Fraction-order total variation blind image restoration based on L1-norm

Zhou, Luoyu; Tang, Jiaxin

doi:10.1016/j.apm.2017.07.009

Cited by 26 publications

(13 citation statements)

References 13 publications

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“…2. Zhou L et al proposed the blind restoration method in [5] which is based on fraction-order variation with no prior.…”

Section: Resultsmentioning

confidence: 99%

“…It is firstly applied in image denoising and obtains excellent denosing results. Motivated by successful application in denoising, it is applied in image blind restoration to achieve details and suppress the artificial edges simultaneously [5], shown as…”

Section: Blind Restoration Model Based On Prior Information a Frmentioning

confidence: 99%

“…Chen R et al proposed a high-order regularization term for aerial image blind restoration in [4]. Zhou L et al proposed a fraction-order TV image blind restoration method in [5]. However, in these methods, there is no other prior information apart from TV regularization terms, and thus the restoration results still need to be improved.…”

Section: Introductionmentioning

confidence: 99%

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Fraction-Order Total Variation Image Blind Restoration Based on Self-Similarity Features

et al. 2020

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To improve the artifacts of the restoration results restored by existing blind restoration method, an effective image blind restoration method using self-similarity as prior information is proposed for restoring the blurry images. Firstly, the fraction-order model is achieved by extending integer-order total variation, which is prone to reduce artifacts. Motivated by the fact that the introduction of prior information is beneficial to improve the restoration results, we found that natural images usually exhibit some texture features. Self-similarity is a popular texture features and well-defined in the statistics. Therefore, this texture feature is introduced as prior information for the restoration model and further improving the restoration results. Finally, the cost function is generated and solved by semi-quadratic regularization. Experiments on various natural images showed that the proposed method can improve the performance relative to other image blind restoration algorithms in terms of both subjective vision and objective evaluation. The subjective analysis revealed that the proposed algorithm resulted in improved translation and improved artifact appearance. The objective evaluation showed that the proposed algorithm showed the best evaluation values, including Structural Similarity and Peak Signal-to-noise ratio. The restoration results of various images reveal that the proposed method is practical and effective in image restoration. INDEX TERMS Image blind restoration, texture features, fraction-order total variation, prior information.

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“…2. Zhou L et al proposed the blind restoration method in [5] which is based on fraction-order variation with no prior.…”

Section: Resultsmentioning

confidence: 99%

Section: Blind Restoration Model Based On Prior Information a Frmentioning

confidence: 99%

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Fraction-Order Total Variation Image Blind Restoration Based on Self-Similarity Features

et al. 2020

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“…In some situations, an anisotropic scheme ( 1 norm) may be used [31], leading to the anisotropic discrete TV that can be written as…”

Section: The Shannon Total Variationmentioning

confidence: 99%

Low-Rank Tensor Completion and Total Variation Minimization for Color Image Inpainting

Qin

Chen

et al. 2020

IEEE Access

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Low-rank (LR) and total variation (TV) are two most frequent priors that occur in image processing problems, and they have sparked a tremendous amount of researches, particularly for moving from scalar to vector, matrix or even high-order based functions. However, discretization schemes used for TV regularization often ignore the difference of the intrinsic properties, so it will lead to the problem that local smoothness cannot be effectively generated, let alone the problem of blurred edges. To address the image inpainting problem with corrupted data, in this paper, the color images are naturally considered as three-dimensional tensors, whose prior of smoothness can be measured by varietal TV norm along different dimensions. Specifically, we propose incorporating Shannon total variation (STV) and low-rank tensor completion (LRTC) into the construction of the final cost function, in which a new nonconvex low-rank constraint, namely truncated γ-norm, is involved for closer rank approximation. Moreover, two methods are developed, i.e., LRRSTV and LRRSTV-T, due to the fact that LRTC can be represented by tensor unfolding and tensor decomposition. The final solution can be achieved by a practical variant of the augmented Lagrangian alternating direction method (ALADM). Experiments on color image inpainting tasks demonstrate that the proposed methods perform better then the state-of-the-art algorithms, both qualitatively and quantitatively.

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“…Roughly, the existing construction algorithms can be divided into four classes: greedy pursuit algorithms such as matching pursuit (MP) [ 11 ], orthogonal matching pursuit (OMP) [ 12 , 13 ], etc. ; convex regularization methods such as the family of L1-norm [ 14 ]; non-convex regularization methods such as the family of nonconvex Lp-norm (0 < p < 1) [ 15 , 16 ]; and sparse low rank matrix (SLRM) approaches such as non-separable SLRM regularization [ 17 , 18 , 19 ], etc. …”

Section: Introductionmentioning

confidence: 99%

Multichannel Signals Reconstruction Based on Tunable Q-Factor Wavelet Transform-Morphological Component Analysis and Sparse Bayesian Iteration for Rotating Machines

Hu²,

Peng³

2018

Entropy

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High-speed remote transmission and large-capacity data storage are difficult issues in signals acquisition of rotating machines condition monitoring. To address these concerns, a novel multichannel signals reconstruction approach based on tunable Q-factor wavelet transform-morphological component analysis (TQWT-MCA) and sparse Bayesian iteration algorithm combined with step-impulse dictionary is proposed under the frame of compressed sensing (CS). To begin with, to prevent the periodical impulses loss and effectively separate periodical impulses from the external noise and additive interference components, the TQWT-MCA method is introduced to divide the raw vibration signal into low-resonance component (LRC, i.e., periodical impulses) and high-resonance component (HRC), thus, the periodical impulses are preserved effectively. Then, according to the amplitude range of generated LRC, the step-impulse dictionary atom is designed to match the physical structure of periodical impulses. Furthermore, the periodical impulses and HRC are reconstructed by the sparse Bayesian iteration combined with step-impulse dictionary, respectively, finally, the final reconstructed raw signals are obtained by adding the LRC and HRC, meanwhile, the fidelity of the final reconstructed signals is tested by the envelop spectrum and error analysis, respectively. In this work, the proposed algorithm is applied to simulated signal and engineering multichannel signals of a gearbox with multiple faults. Experimental results demonstrate that the proposed approach significantly improves the reconstructive accuracy compared with the state-of-the-art methods such as non-convex Lq (q = 0.5) regularization, spatiotemporal sparse Bayesian learning (SSBL) and L1-norm, etc. Additionally, the processing time, i.e., speed of storage and transmission has increased dramatically, more importantly, the fault characteristics of the gearbox with multiple faults are detected and saved, i.e., the bearing outer race fault frequency at 170.7 Hz and its harmonics at 341.3 Hz, ball fault frequency at 7.344 Hz and its harmonics at 15.0 Hz, and the gear fault frequency at 23.36 Hz and its harmonics at 47.42 Hz are identified in the envelope spectrum.

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Fraction-order total variation blind image restoration based on L1-norm

Cited by 26 publications

References 13 publications

Fraction-Order Total Variation Image Blind Restoration Based on Self-Similarity Features

Fraction-Order Total Variation Image Blind Restoration Based on Self-Similarity Features

Low-Rank Tensor Completion and Total Variation Minimization for Color Image Inpainting

Multichannel Signals Reconstruction Based on Tunable Q-Factor Wavelet Transform-Morphological Component Analysis and Sparse Bayesian Iteration for Rotating Machines

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