Sliced sparsity measure for tensor to multispectral image denoising

From the sparsity of vector to the sparsity of singular values, which essentially characterizes the low rank property of matrix. The sparsity measure based model is of significant interest in a range of contemporary applications in data analysis. However, there are different measurement strategies for sparse characterization of high dimensional tensor data. Albeit, most of the existing sparsity measures only consider the number of non-zero factor components, but ignore the geometric position distribution structure of non-zero elements in high-dimensional space. In this paper, based on the fact that sliced sparse distribution of the core tensor, a novel high order structure sparsity measure is proposed. More specifically, the sparsity measure unifies Tucker and CP tensor decomposition into a framework for general tensor. The CP decomposition of the core tensor with factor group sparse constraint realizes modeling the global low CP rank and the sliced sparse distribution of the non-zeros elements of the core tensor simultaneously. We apply minimizing high order structure sparse measurement to multispectral image denoising and deduce Alternating Direction Method of Multipliers (ADMM) optimization method to solve the model effectively. The subsequent experimental results show that the proposed algorithm is competitive with state-of-the art denoising methods.¹