Multispectral Images Denoising by Intrinsic Tensor Sparsity Regularization

Xie, Qi; Zhao, Qian; Meng, Deyu; Zhao, Xu; Gu, Shuhang; Zuo, Wangmeng; Zhang, Lei

doi:10.1109/cvpr.2016.187

Cited by 199 publications

(104 citation statements)

References 27 publications

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“…However, the low-rank formulation neglects the structure information among spatial dimension. One of the promising solutions is to utilize the tensor properties in the static anatomical component ℬ [21], [25]. In this study, two tensor-based models are introduced to describe the static anatomical component ℬ, i.e., Tensor-based regularization model and Nonlocal Tensor-based regularization model …”

Section: Methodsmentioning

confidence: 99%

“…Because both Tucker decomposition [22] and CP decomposition [23] contain insightful tensor sparsity, by integrating rational sparsity understanding elements from both decomposition forms, the low-rankness characteristic of the static anatomical component ℬ can be constructed by a powerful KBR measure, for measuring low-rankness extent of a tensor, which is proposed in [25]:

Ω_{2} false(ℬ false) = {false‖ 𝒞 false‖}_{0} + ζ \prod_{i = 1}^{3} italicrank false(B_{false(i false)} false),

where 𝒞 denotes the core tensor of ℬ in the Tucker decomposition. B ( i ) represents the mode- i (1 ≤ i ≤ 3) unfolding matrix, and ζ is the penalty parameter controlling the tradeoff between two terms B ( i ) = unfold i (ℬ).…”

Section: Methodsmentioning

confidence: 99%

“…In addition, it is noted that the R (ℬ) in Eq. (6) takes both intrinsic sparsity existing in Tucker and CP decompositions into consideration, i.e., the first term constrains the number of Kronecker bases that describe the static anatomical component ℬ, and the second term physically represents the size of core tensor in the Tucker decomposition by penalizing the low-rank property along each tensor mode [25]. …”

Section: Methodsmentioning

confidence: 99%

“…(17) can be transformed into as follows:

max_{U_{1}^{T} U_{1} = 1} false〈 A_{1}, U_{1} false〉,

where

A_{1} = - {true(\frac{false(γ false(𝒳 - ℱ false) + \sum_{i} italicFold false(η_{i}^{B} B_{false(i false)} - Λ_{i} B false) false)}{γ + 3 μ} true)}_{false(1 false)} \times false(U_{2} \otimes U_{3} false) 𝒞_{false(1 false)}^{T}

According to Xie’s work [25], the solution of Eq. (18) can be written as

U_{1}^{+} = D_{1} E_{1}^{T}

, where

A_{1} = D_{1} normalΦ E_{1}^{T}

is the SVD decomposition of A 1 .…”

Section: Methodsmentioning

confidence: 99%

See 3 more Smart Citations

Low-Dose Dynamic Cerebral Perfusion Computed Tomography Reconstruction via Kronecker-Basis-Representation Tensor Sparsity Regularization

Zeng

Xie

Cao

et al. 2017

IEEE Trans. Med. Imaging

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Dynamic cerebral perfusion computed tomography (DCPCT) has the ability to evaluate the hemodynamic information throughout the brain. However, due to multiple 3-D image volume acquisitions protocol, DCPCT scanning imposes high radiation dose on the patients with growing concerns. To address this issue, in this paper, based on the robust principal component analysis (RPCA, or equivalently the low-rank and sparsity decomposition) model and the DCPCT imaging procedure, we propose a new DCPCT image reconstruction algorithm to improve low dose DCPCT and perfusion maps quality via using a powerful measure, called Kronecker-basis-representation tensor sparsity regularization, for measuring low-rankness extent of a tensor. For simplicity, the first proposed model is termed tensor-based RPCA (T-RPCA). Specifically, the T-RPCA model views the DCPCT sequential images as a mixture of low-rank, sparse, and noise components to describe the maximum temporal coherence of spatial structure among phases in a tensor framework intrinsically. Moreover, the low-rank component corresponds to the “background” part with spatial–temporal correlations, e.g., static anatomical contribution, which is stationary over time about structure, and the sparse component represents the time-varying component with spatial–temporal continuity, e.g., dynamic perfusion enhanced information, which is approximately sparse over time. Furthermore, an improved nonlocal patch-based T-RPCA (NL-T-RPCA) model which describes the 3-D block groups of the “background” in a tensor is also proposed. The NL-T-RPCA model utilizes the intrinsic characteristics underlying the DCPCT images, i.e., nonlocal self-similarity and global correlation. Two efficient algorithms using alternating direction method of multipliers are developed to solve the proposed T-RPCA and NL-T-RPCA models, respectively. Extensive experiments with a digital brain perfusion phantom, preclinical monkey data, and clinical patient data clearly demonstrate that the two proposed models can achieve more gains than the existing popular algorithms in terms of both quantitative and visual quality evaluations from low-dose acquisitions, especially as low as 20 mAs.

