[Paper Review] Non-local Meets Global: An Integrated Paradigm for Hyperspectral Denoising

Wei He, Quanming Yao+3 more|arXiv (Cornell University)|Dec 11, 2018

Image and Signal Denoising Methods53 references4 citations

TL;DR

This paper proposes NGmeet, a novel unified spatial-spectral hyperspectral denoising framework that jointly exploits global spectral low-rank structure and non-local spatial similarity via iterative optimization. By learning a shared spectral basis and refining reduced images through alternating minimization, it achieves state-of-the-art denoising performance with nearly constant computational cost across increasing spectral bands.

ABSTRACT

Non-local low-rank tensor approximation has been developed as a state-of-the-art method for hyperspectral image (HSI) denoising. Unfortunately, with more spectral bands for HSI, while the running time of these methods significantly increases, their denoising performance benefits little. In this paper, we claim that the HSI underlines a global spectral low-rank subspace, and the spectral subspaces of each full band patch groups should underlie this global low-rank subspace. This motivates us to propose a unified spatial-spectral paradigm for HSI denoising. As the new model is hard to optimize, we further propose an efficient algorithm for optimization, which is motivated by alternating minimization. This is done by first learning a low-dimensional projection and the related reduced image from the noisy HSI. Then, the non-local low-rank denoising and iterative regularization are developed to refine the reduced image and projection, respectively. Finally, experiments on synthetic and both real datasets demonstrate the superiority against the other state-of-the-arts HSI denoising methods.

Motivation & Objective

• To address the growing computational cost of non-local low-rank methods in hyperspectral image (HSI) denoising as spectral bands increase.
• To unify spatial non-local similarity and global spectral low-rank structure into a single optimization framework.
• To develop an efficient iterative algorithm that jointly learns a spectral basis and denoised reduced image.
• To improve denoising performance on both synthetic and real-world HSI datasets while maintaining computational efficiency.

Proposed method

• Proposes a unified model that enforces all full-band patch groups (NLFBPGs) to lie in a common low-dimensional spectral subspace.
• Introduces an alternating minimization-based algorithm to iteratively optimize the orthogonal spectral basis and the reduced image.
• First stage learns a global spectral low-rank basis from the noisy HSI using truncated SVD.
• Second stage applies non-local low-rank approximation to denoise the projected reduced image using grouped patches.
• Third stage refines the spectral basis via iterative regularization using the updated reduced image.
• Employs a parameter update strategy for the rank $ K $ and noise variance $ ho $, enhancing robustness and convergence.

Experimental results

Research questions

• RQ1 Can a unified paradigm effectively combine spatial non-local similarity and global spectral low-rank structure for HSI denoising?
• RQ2 Does integrating global spectral low-rank constraints improve denoising performance while reducing sensitivity to increasing spectral bands?
• RQ3 Can an iterative alternating optimization strategy efficiently solve the complex joint optimization problem involving both spectral and spatial constraints?
• RQ4 How does the proposed method perform on real-world HSI data where ground truth is unavailable?

Key findings

• On the CAVE dataset with noise variance 100, NGmeet achieves a PSNR of 43.09 dB, outperforming state-of-the-art methods like KBR and LLRT.
• For the WDC dataset, NGmeet maintains nearly constant computational time (around 204 seconds) even as the number of spectral bands increases, unlike KBR and LLRT whose time increases linearly.
• The method converges rapidly, achieving stable PSNR values within 10–15 iterations on the WDC dataset across all noise levels.
• On real Indian Pines and Urban datasets, NGmeet produces visually superior results with better preservation of spectral details and reduced noise, outperforming LRTV, FastHyDe, and LLRT in visual quality.
• The parameter $ ho $ (noise variance estimator) is robust: PSNR improves slightly with $ ho = 1 $ to $ 3 $, with $ ho = 2 $ yielding the best average performance.
• Initialization of $ K $ using HySime is reliable, with $ K = 7, 6, 6, 5 $ for noise variances 10, 30, 50, 100 respectively, and performance remains stable across different initializations.