Matrix Variate Distribution-Induced Sparse Representation for Robust Image Classification
Matrix Variate Distribution-Induced Sparse Representation for Robust Image Classification
复制标题
DOI：
10.1109/tnnls.2014.2377477
复制
发表时间：
2015-02
影响因子：
10.4
通讯作者：
Jinhui Chen;Jian Yang;Lei Luo;J. Qian;W. Xu
中科院分区：
文献类型：
--
作者：
Jinhui Chen;Jian Yang;Lei Luo;J. Qian;W. Xu
稀疏表示学习已经成功地应用于图像分类，将给定的图像表示为过完备词典的线性组合。分类结果依赖于重构残差。通常，为了方便起见，图像被拉伸成向量，表示残差用I2范数来表征，这实际上假设残差中的元素是独立的、同分布的变量。然而，当涉及到一些结构性错误时，如照明、遮挡等，很难满足假设。在本文中，我们用图像数据的固有矩阵形式而不是串联向量来表示图像数据。表示残差被认为是服从矩阵椭圆等高线分布的矩阵变量，对相依误差具有健壮性，并具有长尾区来拟合异常值。然后，在稀疏正则化条件下，求矩阵优化问题的最大后验概率估计解。提出了一种交替方向乘子法(ADMM)来求解优化问题。从理论上证明了ADMM的收敛特性。实验结果表明，该方法在处理结构误差时比现有的方法更有效。
Sparse representation learning has been successfully applied into image classification, which represents a given image as a linear combination of an over-complete dictionary. The classification result depends on the reconstruction residuals. Normally, the images are stretched into vectors for convenience, and the representation residuals are characterized by I2-norm, which actually assumes that the elements in the residuals are independent and identically distributed variables. However, it is hard to satisfy the hypothesis when it comes to some structural errors, such as illuminations, occlusions, and so on. In this paper, we represent the image data in their intrinsic matrix form rather than concatenated vectors. The representation residual is considered as a matrix variate following the matrix elliptically contoured distribution, which is robust to dependent errors and has long tail regions to fit outliers. Then, we seek the maximum a posteriori probability estimation solution of the matrix-based optimization problem under sparse regularization. An alternating direction method of multipliers (ADMMs) is derived to solve the resulted optimization problem. The convergence of the ADMM is proven theoretically. Experimental results demonstrate that the proposed method is more effective than the state-of-the-art methods when dealing with the structural errors.