Local block operators and TV regularization based image inpainting

Wan, Wei; Huang, Haiyang; Li, Jun

doi:10.3934/ipi.2018058

Cited by 3 publications

(2 citation statements)

References 27 publications

(48 reference statements)

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“…Next, we will state the convergence result of our algorithm for C (k) in the following theorem. The basic convergence result can be found in several references, such as [27,34].…”

Section: Algorithm 1 (Blind Algorithm)mentioning

confidence: 99%

Non-local blind hyperspectral image super-resolution via 4d sparse tensor factorization and low-rank

Guo¹,

Wan²,

Li³

et al. 2020

Inverse Problems &Amp; Imaging

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Hyperspectral image (HSI) super-resolution is a technique to improve the spatial resolution of a HSI for better visual perception and down stream applications. This is a very ill-posed inverse problem and is often solved by fusing the low-resolution (LR) HSI with a high-resolution (HR) multispectral image (MSI). It is more challenging for blind HSI super-resolution, i.e., when the spatial degradation operators are completely unknown. In this paper, we propose a novel sparse tensor factorization model for the task of blind HSI super-resolution using the spatial non-local self-similarity and spectral global correlation of HSIs. Image clustering method is employed to collect some similar 3D cubes of HSIs which can be formed as some 4D image clusters with high correlation. We conduct cluster wise computation to not only save computation time but also to introduce a non-local regularity originated from the redundancy of cubes. By using the sparsity of tensor decomposition and the low-rank in non-local self-similarity direction underlying 4D similar clusters, we design a sparse tensor regularization term, which preserves the spatial-spectral structural correlation of HSIs. In addition, we present a proximal alternating direction method of multipliers (ADMM) based algorithm to efficiently solve the proposed model. Numerical experiments demonstrate that the proposed model outperforms many state-of-the-art HSI super-resolution methods.

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“…Next, we will state the convergence result of our algorithm for C (k) in the following theorem. The basic convergence result can be found in several references, such as [27,34].…”

Section: Algorithm 1 (Blind Algorithm)mentioning

confidence: 99%

Non-local blind hyperspectral image super-resolution via 4d sparse tensor factorization and low-rank

Guo¹,

Wan²,

Li³

et al. 2020

Inverse Problems &Amp; Imaging

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“…Then patch based regularization operator such as BM3D transform can be used in this method. Meanwhile, a block based inpainting model using group sparsity and TV regularization was considered by Wan et al [20]. The updated local SVD operators are effective in promoting the sparse representation and play the role of dictionary learning.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal Patches based Gaussian Mixture Model for Image Inpainting

Wan¹,

Li²

2019

Preprint

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We consider the inpainting problem for noisy images. It is very challenge to suppress noise when image inpainting is processed. An image patches based nonlocal variational method is proposed to simultaneously inpainting and denoising in this paper. Our approach is developed on an assumption that the small image patches should be obeyed a distribution which can be described by a high dimension Gaussian Mixture Model. By a maximum a posteriori (MAP) estimation, we formulate a new regularization term according to the log-likelihood function of the mixture model. To optimize this regularization term efficiently, we adopt the idea of the Expectation Maximum (EM) algorithm. In which, the expectation step can give an adaptive weighting function which can be regarded as a nonlocal connections among pixels. Using this fact, we built a framework for non-local image inpainting under noise. Moreover, we mathematically prove the existence of minimizer for the proposed inpainting model. By using a spitting algorithm, the proposed model are able to realize image inpainting and denoising simultaneously. Numerical results show that the proposed method can produce impressive reconstructed results when the inpainting region is rather large.

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Nonlocal patches based Gaussian mixture model for image inpainting

Wan

2020

Applied Mathematical Modelling

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Local block operators and TV regularization based image inpainting

Cited by 3 publications

References 27 publications

Non-local blind hyperspectral image super-resolution via 4d sparse tensor factorization and low-rank

Non-local blind hyperspectral image super-resolution via 4d sparse tensor factorization and low-rank

Nonlocal Patches based Gaussian Mixture Model for Image Inpainting

Nonlocal patches based Gaussian mixture model for image inpainting

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