Non-local Meets Global: An Iterative Paradigm for Hyperspectral Image Restoration (2010.12921v1)

Abstract: Non-local low-rank tensor approximation has been developed as a state-of-the-art method for hyperspectral image (HSI) restoration, which includes the tasks of denoising, compressed HSI reconstruction and inpainting. Unfortunately, while its restoration performance benefits from more spectral bands, its runtime also substantially increases. In this paper, we claim that the HSI lies in a global spectral low-rank subspace, and the spectral subspaces of each full band patch group should lie in this global low-rank subspace. This motivates us to propose a unified paradigm combining the spatial and spectral properties for HSI restoration. The proposed paradigm enjoys performance superiority from the non-local spatial denoising and light computation complexity from the low-rank orthogonal basis exploration. An efficient alternating minimization algorithm with rank adaptation is developed. It is done by first solving a fidelity term-related problem for the update of a latent input image, and then learning a low-dimensional orthogonal basis and the related reduced image from the latent input image. Subsequently, non-local low-rank denoising is developed to refine the reduced image and orthogonal basis iteratively. Finally, the experiments on HSI denoising, compressed reconstruction, and inpainting tasks, with both simulated and real datasets, demonstrate its superiority with respect to state-of-the-art HSI restoration methods.

• The paper introduces an iterative paradigm for hyperspectral image restoration that combines non-local spatial denoising with global low-rank spectral subspace modeling.
• An efficient alternating minimization algorithm iteratively optimizes the latent HSI estimate and learns the spectral orthogonal basis for improved quality.
• Empirical validation on simulated and real datasets shows this method outperforms existing state-of-the-art approaches for various HSI restoration tasks like denoising and inpainting.

Overview of Hyperspectral Image Restoration Paradigm

The paper "Non-local Meets Global: An Iterative Paradigm for Hyperspectral Image Restoration" presents a unified approach for hyperspectral image (HSI) restoration, incorporating both spatial and spectral properties through a non-local low-rank tensor approximation method. The paradigm addresses key HSI restoration tasks: denoising, compressed HSI reconstruction, and inpainting. The novelty lies in the integration of non-local spatial denoising with low-rank orthogonal basis exploration, offering a balance between computational efficiency and restoration performance.

HSI restoration traditionally employs either spatial or spectral priors, but the proposed framework skillfully combines these for enhanced restoration outcomes. HSIs exhibit spectral redundancy, which allows leveraging spatial and spectral correlations to inform restoration processes. The paper's methodology includes an iterative optimization scheme—alternating between estimating the latent input HSI and optimizing the spectral orthogonal basis to refine image quality iteratively. This iterative paradigm demonstrates superiority over existing non-local and low-rank restoration approaches, as evidenced by comprehensive experimental validation on simulated and real-world datasets.

Technical Contributions

1. Proposed Paradigm: The paper introduces a paradigm that models HSIs in a global low-rank spectral subspace, and each full band patch group similarly lies within this subspace. This formulation effectively utilizes spectral and spatial correlations for HSI restoration, optimizing over orthogonal basis matrices and reduced images.
2. Optimization Strategy: An efficient alternating minimization algorithm is developed, focusing on the fidelity term related to the latent input image, followed by spectral basis learning and non-local denoising. This strategy balances computational demands while preserving restoration quality.
3. Efficient Numerical Algorithm: The proposed paradigm includes rank adaptation within an alternating minimization framework, facilitating the dynamic learning of parameters relevant to spectral dimensions while maintaining orthogonality constraints.
4. Empirical Analysis and Robustness: Real-world experimentation substantiates the paradigm’s robustness. Tests on simulated and real datasets highlight its efficacy against various kinds of HSI degradations, affirming its advantage over other state-of-the-art restoration methods.

Implications and Future Directions

The integration of non-local spatial denoising with spectral low-rank subspace modeling represents a promising shift in approach within HSI restoration research. Practically, this paradigm can be extended to other multidimensional image restoration challenges, potentially influencing sensor development and broadening applications in remote sensing, medical imaging, and environmental monitoring.

In theoretical terms, this work invites further exploration into optimization techniques for faster convergence without compromising the accuracy of restoration—especially as imaging technology advances and computational capacities grow. Future developments might investigate adaptive mechanisms for spectral and spatial correlation exploration using machine learning or deep learning methodologies, thus expanding the paradigm's applicability and effectiveness in new imaging domains.