Abstract:  Tensor Principal Component Analysis(TPCA)，which is a generalization of classical PCA(Principal Component Analysis)in multiple dimension space and can make full use of the spatial relationship of images/videos，plays an important role in image analysis and vision processing.The basis vectors of tensor PCA，however，are still dense，which makes it difficult to explain.Various sparse PCA methods，which extract principal components of the given data with sparse non－zero loadings，have been proposed in recent years.In this paper，we extend sparse feature extraction of PCA to tensor analysis and propose a robust and sparse tensor PCA with L1－norm(TPCA－L1S)．Firstly，an objective function for TPCA－L1S is designed.On the one hand，we replace Frobenius－norm with L1－norm in the objective function，which makes it more robust to outlier.On the other hand，the elastic net，which generalizes the sparsity－inducing lasso penalty by combining the ridge penalty，is integrated into the objective function to enhance the interpretability of the tensor PCA.Then，an alternative tensor projection optimization procedure is developed in the second－order tensor PCA which is easy to be formulated and can be extended to much higher order.It is convenient to use U and V to denote the projection matrices and refer V and U as to the left and right projection matrices respectively.The procedure is divided into two steps.At the first step, V is computed while U is fixed，and then at the second step, U is computed while V is fixed.The two steps repeat until convergence.A greedy procedure，which is for computing projection matrices U and V，is designed to extract basic features one by one.Finally，the monotonicity of the iterative greedy procedure is theoretically guaranteed.The proposed TPCA－L1S is applied to several face image analysis problems upon ORL，Yale and Feret databases and compared with some other conventional methods.Experimental results confirm its effectiveness.