A Total Fractional-Order Variation Model for Image Super-Resolution and Its SAV Algorithm

Yao, Wenjuan; Shen, Jie; Guo, Zhichang; Sun, Jinwei; Wu, Boying

doi:10.1007/s10915-020-01185-1

Cited by 14 publications

(5 citation statements)

References 44 publications

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“…Future work will focus on performing further theoretical analysis to provide alternative justifications for the use of the approximate pseudoinverse

, as well as building a solid theoretical framework for adaptive regularization parameter choice within flexible Krylov methods. Possible extensions will include handling high-order or fractional-order TV regularization terms [ 41 , 42 ], even in a 3D or tensorial framework [ 43 ], as well as regularized functionals that involve more than one regularization term. Such future investigations, if successful, may provide an efficient alternative to current regularization methods incorporating infimal convolutions of total-variation-type functionals [ 44 ], which are especially relevant when spatial and temporal regularization should be employed, e.g., in video processing.…”

Section: Discussionmentioning

confidence: 99%

Flexible Krylov Methods for Edge Enhancement in Imaging

2021

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Many successful variational regularization methods employed to solve linear inverse problems in imaging applications (such as image deblurring, image inpainting, and computed tomography) aim at enhancing edges in the solution, and often involve non-smooth regularization terms (e.g., total variation). Such regularization methods can be treated as iteratively reweighted least squares problems (IRLS), which are usually solved by the repeated application of a Krylov projection method. This approach gives rise to an inner–outer iterative scheme where the outer iterations update the weights and the inner iterations solve a least squares problem with fixed weights. Recently, flexible or generalized Krylov solvers, which avoid inner–outer iterations by incorporating iteration-dependent weights within a single approximation subspace for the solution, have been devised to efficiently handle IRLS problems. Indeed, substantial computational savings are generally possible by avoiding the repeated application of a traditional Krylov solver. This paper aims to extend the available flexible Krylov algorithms in order to handle a variety of edge-enhancing regularization terms, with computationally convenient adaptive regularization parameter choice. In order to tackle both square and rectangular linear systems, flexible Krylov methods based on the so-called flexible Golub–Kahan decomposition are considered. Some theoretical results are presented (including a convergence proof) and numerical comparisons with other edge-enhancing solvers show that the new methods compute solutions of similar or better quality, with increased speedup.

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“…Future work will focus on performing further theoretical analysis to provide alternative justifications for the use of the approximate pseudoinverse

Section: Discussionmentioning

confidence: 99%

Flexible Krylov Methods for Edge Enhancement in Imaging

2021

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“…We realized n = 45 simulated LR images following this process: each image is slightly deformed using a nonparametric diffusion registration [36], convolved by a Gaussian filter with a 2 × 2. Then, the convolved frames are down-sampled horizontally and vertically using a factor of r = 4 We measure the efficiency of our model in image features preserving by making some comparison tests with some successful SR approaches, including nonlocal-means (NLM) [48], the adaptive prior regularization (SAPM) [61], fractional-order SR (MFOV) [58] and finally the fourth-order edge preserving SR (EPDE) [37]. The recovered HR images for these two tests are depicted in figures 6 and 7.…”

Section: Simulated Testsmentioning

confidence: 99%

“…We select the first thirteen LR images through each video and we use the diffusion registration approach [36] to estimate the motion between the LR images for all the restored methods including our model. The recovered results are measured to the above relevant approaches, such as: anisotropy local weighted SR (LWASR) [24], Bregman algorithm through morphologic prior function (BIMR) [49], total fractional-order variation model (TFOM) [58], TV regularization with Bregman iteration [44], Bregman distance SR method (IMSR) [38] and features preserving high-order PDE (EPDE) [37]. The super-resolved images with a decimation factor of r = 4 using the above SR methods and compared to our model are depicted in figures 15 and 16.…”

Section: Video Sequencesmentioning

confidence: 99%

Bilevel optimal parameter learning for a high-order nonlocal multiframe super-resolution problem

Laghrib,

Zahra Ait Bella,

Nachaoui

et al. 2023

Inverse Problems

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This work elaborated an improved method to multiframe super-resolution (SR), which involves a nonlocal first-order regularization combined with a nonlocal p-Laplacian term. The nonlocal TV term excels at edge preserving, whilst the nonlocal p-Laplacian is commonly used to perfectly reconstruct image textures. Firstly, we discuss the existence and uniqueness of a solution to our new model in a well posed framework. Then, we derive a modified Primal-dual iteration to compute the super-resolved solution. Furthermore, we introduce a new bilevel optimization approach to learn two regularization parameters. The included tests validate that the introduced optimization procedure performs favorably compared to numerous SR approaches in terms of efficiency and accuracy.

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“…Nevertheless, the TG prior has the similar disadvantage as TV regularization method in [28], which will cause issues such as, stair effects, texture loss and over smooth etc. Recently, the fractional total variation regularization method is widely used in imaging inverse problems, for examples, image denoising, deblurring (or deconvolution), registration, super-resolution [6,33,35,36,7,29,27,37,38,39,23]. They can ease the conflict between staircase elimination and edge preservation by choosing the order of derivative properly compared with TV.…”

Section: Introductionmentioning

confidence: 99%

A Hadamard fractioal total variation-Gaussian (HFTG) prior for Bayesian inverse problems

Wang¹,

Ding²,

Zheng³

2021

Preprint

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This paper studies the infinite-dimensional Bayesian inference method with Hadamard fractional total variation-Gaussian (HFTG) prior for solving inverse problems. First, Hadamard fractional Sobolev space is established and proved to be a separable Banach space under some mild conditions. Afterwards, the HFTG prior is constructed in this separable fractional space, and the proposed novel hybrid prior not only captures the texture details of the region and avoids step effects, but also provides a complete theoretical analysis in the infinite dimensional Bayesian inversion. Based on the HFTG prior, the well-posedness and finite-dimensional approximation of the posterior measure of the Bayesian inverse problem are given, and samples are extracted from the posterior distribution using the standard pCN algorithm. Finally, numerical results under different models indicate that the Bayesian inference method with HFTG prior is effective and accurate.

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A Total Fractional-Order Variation Model for Image Super-Resolution and Its SAV Algorithm

Cited by 14 publications

References 44 publications

Flexible Krylov Methods for Edge Enhancement in Imaging

Flexible Krylov Methods for Edge Enhancement in Imaging

Bilevel optimal parameter learning for a high-order nonlocal multiframe super-resolution problem

A Hadamard fractioal total variation-Gaussian (HFTG) prior for Bayesian inverse problems

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