Robust Rank-Revealing Block-Term Decomposition and Hyperspectral Image Denoising

Mixed noise suppression in hyperspectral imagery (HSI) constitutes an important preprocessing step in numerous remote sensing applications. Tensor decomposition-based approaches have proved successful also in this HSI data processing task, given the multi-way nature of the HSI cube and its underlying spatial-spectral correlation. Block-term decomposition (BTD), in its special yet widely applicable format of decomposition into rank-(L
r
,L
r
,1) terms, has been more recently adopted in HSI processing as a natural generative model, in which the R block terms represent the constituent endmembers, and their ranks, L
r
, r = 1,2,…,R, quantify the spatial correlation in the corresponding abundance maps. In this paper, a BTD-based denoising method is developed, robust to sparse outliers, and with the model ranks a-priori unknown and recovered in the course of the algorithm with the aid of appropriate ℓ
1,2
-norm regularization. Its computational efficiency and effectiveness in rank determination and mixed noise removal are demonstrated via simulations involving both synthetic and HSI noisy tensors. For the latter, it is also seen to be robust to model order under-estimation.