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Application of fractional derivatives in image quality assessment indices 分数导数在图像质量评估指数中的应用
IF 2.8 2区 数学
Applied Numerical Mathematics Pub Date : 2024-06-07 DOI: 10.1016/j.apnum.2024.06.005
Mariusz Frackiewicz, Henryk Palus
{"title":"Application of fractional derivatives in image quality assessment indices","authors":"Mariusz Frackiewicz,&nbsp;Henryk Palus","doi":"10.1016/j.apnum.2024.06.005","DOIUrl":"10.1016/j.apnum.2024.06.005","url":null,"abstract":"<div><p>Objective image quality assessment involves the use of mathematical models to quantitatively describe image quality. FR-IQA (Full-Reference Image Quality Assessment) methods using reference images are also often used to evaluate image processing and computer vision algorithms. Quality indices often use gradient operators to express relevant visual information, such as edges. Fractional calculus has been applied in the last two decades in various fields such as signal processing, image processing, and pattern recognition. Fractional derivatives are generalizations of integer-order derivatives and can be computed using various operators such as the Riemann-Liouville, Caputo-Fabrizio, and Grünwald-Letnikov operators. In this paper, we propose a modification of the FSIMc image quality index by including fractional derivatives to extract and enhance edges. A study of the usefulness of fractional derivative in the FSIMc model was conducted by assessing Pearson, Spearman and Kendall correlations with MOS scores for images from the TID2013 and KADID-10k databases. Comparison of FD_FSIMc with the classic FSIMc shows an increase of several percent in the correlation coefficients for the modified index. The results obtained are superior to those other known approaches to FR-IQA that use fractional derivatives. The results encourage the use of fractional calculus.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0168927424001442/pdfft?md5=c5b941ec0099c65d784aced80ddf399e&pid=1-s2.0-S0168927424001442-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141403595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A structure-preserving local discontinuous Galerkin method for the stochastic KdV equation 随机 KdV 方程的结构保持局部非连续伽勒金方法
IF 2.8 2区 数学
Applied Numerical Mathematics Pub Date : 2024-06-06 DOI: 10.1016/j.apnum.2024.06.001
Xuewei Liu , Zhanwen Yang , Qiang Ma , Xiaohua Ding
{"title":"A structure-preserving local discontinuous Galerkin method for the stochastic KdV equation","authors":"Xuewei Liu ,&nbsp;Zhanwen Yang ,&nbsp;Qiang Ma ,&nbsp;Xiaohua Ding","doi":"10.1016/j.apnum.2024.06.001","DOIUrl":"https://doi.org/10.1016/j.apnum.2024.06.001","url":null,"abstract":"<div><p>This paper proposes a local discontinuous Galerkin (LDG) method for the stochastic Korteweg-de Vries (KdV) equation with multi-dimensional multiplicative noise. In the mean square sense, we show that the numerical method is <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> stable and it preserves energy conservation and energy dissipation. If the degree of the polynomial is <em>n</em>, the optimal error estimate in the mean square sense can reach as <span><math><mi>n</mi><mo>+</mo><mn>1</mn></math></span>. Finally, structure-preserving and convergence are verified by numerical experiments.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141322521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A fast solvable operator-splitting scheme for time-dependent advection diffusion equation 时变平流扩散方程的快速可解算子分割方案
IF 2.8 2区 数学
Applied Numerical Mathematics Pub Date : 2024-06-05 DOI: 10.1016/j.apnum.2024.05.024
Chengyu Chen , Xue-Lei Lin
{"title":"A fast solvable operator-splitting scheme for time-dependent advection diffusion equation","authors":"Chengyu Chen ,&nbsp;Xue-Lei Lin","doi":"10.1016/j.apnum.2024.05.024","DOIUrl":"https://doi.org/10.1016/j.apnum.2024.05.024","url":null,"abstract":"<div><p>It is well known that the implicit central difference discretization for unsteady advection diffusion equation (ADE) suffers from being time-consuming to solve when the advection term dominates. In this paper, we propose an operator-splitting scheme for the unsteady ADE, in which the ADE is firstly discretized by Crank-Nicolson (CN) scheme in time and central difference scheme in space; and then the discrete advection-diffusion problem is split as advection sub-problem and diffusion sub-problem at each time-level. The significance of the new scheme is that these sub-problems can be fast and directly solved within a linearithmic complexity (a linear-times-logarithm complexity) by means of fast sine transforms (FSTs). In particular, the complexity is independent of the dominance of the advection term. Theoretically, we show that proposed scheme is unconditionally stable and of second-order convergence in time and space. Numerical results are reported to show the efficiency of the proposed scheme.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141322523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two one-parameter families of nonconforming enrichments of the Crouzeix–Raviart finite element 克鲁泽克-拉维亚特有限元的两个单参数非顺应富集族
IF 2.8 2区 数学
Applied Numerical Mathematics Pub Date : 2024-06-04 DOI: 10.1016/j.apnum.2024.05.023
Federico Nudo
{"title":"Two one-parameter families of nonconforming enrichments of the Crouzeix–Raviart finite element","authors":"Federico Nudo","doi":"10.1016/j.apnum.2024.05.023","DOIUrl":"https://doi.org/10.1016/j.apnum.2024.05.023","url":null,"abstract":"<div><p>In this paper, we introduce two one-parameter families of quadratic polynomial enrichments designed to enhance the accuracy of the classical Crouzeix–Raviart finite element. These enrichments are realized by using weighted line integrals as enriched linear functionals and quadratic polynomial functions as enrichment functions. To validate the effectiveness of our approach, we conduct numerical experiments that confirm the improvement achieved by the proposed method.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0168927424001375/pdfft?md5=94fcf67e97df0d893b8352a366187794&pid=1-s2.0-S0168927424001375-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141292365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Algebraically stable high-order multi-physical property-preserving methods for the regularized long-wave equation 正则化长波方程的代数稳定高阶多物理属性保留方法
