Hyperspectral Image Restoration via Subspace-Based Nonlocal Low-Rank Tensor Approximation

In this letter, we present a subspace-based nonlocal low-rank tensor approximation framework (SNLRTA) for hyperspectral image (HSI) restoration. The proposed method consists of a subspace learning method to achieve an accurate subspace characterization of HSI and a nonlocal low-rank tensor approximation to take spatial nonlocal self-similarity into consideration. Specifically, the HSI first exploits residual statistics on median filtered image to estimate a robust subspace. Laplacian scale mixture (LSM) modeling is then investigated to model tensor coefficients from overlapping cubes in low-rank subspace. Both the hidden scale parameters and the sparse coefficients therein are adaptively shrink, characterizing the sparsity of similar patches. Meanwhile, the $\ell _{1}$ data fidelity facilitates the implicit detection of outliers after median filtering. Substantiated by extensive experimental results, the proposed method outperforms several state-of-the-art approaches on mixed noise removal, qualitatively and quantitatively.

I. Introduction

Hyperspectral image (HSI) with hundreds of spectral channels can reflect wealthy spatial information of real scenes and facilitate many applications in geography, agriculture, and military [1]. However, during the imaging process, real-world HSIs are often contaminated by various noises, such as Gaussian noise, impulse noise, and stripes [2], [3], which restricts subsequent applications and analysis. Therefore, restoring clean HSI plays a critical role in HSI-related tasks.