Exact Decomposition of Joint Low Rankness and Local Smoothness Plus Sparse Matrices

Peng, Jiangjun; Wang, Yao; Zhang, Hongying; Wang, Jianjun; Meng, Deyu

doi:10.1109/tpami.2022.3204203

Cited by 26 publications

(5 citation statements)

References 65 publications

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“…Wang et al [19] integrated the spatial-spectral joint TV into low-Tucker-rank tensor decomposition. Besides, there has also emerged several transform-based TV variants, such as group TV [34], E3DTV [35], CTV [36], and t-CTV [37], gaining improved denoising performance. Except for the local prior, the nonlocal self-similarity is more widely used in many works for normal Gaussian denoising tasks [17], [20], [21], [22], [23].…”

Section: A Nsr-unrelated Workmentioning

confidence: 99%

“…We first conduct denoising experiments on simulated datasets with ground truth to quantitatively evaluate the performance of the proposed NS3R method. The following 13 related methods are used for comparison, which can be divided into two categories corresponding to the related works in Section II, i.e., the NSR -unrelated methods, including BM4D [55], LRMR [10], E3DTV [35], CTV [36], TDL [17], LLRT [20], KBR [21], and RCTV [42], and NSR -related methods, including FastHyDe [25], SNLRSF [27], NGmeet [28], GLF [26], and TenSRDe [29]. They are mostly representative of the state-of-the-art for HSI denoising.…”

Section: A Simulated Experimentsmentioning

confidence: 99%

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Hyperspectral Image Denoising via Nonlocal Spectral Sparse Subspace Representation

Wang

Peng

Cao

et al. 2023

IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing

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Hyperspectral image (HSI) denoising based on nonlocal subspace representation has attracted a lot of attention recently. However, most of the existing works mainly focus on refining the representation coefficient images (RCIs) using certain nonlocal denoiser but ignore the understanding why these pseudoimages have a similar spatial structure as the original HSI. In this work, we revisit such vein from the respective of principal component analysis (PCA). Inspired by an alternative sparse PCA, we propose a spectral sparse subspace representation strategy to simultaneously learn low-dimensional spectral subspace and novel RCIs with sparse loadings. It turns out that the resulting RCIs possess a more significant spatial structure due to the adaptive sparse combination of spectral bands. A simple nonlocal low-rank approximation is then employed to further remove the residual noise of the RCIs. Finally, the entire denoised HSI is obtained by inverse spectral sparse PCA. Extensive experiments on the simulated and real HSI datasets show that the proposed nonlocal spectral sparse subspace representation method, dubbed as NS3R, has excellent performance both in denoising effect and running time compared with many other state-of-the-art methods.

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Section: A Nsr-unrelated Workmentioning

confidence: 99%

Section: A Simulated Experimentsmentioning

confidence: 99%

Hyperspectral Image Denoising via Nonlocal Spectral Sparse Subspace Representation

Wang

Peng

Cao

et al. 2023

IEEE J. Sel. Top. Appl. Earth Observations Remote Sensing

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“…4) Fused Low-Rank and Local Smoothness Prior: Recently, there has been a trend to combine gradient sparsity and lowrank priors into a single regularization term [50]- [52]. One typical method is the Representative Coefficient Total Variation (RCTV), which operates within the matrix factorization framework, formulated as X = UV T in matrix notation, or expressed as X = U × 3 V in tensor notation.…”

Section: B Internal Prior Modelingmentioning

confidence: 99%

“…The compared methods include tensor dictionary learning (TDL) 2 [48], TCTV 3 [51], LMHTV 4 [39], LTHTV 5 [39], LRTV 6 [16], non-local meets global (NGMeet) 7 [69], RCTV 8 [52], weighted non-local low-rank model with adaptive TV regularization (WNLRATV) 9 [44], BALMF 10 [11], and CTV 11 [50]. Besides these internal information based methods, it also compares deep learning methods, including RC image learnable denoiser (RCILD) 12 [70], and hierarchical low-rank tensor factorization (HLRTF) 13 [71].…”

