Hyperspectral image denoising via group-sparsity constrained low-rank matrix triple factorization and spatial–spectral residual total variation

Abstract

Mixed noise, such as Gaussian noise, impulse noise, deadline noise, stripe noise, and many others, distorts the hyperspectral image (HSI), usually causing severe difficulties in subsequent applications. Due to the rise of artificial intelligence technology, matrix triple factorization is attached importance again in the field of HSI denoising. However, for convenient computations, these factor matrices are commonly imposed by the orthogonality, which is inconsistent with the physical meanings in practice. To address this issue, this article proposes a group-sparsity constrained triple factorization method to explore the shared sparse pattern and yields a tighter approximation to the low-rank prior. Specifically, the Casorati matrix of each local cube in HSIs, is firstly decomposed into a core matrix and two factor matrices. Then, the group-sparsity regularization is imposed on the factor matrices and the core matrix, simultaneously representing the low-rank and sparse prior in local cubes. Moreover, we also use the tensor group-sparsity based spatial–spectral residual total variation to globally explore the shared sparse pattern in both spatial and spectral difference images of HSIs. Ultimately, the group-sparsity constrained local low-rank matrix triple factorization and global spatial–spectral residual total variation model is proposed for HSI denoising. In the framework of the alternating direction method of multipliers, the proposed model can be solved efficiently. Simulated and real HSI experiments demonstrate the effectiveness of the proposed model. Across all datasets and noise conditions, our method achieves an average increase of nearly 1.93 decibels in overall peak signal-to-noise ratio compared to state-of-the-art HSI denoising methods.