Combinatorics

Physics

Iterative method

Noise reduction

Mathematics

Matrix norm

Noise (video)

Algorithm

Image (mathematics)

Matrix (chemical analysis)

Mathematical optimization

Hyperspectral imaging

Rank (graph theory)

Mathematical analysis

Political science

Augmented Lagrangian method

Artificial intelligence

Norm (philosophy)

Eigenvalues and eigenvectors

Composite material

Hankel matrix

Materials science

Computer science

Quantum mechanics

Low-rank approximation

IEEE Transactions on Geoscience and Remote Sensing

Hyperspectral image (HSI) denoising is challenging not only because of the difficulty in preserving both spectral and spatial structures simultaneously, but also due to the requirement of removing various noises, which are often mixed together. In this paper, we present a nonconvex low rank matrix approximation (NonLRMA) model and the corresponding HSI denoising method by reformulating the approximation problem using nonconvex regularizer instead of the traditional nuclear norm, resulting in a tighter approximation of the original sparsity-regularised rank function. NonLRMA aims to decompose the degraded HSI, represented in the form of a matrix, into a low rank component and a sparse term with a more robust and less biased formulation. In addition, we develop an iterative algorithm based on the augmented Lagrangian multipliers method and derive the closed-form solution of the resulting subproblems benefiting from the special property of the nonconvex surrogate function. We prove that our iterative optimization converges easily. Extensive experiments on both simulated and real HSIs indicate that our approach can not only suppress noise in both severely and slightly noised bands but also preserve large-scale image structures and small-scale details well. Comparisons against state-of-the-art LRMA-based HSI denoising approaches show our superior performance.

Denoising of Hyperspectral Images Using Nonconvex Low Rank Matrix Approximation