Section: B Experiments On Synthetic Datasetsmentioning

confidence: 99%

Hyperspectral Image Denoising by Asymmetric Noise Modeling

Cao

Peng

et al. 2022

IEEE Trans. Geosci. Remote Sensing

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This paper introduces a novel paradigm for hyperspectral image (HSI) denoising, which is termed pan-denoising. In a given scene, panchromatic (PAN) images capture similar structures and textures to HSIs but with less noise. This enables the utilization of PAN images to guide the HSI denoising process. Consequently, pan-denoising, which incorporates an additional prior, has the potential to uncover underlying structures and details beyond the internal information modeling of traditional HSI denoising methods. However, the proper modeling of this additional prior poses a significant challenge. To alleviate this issue, the paper proposes a novel regularization term, Panchromatic Weighted Representation Coefficient Total Variation (PWRCTV). It employs the gradient maps of PAN images to automatically assign different weights of TV regularization for each pixel, resulting in larger weights for smooth areas and smaller weights for edges. This regularization forms the basis of a pan-denoising model, which is solved using the Alternating Direction Method of Multipliers. Extensive experiments on synthetic and realworld datasets demonstrate that PWRCTV outperforms several state-of-the-art methods in terms of metrics and visual quality. Furthermore, an HSI classification experiment confirms that PWRCTV, as a preprocessing method, can enhance the performance of downstream classification tasks. The code and data are available at https://github.com/shuangxu96/PWRCTV.

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“…To address the challenges, most conventional approaches borrow certain hand-crafted priors to enforce the reconstructed images enjoy truthful visual properties. For example, techniques such as sparse representation (Wang et al 2023a), low rankness (Peng et al 2023), edge sharpness (Huang et al 2022), and non-local similarity (Wen et al 2023) have been extensively investigated and yield commendable performance. These solutions incrementally ameliorate image quality through iterative updates, which often suffer from the expense of massive execution time and the risk of oversmoothed recoveries.…”

Section: Introductionmentioning

confidence: 99%

Null Space Matters: Range-Null Decomposition for Consistent Multi-Contrast MRI Reconstruction

Chen,

Jiang,

et al. 2024

AAAI

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Consistency and interpretability have long been the critical issues in MRI reconstruction. While interpretability has been dramatically improved with the employment of deep unfolding networks (DUNs), current methods still suffer from inconsistencies and generate inferior anatomical structure. Especially in multi-contrast scenes, different imaging protocols often exacerbate the concerned issue. In this paper, we propose a range-null decomposition-assisted DUN architecture to ensure consistency while still providing desirable interpretability. Given the input decomposed, we argue that the inconsistency could be analytically relieved by feeding solely the null-space component into proximal mapping, while leaving the range-space counterpart fixed. More importantly, a correlation decoupling scheme is further proposed to narrow the information gap for multi-contrast fusion, which dynamically borrows isotropic features from the opponent while maintaining the modality-specific ones. Specifically, the two features are attached to different frequencies and learned individually by the newly designed isotropy encoder and anisotropy encoder. The former strives for the contrast-shared information, while the latter serves to capture the contrast-specific features. The quantitative and qualitative results show that our proposal outperforms most cutting-edge methods by a large margin. Codes will be released on https://github.com/chenjiachengzzz/RNU.

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Exact Decomposition of Joint Low Rankness and Local Smoothness Plus Sparse Matrices

Cited by 26 publications

References 65 publications

Hyperspectral Image Denoising via Nonlocal Spectral Sparse Subspace Representation

Hyperspectral Image Denoising via Nonlocal Spectral Sparse Subspace Representation

Hyperspectral Image Denoising by Asymmetric Noise Modeling

Null Space Matters: Range-Null Decomposition for Consistent Multi-Contrast MRI Reconstruction

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