This paper studies the problem of tensor principal component analysis (PCA). Usually the tensor PCA is viewed as a low-rank matrix completion problem via matrix factorization technique, and nuclear norm is used as a c...This paper studies the problem of tensor principal component analysis (PCA). Usually the tensor PCA is viewed as a low-rank matrix completion problem via matrix factorization technique, and nuclear norm is used as a convex approximation of the rank operator under mild condition. However, most nuclear norm minimization approaches are based on SVD operations. Given a matrix , the time complexity of SVD operation is O(mn2), which brings prohibitive computational complexity in large-scale problems. In this paper, an efficient and scalable algorithm for tensor principal component analysis is proposed which is called Linearized Alternating Direction Method with Vectorized technique for Tensor Principal Component Analysis (LADMVTPCA). Different from traditional matrix factorization methods, LADMVTPCA utilizes the vectorized technique to formulate the tensor as an outer product of vectors, which greatly improves the computational efficacy compared to matrix factorization method. In the experiment part, synthetic tensor data with different orders are used to empirically evaluate the proposed algorithm LADMVTPCA. Results have shown that LADMVTPCA outperforms matrix factorization based method.展开更多
在计算机辅助诊断系统中,视网膜眼底图像序列的变化检测是一项重要且具有挑战性的任务。针对视网膜眼底图像序列采样帧少、光照干扰大、难以获得稳健的背景模型,提出了一种基于张量鲁棒主成分分析(tensor robust principal component an...在计算机辅助诊断系统中,视网膜眼底图像序列的变化检测是一项重要且具有挑战性的任务。针对视网膜眼底图像序列采样帧少、光照干扰大、难以获得稳健的背景模型,提出了一种基于张量鲁棒主成分分析(tensor robust principal component analysis,TRPCA)的变化检测方法。该方法以TRPCA为模型,通过对序列背景扩充,再利用张量分解而获得变化区域:首先,先选择出序列中最接近正常状态的一张图像作为背景模型;然后,通过预处理将单帧背景模型扩张成多帧背景使得背景模型包含更丰富的光照变化;接着,将整个序列建模为一个3维张量体;最后,利用总变分约束背景模型和变化区域的时空连续性,通过Tucker分解分离出背景模型,获得变化区域。实验结果表明,与基于矩阵的鲁棒主成分分析(matrix robust principal component analysis,Matrix RPCA)方法,Masked-RPCA方法以及不加总变分约束的TRPCA方法相比,基于总变分约束的TRPCA方法能够更准确地分离出变化区域,对血管和光照干扰更具有鲁棒性。展开更多
文摘This paper studies the problem of tensor principal component analysis (PCA). Usually the tensor PCA is viewed as a low-rank matrix completion problem via matrix factorization technique, and nuclear norm is used as a convex approximation of the rank operator under mild condition. However, most nuclear norm minimization approaches are based on SVD operations. Given a matrix , the time complexity of SVD operation is O(mn2), which brings prohibitive computational complexity in large-scale problems. In this paper, an efficient and scalable algorithm for tensor principal component analysis is proposed which is called Linearized Alternating Direction Method with Vectorized technique for Tensor Principal Component Analysis (LADMVTPCA). Different from traditional matrix factorization methods, LADMVTPCA utilizes the vectorized technique to formulate the tensor as an outer product of vectors, which greatly improves the computational efficacy compared to matrix factorization method. In the experiment part, synthetic tensor data with different orders are used to empirically evaluate the proposed algorithm LADMVTPCA. Results have shown that LADMVTPCA outperforms matrix factorization based method.
文摘在计算机辅助诊断系统中,视网膜眼底图像序列的变化检测是一项重要且具有挑战性的任务。针对视网膜眼底图像序列采样帧少、光照干扰大、难以获得稳健的背景模型,提出了一种基于张量鲁棒主成分分析(tensor robust principal component analysis,TRPCA)的变化检测方法。该方法以TRPCA为模型,通过对序列背景扩充,再利用张量分解而获得变化区域:首先,先选择出序列中最接近正常状态的一张图像作为背景模型;然后,通过预处理将单帧背景模型扩张成多帧背景使得背景模型包含更丰富的光照变化;接着,将整个序列建模为一个3维张量体;最后,利用总变分约束背景模型和变化区域的时空连续性,通过Tucker分解分离出背景模型,获得变化区域。实验结果表明,与基于矩阵的鲁棒主成分分析(matrix robust principal component analysis,Matrix RPCA)方法,Masked-RPCA方法以及不加总变分约束的TRPCA方法相比,基于总变分约束的TRPCA方法能够更准确地分离出变化区域,对血管和光照干扰更具有鲁棒性。
