Adaptive Low Rank Approximation for Tensors

In this paper, we propose a novel framework for finding low rank approximation of a given tensor. This framework is based on the adaptive lasso with coefficient weights for sparse computation in tensor rank detection. We also provide an algorithm for solving the adaptive lasso model problem for tensor approximation. In a special case, the convergence of the algorithm and the probabilistic consistency of the sparsity have been addressed [15] when each weight equals to one. The method is applied to background extraction and video compression problems.