Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition (1707.02477v1)

Abstract: Hyperspectral images (HSIs) are often corrupted by a mixture of several types of noise during the acquisition process, e.g., Gaussian noise, impulse noise, dead lines, stripes, and many others. Such complex noise could degrade the quality of the acquired HSIs, limiting the precision of the subsequent processing. In this paper, we present a novel tensor-based HSI restoration approach by fully identifying the intrinsic structures of the clean HSI part and the mixed noise part respectively. Specifically, for the clean HSI part, we use tensor Tucker decomposition to describe the global correlation among all bands, and an anisotropic spatial-spectral total variation (SSTV) regularization to characterize the piecewise smooth structure in both spatial and spectral domains. For the mixed noise part, we adopt the $\ell_1$ norm regularization to detect the sparse noise, including stripes, impulse noise, and dead pixels. Despite that TV regulariztion has the ability of removing Gaussian noise, the Frobenius norm term is further used to model heavy Gaussian noise for some real-world scenarios. Then, we develop an efficient algorithm for solving the resulting optimization problem by using the augmented Lagrange multiplier (ALM) method. Finally, extensive experiments on simulated and real-world noise HSIs are carried out to demonstrate the superiority of the proposed method over the existing state-of-the-art ones.

• The paper proposes a novel hyperspectral image restoration method that combines low-rank tensor decomposition with anisotropic spatial-spectral TV regularization.
• It leverages Tucker decomposition to efficiently capture spatial-spectral correlations and separates mixed noise components via ℓ1 and Frobenius norms.
• Empirical results demonstrate significant improvements in MPSNR and MSSIM, outperforming conventional methods in simulated and real-world data.

Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition

The paper "Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition" introduces an advanced method for restoring hyperspectral images (HSIs) afflicted by complex noise typically encountered in the acquisition process. The focus of this research is to effectively address the mixed noise challenge, which includes various noise types such as Gaussian noise, impulse noise, dead lines, and stripes.

Methodological Approach

The authors propose a novel restoration framework leveraging low-rank tensor decomposition and total variation (TV) regularization tailored explicitly for hyperspectral data. The key contributions of their method include:

1. Tensor-based Decomposition: The clean hyperspectral image is assumed to have low-rank characteristics, which are exploited using Tucker decomposition. This decomposition captures the spatial and spectral correlations efficiently, which are inherent in hyperspectral data.
2. Anisotropic Spatial-Spectral TV (SSTV) Regularization: Unlike traditional TV approaches, the SSTV regularizer simultaneously considers spatial and spectral dimensions, preserving edge and texture details while reducing noise. This dual consideration of spatial and spectral smoothness is a critical advancement for hyperspectral image processing.
3. Separation of Noise Components: The method explicitly models both sparse noise using the $\ell_1$ norm and Gaussian noise with the Frobenius norm, providing a comprehensive approach to noise separation and removal.
4. Optimization via ALM: The paper develops an efficient algorithm based on the augmented Lagrange multiplier method to solve the resulting complex optimization problem. This ensures the method's applicability to real-world datasets despite the nonconvex nature of the issue.

Empirical Evaluation

The extensive empirical evaluations underscore the effectiveness of the proposed method. Noteworthy results include:

• The demonstrated outperformance over several prevailing methods such as NNM, WNNM, LRMR, and LRTV in both simulated and real data scenarios.
• Significant improvements in quantitative metrics like MPSNR and MSSIM, and superior visual quality of restored images.
• Enhanced capability to handle real-world HSIs where noise components are not uniform, exemplifying robustness against varied noise intensities.

Implications and Future Directions

The research has meaningful implications for fields relying on hyperspectral imagery, such as remote sensing, agriculture, and mineral exploration. The enhanced clarity and accuracy in restored images can significantly impact downstream tasks like classification, monitoring, and anomaly detection.

Looking toward future research, this method paves the way for further exploration into tensor-based models, possibly incorporating machine learning techniques for automated noise parameter estimation. Additionally, advancements in hardware for real-time tensor computations could enhance the method's practicability in operational settings. Integrating deep learning frameworks to automate and possibly improve the heuristic parameter settings of the existing method could be a rewarding pursuit.

In summary, this paper contributes a nuanced and effective approach to hyperspectral image restoration, addressing a pivotal gap in dealing with mixed noise through an innovative combination of low-rank tensor decomposition and TV regularization.