Sparsity Regularized Rank-(L,M,N) Block Term Decomposition for Hyperspectral Image Mixed Noise Removal

Tensor decomposition-based models have received increasing attention in hyperspectral image (HSI) denoising. However, tensor decompositions (e.g., Tucker decomposition and tensor singular value decomposition) in these HSI denoising models ignore exploiting the multiple components of the HSI, resulting in unsatisfactory denoising performance. To fully exploit the multiple components of the HSI, we develop a sparsity regularized rank-(L,M,N) block term decomposition (SR-BTD). In SR-BTD, the clean HSI is decomposed as the sum of multiple components, where each component is a sparse core tensor multiplied by matrices along each mode. The sparse regularization on each core tensor can benefit determining the low-rankness of each component with the unknown rank-(L,M,N) in the real world, leading to more accurately exploiting each component. Equipped with SR-BTD, we establish the HSI denoising model and design a hierarchical alternating least squares-based algorithm to efficiently solve the resulting model. Extensive experiments on simulated and real HSI denoising tasks demonstrate SR-BTD is superior to the competing tensor decompositions in terms of numerical results and visual quality.