Nonlocal B-spline representation of tensor decomposition for hyperspectral image inpainting

Abstract

Hyperspectral image (HSI) completion is a fundamental problem in image processing and remote sensing. Typical methods, either perform suboptimally due to lack of appropriate priors or suffer from excessive complexity since the combination of too many constraints. Recently, nonlocal low-rank tensor approximation-based (NLTA) HSI completion methods are widespreadly investigated taking full advantage of global spectral correlation and non-local self-similarity. Common NLTA methods are mainly based on tensor train (TT) and tensor ring (TR) decompositions, but their representation of tensors is inadequate and inflexible. In this paper, a fully-connected tensor network (FCTN) decomposition is introduced for HSI completion exploring both the global spectral correlation and the spatial structure. FCTN approximates an N-order tensor as a sequence of smaller sized N-order tensors, which has outstanding capability to explore the essential invariance for transposition and also to improve intrinsic correlations among factors. Furthermore, motivated by the transformation based methods on HSI reconstruction and after deeply comparing its superiority over other techniques, we employ an iterative B-spline representation to construct a transformed tensor for better revelation of prior information. The proposed model can be efficiently solved using proximal alternating minimization (PAM) approach. Extensive experiments results demonstrate that our method achieves state-of-the-art performance both in quantitative metrics and visual effect evaluations.