Hyperspectral Image Denoising Using a Spatial–Spectral Monte Carlo Sampling Approach

Hyperspectral image (HSI) denoising is essential for enhancing HSI quality and facilitating HSI processing tasks. However, the reduction of noise in HSI is a difficult work, primarily due to the fact that HSI consists much more spectral bands than other remote sensing images. Therefore, comparing with other image denoising jobs that rely primarily on spatial information, efficient HSI denoising requires the utilization of both spatial and spectral information. In this paper, we design an unsupervised spatial–spectral HSI denoising approach based on Monte Carlo sampling (MCS) technique. This approach allows the incorporation of both spatial and spectral information for HSI denoising. Moreover, it addresses the noise variance heterogeneity effect among different HSI bands. In the proposed HSI denoising scheme, MCS is used to estimate the posterior distribution, in order to solve a Bayesian least squares optimization problem. Based on the proposed scheme, we iterate all pixels in HIS and denoise them sequentially. A referenced pixel in hyperspectral image is denoised as follows. First, some samples are randomly drawn from image space close to the referenced pixel. Second, based on a spatial–spectral similarity likelihood, relevant samples are accepted into a sample set. Third, all samples in the accepted set will be used for calculating the estimation of posterior distribution. Finally, based on the posterior, the noise-free pixel value is estimated as the discrete conditional mean. The proposed method is tested on both simulated and real hyperspectral images, in comparison with several other popular methods. The results demonstrate that the proposed method is capable of removing the noise largely, while also preserving image details very well.