Rank-1 tensor decomposition for hyperspectral image denoising with nonlocal low-rank regularization

In hyperspectral imagery denoising, rank-1 tensor decomposition (R1TD) model can utilize the spatial and spectral information jointly and reduce the noise efficiently. It is difficult to estimate the rank of hyperspectral imagery accurately, and the rank uncertainty will make the R1TD denoising algorithm inefficient. The nonlocal similar patches have lower rank than image, it can be used in rank-1 tensor decomposition process instead of explicitly estimating rank parameters. In this work, a nonlocal low-rank regularization is introduced to avoid the rank uncertainty to influence denoising performance. Then an alternating direction method of multipliers (ADMM) optimization technique is designed to solve the minimum problem. Compared with the state of art methods, proposed algorithm significantly improves the hyperspectral imagery quality both in visual inspection and image quality indices.