Nonlocal Block-Term Decomposition for Hyperspectral Image Mixed Noise Removal

Since the facility restrictions and weather conditions, hyperspectral image (HSI) is generally seriously polluted by a variety of noises. Recently, the method based on block-term decomposition with rank-(L, L, 1) (BTD) has attracted wide attention in HSI mixed noise removal. BTD factorizes third-order HSI data into the sum of a series of component tensors, where each of the component tensors is represented by the outer product of a rank-L matrix <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</b> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</b> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sup> and a column vector <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</b> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> . BTD has clear physical interpretation because its latent factors <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</b> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</b> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sup> and <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</b> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> can be interpreted abundance map and spectral signature, respectively. The essential uniqueness of BTD is under the low-rank assumption of <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</b> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> <b xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</b> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</sup> . However, the low-rank assumption is not always held in real scenarios. The BTD-based method usually sets L to full rank to achieve satisfactory results. In this article, we suggest a novel model based on nonlocal block-term decomposition (NLBTD) for HSI mixed noise removal. More specifically, for each grouped similar image block, BTD is introduced to capture nonlocal self-similarity and global spectral low-rankness, the unidirectional total variation is introduced to preserve local spectral smoothness. By faithfully exploring nonlocal self-similarity, global spectral low-rankness, and local spectral smoothness, the proposed method is expected to produce promising results with guarantee the essential uniqueness of BTD. To tackle the resulting model, we design an efficient algorithm based on the proximal alternating minimization with the theoretical guarantees. Extensive numerical experiments in HSI mixed noise removal demonstrate that the proposed NLBTD method achieves satisfactory performance compared with state-of-the-art methods.