Abstract

Hyperspectral images (HSIs) are always corrupted by complicated forms of noise during the acquisition process, such as Gaussian noise, impulse noise, stripes, deadlines and so on. Specifically, different bands of the practical HSIs generally contain different noises of evidently distinct type and extent. While current HSI restoration methods give less consideration to such band-noise-distinctness issues, this study elaborately constructs a new HSI restoration technique, aimed at more faithfully and comprehensively taking such noise characteristics into account. Particularly, through a two-level hierarchical Dirichlet process (HDP) to model the HSI noise structure, the noise of each band is depicted by a Dirichlet process Gaussian mixture model (DP-GMM), in which its complexity can be flexibly adapted in an automatic manner. Besides, the DP-GMM of each band comes from a higher level DP-GMM that relates the noise of different bands. The variational Bayes algorithm is also designed to solve this model, and closed-form updating equations for all involved parameters are deduced. The experiment indicates that, in terms of the mean peak signal-to-noise ratio (MPSNR), the proposed method is on average 1 dB higher compared with the existing state-of-the-art methods, as well as performing better in terms of the mean structural similarity index (MSSIM) and Erreur Relative Globale Adimensionnelle de Synthèse (ERGAS).

Highlights

  • Hyperspectral images (HSIs) are collected by high spectral resolution sensors, and consist of hundreds of bands ranging from ultraviolet to infrared wavelengths

  • In order to comprehensively evaluate the performance of the proposed method, we compared the results with eight popular HSI restoration methods: the traditional image denoising method SVD [52], low-rank matrix factorization (LRMF)-based methods LRMR [20], LRTV [38], weighted nuclear norm minimization (WNNM) [24] and WSNM [23], tensor-based methods

  • In order to further compare the performance of all the restoration methods, we show the spectral signatures of some pixels before and after restoration; for example, Figure 6 shows the spectrum of pixels (55, 110) and (110, 184) for the DC Mall HSI dataset under Case 6, and Figure 7 shows similar results for the RemoteImage HSI dataset

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Summary

Introduction

Hyperspectral images (HSIs) are collected by high spectral resolution sensors, and consist of hundreds of bands ranging from ultraviolet to infrared wavelengths. He et al [38] considered the noise as a mixture of Gaussian and Laplacian distribution while Cao et al [39] modelled the noise using a more general mixture of exponential power (MoEP) distributions These methods all assume the noise in each HSI band as an identical distribution. Chen et al [40] proposed modelling the noise distribution of each band as a mixture of Gaussian (MoG) distributions with different parameters sharing with the unique conjugate prior. This method, still assumes the same complexity (i.e., the number of components) of MoGs in all HSI bands.

Dirichlet Process
Hierarchical Dirichlet Process
Notation Explanation
Model Formulation
The DP-GMM Model
LRMF Model
The Entire Graphical Model
Variational Inference
Experimental Results
Simulated Data Experiments
Real Data Experiments
Conclusions

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