# Denoising Hyperspectral Image with Non-i.i.d. Noise Structure

## TL;DR

This paper introduces a novel hyperspectral image denoising method that models complex non-i.i.d. noise using a mixture of Gaussians within a Bayesian low-rank matrix factorization framework, improving robustness over existing methods.

## Contribution

It is the first to model non-i.i.d. noise in hyperspectral images with a mixture of Gaussians and integrates this into a Bayesian low-rank matrix factorization approach.

## Key findings

- Outperforms existing denoising methods on synthetic data.
- Demonstrates robustness on real noisy hyperspectral images.
- Achieves better noise removal while preserving image details.

## Abstract

Hyperspectral image (HSI) denoising has been attracting much research attention in remote sensing area due to its importance in improving the HSI qualities. The existing HSI denoising methods mainly focus on specific spectral and spatial prior knowledge in HSIs, and share a common underlying assumption that the embedded noise in HSI is independent and identically distributed (i.i.d.). In real scenarios, however, the noise existed in a natural HSI is always with much more complicated non-i.i.d. statistical structures and the under-estimation to this noise complexity often tends to evidently degenerate the robustness of current methods. To alleviate this issue, this paper attempts the first effort to model the HSI noise using a non-i.i.d. mixture of Gaussians (NMoG) noise assumption, which is finely in accordance with the noise characteristics possessed by a natural HSI and thus is capable of adapting various noise shapes encountered in real applications. Then we integrate such noise modeling strategy into the low-rank matrix factorization (LRMF) model and propose a NMoG-LRMF model in the Bayesian framework. A variational Bayes algorithm is designed to infer the posterior of the proposed model. All involved parameters can be recursively updated in closed-form. Compared with the current techniques, the proposed method performs more robust beyond the state-of-the-arts, as substantiated by our experiments implemented on synthetic and real noisy HSIs.