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Section: Methodsmentioning

confidence: 99%

Ω_{2} false(ℬ false) = {false‖ 𝒞 false‖}_{0} + ζ \prod_{i = 1}^{3} italicrank false(B_{false(i false)} false),

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

“…(17) can be transformed into as follows:

max_{U_{1}^{T} U_{1} = 1} false〈 A_{1}, U_{1} false〉,

where

A_{1} = - {true(\frac{false(γ false(𝒳 - ℱ false) + \sum_{i} italicFold false(η_{i}^{B} B_{false(i false)} - Λ_{i} B false) false)}{γ + 3 μ} true)}_{false(1 false)} \times false(U_{2} \otimes U_{3} false) 𝒞_{false(1 false)}^{T}

According to Xie’s work [25], the solution of Eq. (18) can be written as

U_{1}^{+} = D_{1} E_{1}^{T}

, where

A_{1} = D_{1} normalΦ E_{1}^{T}

is the SVD decomposition of A 1 .…”

Section: Methodsmentioning

confidence: 99%

See 2 more Smart Citations

Low-Dose Dynamic Cerebral Perfusion Computed Tomography Reconstruction via Kronecker-Basis-Representation Tensor Sparsity Regularization

Zeng

Xie

Cao

et al. 2017

IEEE Trans. Med. Imaging

Self Cite

View full text Add to dashboard Cite

show abstract

“…A common relaxation is the use of ℓ 1 plus the nuclear norm. An alternative relaxation is the use of concave penalties (Table 1, such as MCP, log or exponential type penalty, and SCAD), which have been verified to be very effective including biomolecular network reconstruction and image denoising [7, 8]. However, this concave approach so far has only been applied in sparse estimation problems.…”

Section: Introductionmentioning

confidence: 99%

Learning Latent Variable Gaussian Graphical Model for Biomolecular Network with Low Sample Complexity

Wang

Liu

Yuan

2016

Computational and Mathematical Methods in Medicine

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Learning a Gaussian graphical model with latent variables is ill posed when there is insufficient sample complexity, thus having to be appropriately regularized. A common choice is convex ℓ 1 plus nuclear norm to regularize the searching process. However, the best estimator performance is not always achieved with these additive convex regularizations, especially when the sample complexity is low. In this paper, we consider a concave additive regularization which does not require the strong irrepresentable condition. We use concave regularization to correct the intrinsic estimation biases from Lasso and nuclear penalty as well. We establish the proximity operators for our concave regularizations, respectively, which induces sparsity and low rankness. In addition, we extend our method to also allow the decomposition of fused structure-sparsity plus low rankness, providing a powerful tool for models with temporal information. Specifically, we develop a nontrivial modified alternating direction method of multipliers with at least local convergence. Finally, we use both synthetic and real data to validate the excellence of our method. In the application of reconstructing two-stage cancer networks, “the Warburg effect” can be revealed directly.

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Framelet tensor sparsity with block matching for spectral CT reconstruction

Cai

Wang

et al. 2022

Medical Physics

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Spectral computed tomography (CT) based on the photon-counting detection system has the capability to produce energy-discriminative attenuation maps of objects with a single scan. However, the insufficiency of photons collected into the narrow energy bins results in high quantum noise levels causing low image quality. This work aims to improve spectral CT image quality by developing a novel regularization based on framelet tensor prior. Methods: First, similar patches are extracted from highly correlated interchannel images in spectral and spatial domains, and stacked to form a third-order tensor after vectorization along the energy channels. Second, the framelet tensor nuclear norm (FTNN) is introduced and applied to construct the regularization to exploit the sparsity embedded in nonlocal similarity of spectral images, and thus the reconstruction problem is modeled as a constrained optimization. Third, an iterative algorithm is proposed by utilizing the alternating direction method of multipliers framework in which efficient solvers are developed for each subproblem. Results: Both numerical simulations and real data verifications were performed to evaluate and validate the proposed FTNN-based method. Compared to the analytic, TV-based, and the state-of -the-art tensor-based methods, the proposed method achieves higher numerical accuracy on both reconstructed CT images and decomposed material maps in the mouse data indicating the capability in noise suppression and detail preservation of the proposed method. Conclusions: A framelet tensor sparsity-based iterative algorithm is proposed for spectral reconstruction. The qualitative and quantitative comparisons show a promising improvement of image quality, indicating its promising potential in spectral CT imaging.

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Multispectral Images Denoising by Intrinsic Tensor Sparsity Regularization

Cited by 199 publications

References 27 publications

Low-Dose Dynamic Cerebral Perfusion Computed Tomography Reconstruction via Kronecker-Basis-Representation Tensor Sparsity Regularization

Low-Dose Dynamic Cerebral Perfusion Computed Tomography Reconstruction via Kronecker-Basis-Representation Tensor Sparsity Regularization

Learning Latent Variable Gaussian Graphical Model for Biomolecular Network with Low Sample Complexity

Framelet tensor sparsity with block matching for spectral CT reconstruction

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