Bayesian K-SVD Using Fast Variational Inference

Serra, Juan G.; Testa, Matteo; Molina, Rafael; Katsaggelos, Aggelos K.

doi:10.1109/tip.2017.2681436

Cited by 29 publications

(12 citation statements)

References 43 publications

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“…In this subsection, we apply the proposed SPG-SC algorithm to image inpainting task. We compare it with nine advanced methods, including BPFA [ 64 ], IPPO [ 65 ], ISD-SB [ 66 ], JSM [ 7 ], Aloha [ 60 ], NGS [ 67 ], BKSVD [ 68 ], WNNM [ 40 ] and TSLRA [ 69 ]. It is worth nothing that nonlocal redundancies are used for IPPO, JSM, Aloha, NGS, WNNM and TSLRA methods.…”

Section: Resultsmentioning

confidence: 99%

Simultaneous Patch-Group Sparse Coding with Dual-Weighted ℓp Minimization for Image Restoration

2021

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Sparse coding (SC) models have been proven as powerful tools applied in image restoration tasks, such as patch sparse coding (PSC) and group sparse coding (GSC). However, these two kinds of SC models have their respective drawbacks. PSC tends to generate visually annoying blocking artifacts, while GSC models usually produce over-smooth effects. Moreover, conventional ℓ1 minimization-based convex regularization was usually employed as a standard scheme for estimating sparse signals, but it cannot achieve an accurate sparse solution under many realistic situations. In this paper, we propose a novel approach for image restoration via simultaneous patch-group sparse coding (SPG-SC) with dual-weighted ℓp minimization. Specifically, in contrast to existing SC-based methods, the proposed SPG-SC conducts the local sparsity and nonlocal sparse representation simultaneously. A dual-weighted ℓp minimization-based non-convex regularization is proposed to improve the sparse representation capability of the proposed SPG-SC. To make the optimization tractable, a non-convex generalized iteration shrinkage algorithm based on the alternating direction method of multipliers (ADMM) framework is developed to solve the proposed SPG-SC model. Extensive experimental results on two image restoration tasks, including image inpainting and image deblurring, demonstrate that the proposed SPG-SC outperforms many state-of-the-art algorithms in terms of both objective and perceptual quality.

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Section: Resultsmentioning

confidence: 99%

Simultaneous Patch-Group Sparse Coding with Dual-Weighted ℓp Minimization for Image Restoration

2021

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“…Lemma 2: For any x, D, and λ > 0, (27) has a unique solution if rank (D ℰ ) = ℰ , and one has α −ℰ ⋆ = 0 and α…”

Section: Proposed Algorithm Based On Larsmentioning

confidence: 99%

“…However, despite the sparse solution α given under the l 1constraint, the value of λ and the corresponding effective sparsity ∥ α ∥ 0 cannot be analytically linked. Unlike problem (23), (27) is a convex problem, and also many methods have been proposed for its efficient resolution such as the LARS [71]. To reduce the failure in capturing complex sparse structures that suffers l 0 and l 1 -based minimisations from, we propose to use an elastic net (EN) constraint [72]…”

Section: Proposed Algorithm Based On Larsmentioning

confidence: 99%

“…Let us also quote the work in [25] where the optimal reconstruction was based on a data‐driven method called empirical mode decomposition (EMD) [26]. An approach was proposed in [27] in order to build a well‐suited overcomplete dictionary with a redundant set of atoms, and meanwhile to find a sparse representation of a given signal with regard to the chosen dictionary.…”

Section: Introductionmentioning

confidence: 99%

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Multicomponent AM–FM signal analysis based on sparse approximation

Diop¹,

Skretting²,

Boudraa

2020

IET signal process.

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The authors propose in this work to formulate multicomponent amplitude modulation (AM)-frequency modulation (FM) representations as a sparse approximation (SA) problem, which is solved using orthogonal matching pursuits (OMP) and least angle regression (LARS). The approach appears to be an efficient tool to separate the frequency content of linear and nonlinear signals and behaves in a better way like the well-known data-driven empirical mode decomposition (EMD). Contrary to related works where AM-FM models and/or EMD are used to improve sparsity or learned dictionaries, they propose instead a sparse approach framework in AM-FM modelling and EMD. Recasting EMD as a SA problem provides a new framework towards its comprehension, formulation, and convergence since OMP and LARS converge. Doing so presents an alternative to getting rid of the interpolation process that EMD terribly suffers from. Conducted experiments show noticeable improvements in terms of frequency separation of linear and non-linear signals, tone separation capability and robustness in a noisy environment.

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“…In [25], a novel supervised dictionary learning model with smooth shrinkage was proposed for image denoising. The uncertainty of estimation was considered and an adaptive Bayesian method was used to generate the sparse representation in [26]. Moreover, a polarization image sensor denoising algorithm based on K-singular value decomposition (K-SVD) was proposed in [27].…”

Section: Introductionmentioning

confidence: 99%

Speckle Noise Reduction in Sonar Image Based on Adaptive Redundant Dictionary

Huang

Yuan

2020

JMSE

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As acoustic waves are affected by the channel characteristics, such as scattering and reverberation when propagating in water, sonar images often exhibit speckle noise which will cause visual quality of the image to decrease. Therefore, denoising is a crucial preprocessing technique in sonar image applications. However, speckle noise is mainly caused by the sediment echo signals which are related to the background of seafloor sediment and can be obtained by prior modeling. Although deep learning-based denoising algorithms represent a research hotspot now, they are not suitable for such applications due to the high calculation amount and the large requirement of original images considering that sonar is carried by Autonomous Underwater Vehicles (AUVs) for collecting sonar images and performing calculation. In contrast, dictionary learning-based denoising method is more suitable and easier to be modeled. Compared with deep learning, it can greatly reduce the calculation amount and is more easily integrated into AUV systems. In addition, dictionary learning method based on image sparse representation can effectively achieve image denoising similarly. In order to solve the above problems, we propose a new adaptive dictionary learning method based on multi-resolution characteristics, which combines K-SVD dictionary learning with wavelet transform. Our method has the characteristics of dictionary learning and inherits the features of wavelet analysis as well. Compared with several classical methods, the proposed method is better at speckle noise reduction and edge detail preservation. At the same time, the calculation time is greatly reduced and the efficiency is significantly improved.

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Bayesian K-SVD Using Fast Variational Inference

Cited by 29 publications

References 43 publications

Simultaneous Patch-Group Sparse Coding with Dual-Weighted ℓp Minimization for Image Restoration

Simultaneous Patch-Group Sparse Coding with Dual-Weighted ℓp Minimization for Image Restoration

Multicomponent AM–FM signal analysis based on sparse approximation

Speckle Noise Reduction in Sonar Image Based on Adaptive Redundant Dictionary

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