| Author: | Yu, Shijie |
| Title: | Orthogonal constrained minimization with tensor group sparsity regularization for hyperspectral image restoration |
| Advisors: | Chen, Xiaojun (AMA) |
| Degree: | Ph.D. |
| Year: | 2025 |
| Department: | Department of Applied Mathematics |
| Pages: | xxii, 106 pages : color illustrations |
| Language: | English |
| Abstract: | Hyperspectral images (HSIs) captured by hyperspectral sensors often suffer from noise, blurring, and other degradations, which can significantly reduce their visual quality and the accuracy of the subsequent tasks. Traditional HSI restoration methods typically process the spatial information of HSIs on a band-by-band basis, which neglects the spectral information inherent. Also, those methods often use elementwise sparsity measures to characterize sparse components, which fail to recognize the linear structures within these components. This thesis aims to develop new approaches based on (nonlocal) low-rank tensor regularization and tensor group sparsity ℓ2,p norm (0 < p < 1), along with some spatial and spectral priors, to provide a more comprehensive method that preserves the structure of HSIs. It includes two optimization models and two algorithms for solving two important problems in HSI processing. Firstly, we present a class of orthogonal constrained minimization problems to tackle HSI restoration problems, such as removing mixed noise like Gaussian noise, stripes, and dead lines. The proposed class of models employs two types of regularization terms. One is a tensor group sparsity regularization term for removing structured noise. We use the tensor ℓ2,p norm, extended from the matrix ℓ2,p norm, and provide a solution for the proximal operator of the tensor ℓ2,p norm. The other term is a new sparsity-enhanced nonlocal low-rank tensor regularization for removing Gaussian noise. This regularization term exploits the spatial nonlocal self-similarity and spectral correlation in HSIs to enhance restoration, ensuring that similar patterns in distant regions are jointly considered for improved denoising. Specifically, we propose a weighted tensor ℓ2,p norm to enhance sparsity in the core tensor, promoting low-rankness in nonlocal similar matching blocks. Secondly, we adopt a proximal block coordinate descent (P-BCD) algorithm to solve the proposed nonconvex nonsmooth minimization with orthogonal constraints. The solution to each subproblem in the P-BCD algorithm can be efficiently computed. The first order optimality condition of the problem is defined by substationarity, symmetry, and feasibility. We prove that any accumulation point of the generated sequence by the P-BCD algorithm is a first order stationary point. Thirdly, we apply the proposed approach to HSI denoising and destriping, and conduct numerical experiments to validate the superiority of our proposed approach. We test it on simulated noisy HSIs generated from several datasets under various mixed noise conditions, as well as on a real dataset. The results demonstrate that our method outperforms others in metrics such as mean peak signal-to-noise ratio. In terms of visual quality, our method effectively restores HSIs by preserving important image details and removing noise, particularly highly structured noise like stripes and dead lines. Lastly, we combine the proposed model with a deep neural network to incorporate an implicit proximal denoiser prior. Specifically, for detecting anomaly objections in noisy HSIs, the tensor ℓ2,p norm in the original model is utilized to characterize the anomalies, while the implicit proximal denoiser prior is employed to remove Gaussian noise. The P-BCD method remains effective for solving the newly proposed model, with certain steps updated using a proximal denoiser within a plug-and-play (PnP) framework. We evaluate this PnP version of the P-BCD method (PnP-PBCD) on anomaly detection in HSI contaminated with or without Gaussian noise. The results demonstrate that the proposed method can effectively detect anomalous objects, whereas competing methods may mistakenly identify noise as anomalies or incorrectly match the anomalous objects due to noise interference. In summary, the orthogonal constrained minimization models with tensor group sparsity regularization are well-suited for various image restoration problems. Additionally, the P-BCD method and its PnP version are reliable with convergence guarantees. |
| Rights: | All rights reserved |
| Access: | open access |
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