a mechanism which decomposes the known data matrix to the low rank and sparse components, and can be used to the practical applications such as video foreground and background separation, image denoising and so on. This paper gives these models, advantages and disadvantages of many LRSD methods based on the analysis of the current researches at home and abroad. Many methods are applied to the video foreground and background separation and image denoising. The experimental results of the video foreground and background separation include the extracted foreground objects, the F-measure values and the running time. The experimental results of image denoising include the denoising image, the PSNR values and the FSIM values. The results of the video foreground and background separation and image denoising show the advantages and disadvantages of these LRSD methods from the visual and quantitative perspectives.

Key words: low rank and sparse decomposition, robust principal component analysis, video foreground and background separation, image denoising, robustness

摘要：

低秩稀疏分解（Low Rank and Sparse Decomposition，LRSD）是一种被广泛应用于计算机视觉等领域的数据表示技术，通过将已知矩阵分解为低秩成分和稀疏成分，实现视频前背景分离、图像去噪等的实际应用。分析了这一技术的研究现状，针对11种经典低秩稀疏分解方法，给出了各种方法的模型及算法的优缺点。将各种算法应用于视频前背景分离和图像去噪实验中，视频前背景分离的实验结果包括使用各种算法提取的不同视频的前景效果图、视频前背景分离的F-measure值和运行时间，图像去噪实验结果展示了各种算法对不同图像的去噪效果图、PSNR值和FSIM值，从视觉效果和定量评价两个角度验证了各种算法在视频前背景分离和图像去噪这两个实际应用中的优缺点。

关键词: 低秩稀疏分解, 鲁棒主成分分析, 视频前背景分离, 图像去噪, 鲁棒性