Super-resolution by polar Newton–Thiele׳s rational kernel in centralized sparsity paradigm

He, Lei; Tan, Jieqing; Su, Zhuo; Luo, Xiangfeng; Xie, Chengjun

doi:10.1016/j.image.2014.12.003

Cited by 6 publications

(12 citation statements)

References 44 publications

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“…Our approach was based on the observation that the texture details of repaired images by most image inpainting algorithms were not prominent. Inspired by the applications of continued fractions in image processing [11,[18][19][20], we proposed a novel image inpainting algorithm by using continued fractions rational interpolation. In order to obtain better repaired results, Thiele's rational interpolation was combined with Newton-Thiele's rational interpolation to repair damaged images.…”

Section: Discussionmentioning

confidence: 99%

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An Adaptive Image Inpainting Method Based on Continued Fractions Interpolation

Xing

Xia

et al. 2018

Discrete Dynamics in Nature and Society

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In view of the drawback of most image inpainting algorithms by which texture was not prominent, an adaptive inpainting algorithm based on continued fractions was proposed in this paper. In order to restore every damaged point, the information of known pixel points around the damaged point was used to interpolate the intensity of the damaged point. The proposed method included two steps; firstly, Thiele's rational interpolation combined with the mask image was used to interpolate adaptively the intensities of damaged points to get an initial repaired image, and then Newton-Thiele's rational interpolation was used to refine the initial repaired image to get a final result. In order to show the superiority of the proposed algorithm, plenty of experiments were tested on damaged images. Subjective evaluation and objective evaluation were used to evaluate the quality of repaired images, and the objective evaluation was comparison of Peak Signal to Noise Ratios (PSNRs). The experimental results showed that the proposed algorithm had better visual effect and higher Peak Signal to Noise Ratio compared with the state-of-the-art methods.

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Section: Discussionmentioning

confidence: 99%

“…Considering that the reconstruction images have better visual effect and prominent texture by the continued fractions [11,[18][19][20], in this paper, we propose an adaptive image inpainting method based on continued fractions.…”

Section: Introductionmentioning

confidence: 99%

An Adaptive Image Inpainting Method Based on Continued Fractions Interpolation

Xing

Xia

et al. 2018

Discrete Dynamics in Nature and Society

Self Cite

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“…e interpolation problem has been the subject of many classic studies in approximation theory [1][2][3][4][5]. In the last several years, many researchers have been focusing on this subject and have obtained interesting results.…”

Section: Introductionmentioning

confidence: 99%

“…In the last several years, many researchers have been focusing on this subject and have obtained interesting results. e existing approaches can be divided into polynomial and rational interpolation methods, both of which are applicable to numerical approximation [1,2], image interpolation [3][4][5][6], and arc structuring and surface modeling [7][8][9][10]. Newton's polynomial interpolation and iele's interpolating continued fractions can be incorporated to generate various interpolation schemes based on rectangular grids.…”

Section: Introductionmentioning

confidence: 99%

A New Approach to Newton-Type Polynomial Interpolation with Parameters

Zou

Song

Weise

et al. 2020

Mathematical Problems in Engineering

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Newton’s interpolation is a classical polynomial interpolation approach and plays a significant role in numerical analysis and image processing. The interpolation function of most classical approaches is unique to the given data. In this paper, univariate and bivariate parameterized Newton-type polynomial interpolation methods are introduced. In order to express the divided differences tables neatly, the multiplicity of the points can be adjusted by introducing new parameters. Our new polynomial interpolation can be constructed only based on divided differences with one or multiple parameters which satisfy the interpolation conditions. We discuss the interpolation algorithm, theorem, dual interpolation, and information matrix algorithm. Since the proposed novel interpolation functions are parametric, they are not unique to the interpolation data. Therefore, its value in the interpolant region can be adjusted under unaltered interpolant data through the parameter values. Our parameterized Newton-type polynomial interpolating functions have a simple and explicit mathematical representation, and the proposed algorithms are simple and easy to calculate. Various numerical examples are given to demonstrate the efficiency of our method.

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“…There are mainly two types of interpolations: polynomial interpolation and rational interpolation. In addition to numerical approximation [1], the two interpolations are extensively adopted in circular construction [3], image processing, and other aspects [2][3][4][5][6]. Nowadays, more and more attention has been drawn to continued fractions-based rational interpolation method.…”

Section: Introductionmentioning

confidence: 99%

Information Matrix Algorithm of Block-based Bivariate Thiele-Type Rational Interpolation

Zou¹

2018

IJPE

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Interpolation plays an important role in image processing, numerical computation, and engineering technology. Almost all interpolation computation is based on differences and inverse differences. This paper presents the recursive algorithm of modified bivariate blockbased Thiele-type blending interpolation to meet the nonexistence of partial inverse differences of blocks. Inspired by the basic thoughts of transformation in linear algebra, this paper studies the information matrix algorithm of bivariate block based Thiele-type blending rational interpolation. The algorithm is simple and easy to compute. Through research, the author presents the interpolation theorems and recursive algorithm and also comes up with the modified bivariate block-based Thiele-type blending rational interpolation, together with its information matrix algorithm, under the nonexistence of block-based partial inverse differences. Finally, a numerical example is introduced to show the effectiveness of the proposed algorithm.

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Super-resolution by polar Newton–Thiele׳s rational kernel in centralized sparsity paradigm

Cited by 6 publications

References 44 publications

An Adaptive Image Inpainting Method Based on Continued Fractions Interpolation

An Adaptive Image Inpainting Method Based on Continued Fractions Interpolation

A New Approach to Newton-Type Polynomial Interpolation with Parameters

Information Matrix Algorithm of Block-based Bivariate Thiele-Type Rational Interpolation

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