Fast Hyperspectral Image Denoising and Inpainting Based on Low-Rank and Sparse Representations (2103.06842v1)

Abstract: This paper introduces two very fast and competitive hyperspectral image (HSI) restoration algorithms: fast hyperspectral denoising (FastHyDe), a denoising algorithm able to cope with Gaussian and Poissonian noise, and fast hyperspectral inpainting (FastHyIn), an inpainting algorithm to restore HSIs where some observations from known pixels in some known bands are missing. FastHyDe and FastHyIn fully exploit extremely compact and sparse HSI representations linked with their low-rank and self-similarity characteristics. In a series of experiments with simulated and real data, the newly introduced FastHyDe and FastHyIn compete with the state-of-the-art methods, with much lower computational complexity.

• The paper introduces FastHyDe and FastHyIn, which enhance hyperspectral image restoration using low-rank and sparse representations.
• FastHyDe reduces noise by projecting data onto lower-dimensional subspaces and applying non-local patch-based denoising, achieving superior PSNR and SSIM performance.
• FastHyIn reconstructs missing spectral bands by exploiting spatial and spectral coherence, making it effective for real-time, large-scale hyperspectral applications.

An Analytical Evaluation of "Fast Hyperspectral Image Denoising and Inpainting Based on Low-Rank and Sparse Representations"

The academic work presented in "Fast Hyperspectral Image Denoising and Inpainting Based on Low-Rank and Sparse Representations" introduces two notable algorithms for hyperspectral image (HSI) processing: Fast Hyperspectral Denoising (FastHyDe) and Fast Hyperspectral Inpainting (FastHyIn). Both algorithms exploit the intrinsic properties of HSIs, namely their low-rank spectral structure and spatial self-similarity, to achieve efficient denoising and inpainting with reduced computational complexity compared to existing methods.

Overview and Methodological Contributions

FastHyDe leverages low-rank matrix representations and considers both Gaussian and Poissonian noise. The algorithm capitalizes on the compact representation of hyperspectral data by projecting spectral vectors into lower-dimensional subspaces. Subsequently, it applies state-of-the-art non-local patch-based denoising techniques to the resulting eigen-images, derived from the subspace representation. This formulation allows FastHyDe to achieve significant noise reduction with fewer computational demands.

FastHyIn, the proposed hyperspectral inpainting algorithm, extends the principles of FastHyDe to scenarios where data from certain spectral bands are missing. It reconstructs missing pixel data by utilizing the coherence across spatial and spectral dimensions. With known missing data positions, FastHyIn effectively combines subspace learning with eigen-image denoising to restore the complete data set.

Numerical Evaluations and Performance Analysis

The paper presents extensive evaluations using both simulated and real hyperspectral datasets, establishing FastHyDe and FastHyIn's competitive edge over state-of-the-art methods such as BM3D, BM4D, and PCA+BM4D in terms of PSNR and SSIM metrics. Notably:

• FastHyDe outperforms other techniques in terms of denoising efficacy while maintaining lower complexity, as evidenced by shorter computational times across various test datasets.
• The robustness of FastHyDe with respect to subspace dimension overestimation is highlighted, which minimizes the need for precise parameter tuning.
• FastHyIn effectively handles the inpainting of incomplete hyperspectral data, outperforming methodologies such as PDE, UBD, and LRTV, especially in noise removal from real-world contaminated data.

Practical and Theoretical Implications

From a practical standpoint, the reduced computational complexity of FastHyDe and FastHyIn positions them as efficient tools for real-time and large-scale hyperspectral applications, such as in environmental monitoring and remote sensing. The methods’ reliance on pre-learned subspace representations also facilitates their application in devices with constrained computational resources.

Theoretically, the methodologies reinforce the applicability of low-rank and sparse representation models in hyperspectral imaging, presenting pathways for further research into more complex noise models and transformation techniques that can further improve restoration quality. The paper also suggests potential explorations into the use of machine learning techniques to enhance the subspace learning process of HSIs.

Conclusion

While FastHyDe and FastHyIn have proven to be effective solutions for hyperspectral denoising and inpainting, future work could explore the integration with machine learning frameworks to learn the subspace adaptively in dynamic environments or investigate finer models to account for more complex noise scenarios. The methods contribute substantially to advancing HSI processing, with a balanced focus on computational efficiency and result accuracy.