IF 2.8 2区 数学
Applied Numerical Mathematics Pub Date : 2024-06-04 DOI: 10.1016/j.apnum.2024.05.022
Xin Li , Xiuling Hu
{"title":"Algebraically stable high-order multi-physical property-preserving methods for the regularized long-wave equation","authors":"Xin Li ,&nbsp;Xiuling Hu","doi":"10.1016/j.apnum.2024.05.022","DOIUrl":"https://doi.org/10.1016/j.apnum.2024.05.022","url":null,"abstract":"<div><p>In this paper, based on the framework of the supplementary variable method, we present two classes of high-order, linearized, structure-preserving algorithms for simulating the regularized long-wave equation. The suggested schemes are as accurate and efficient as the recently proposed schemes in Jiang et al. (2022) <span>[20]</span>, but share the nice features in two folds: (i) the first type of schemes conserves the original energy conservation, as opposed to a modified quadratic energy in <span>[20]</span>; (ii) the second type of schemes fills the gap of <span>[20]</span> by constructing high-order linear algorithms that preserve both two invariants of mass and momentum. We discretize the SVM systems by employing the algebraically stable Runge-Kutta method together with the prediction-correction technique in time and the Fourier pseudo-spectral method in space. The implementation benefits from solving the optimization problems subject to PDE constraints. Numerical examples and some comparisons are provided to show the effectiveness, accuracy and performance of the proposed schemes.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2024-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141290982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Accelerated primal-dual methods with adaptive parameters for composite convex optimization with linear constraints 带线性约束的复合凸优化的自适应参数加速原始二元方法
IF 2.8 2区 数学
Applied Numerical Mathematics Pub Date : 2024-05-29 DOI: 10.1016/j.apnum.2024.05.021
Xin He
{"title":"Accelerated primal-dual methods with adaptive parameters for composite convex optimization with linear constraints","authors":"Xin He","doi":"10.1016/j.apnum.2024.05.021","DOIUrl":"https://doi.org/10.1016/j.apnum.2024.05.021","url":null,"abstract":"<div><p>In this paper, we introduce two accelerated primal-dual methods tailored to address linearly constrained composite convex optimization problems, where the objective function is expressed as the sum of a possibly nondifferentiable function and a differentiable function with Lipschitz continuous gradient. The first method is the accelerated linearized augmented Lagrangian method (ALALM), which permits linearization to the differentiable function; the second method is the accelerated linearized proximal point algorithm (ALPPA), which enables linearization of both the differentiable function and the augmented term. By incorporating adaptive parameters, we demonstrate that ALALM achieves the <span><math><mi>O</mi><mo>(</mo><mn>1</mn><mo>/</mo><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> convergence rate and the linear convergence rate under the assumption of convexity and strong convexity, respectively. Additionally, we establish that ALPPA enjoys the <span><math><mi>O</mi><mo>(</mo><mn>1</mn><mo>/</mo><mi>k</mi><mo>)</mo></math></span> convergence rate in convex case and the <span><math><mi>O</mi><mo>(</mo><mn>1</mn><mo>/</mo><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> convergence rate in strongly convex case. We provide numerical results to validate the effectiveness of the proposed methods.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141249733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the separation of solutions to fractional differential equations of order α ∈ (1,2) 关于阶数 α∈ (1,2) 的分数微分方程解的分离
IF 2.8 2区 数学
Applied Numerical Mathematics Pub Date : 2024-05-27 DOI: 10.1016/j.apnum.2024.05.020
Renu Chaudhary, Kai Diethelm, Safoura Hashemishahraki
{"title":"On the separation of solutions to fractional differential equations of order α ∈ (1,2)","authors":"Renu Chaudhary,&nbsp;Kai Diethelm,&nbsp;Safoura Hashemishahraki","doi":"10.1016/j.apnum.2024.05.020","DOIUrl":"10.1016/j.apnum.2024.05.020","url":null,"abstract":"<div><p>Given the Caputo-type fractional differential equation <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>α</mi></mrow></msup><mi>y</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>=</mo><mi>f</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>y</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>)</mo></math></span> with <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>, we consider two distinct solutions <span><math><msub><mrow><mi>y</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>∈</mo><mi>C</mi><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></math></span> to this equation subject to different sets of initial conditions. In this framework, we discuss nontrivial upper and lower bounds for the difference <span><math><mo>|</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo><mo>−</mo><msub><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>t</mi><mo>)</mo><mo>|</mo></math></span> for <span><math><mi>t</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></math></span>. The main emphasis is on describing how such bounds are related to the differences of the associated initial values.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0168927424001260/pdfft?md5=15a5050ef91e9812ea04bb8eb7847034&pid=1-s2.0-S0168927424001260-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141193399","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Approximation of piecewise smooth functions by nonlinear bivariate C2 quartic spline quasi-interpolants on criss-cross triangulations 用十字交叉三角形上的非线性双变量 C2 四分样条准内插法逼近片状平滑函数
IF 2.8 2区 数学
Applied Numerical Mathematics Pub Date : 2024-05-24 DOI: 10.1016/j.apnum.2024.05.018
Francesc Aràndiga , Sara Remogna
{"title":"Approximation of piecewise smooth functions by nonlinear bivariate C2 quartic spline quasi-interpolants on criss-cross triangulations","authors":"Francesc Aràndiga ,&nbsp;Sara Remogna","doi":"10.1016/j.apnum.2024.05.018","DOIUrl":"10.1016/j.apnum.2024.05.018","url":null,"abstract":"<div><p>In this paper we focus on the space of <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> quartic splines on uniform criss-cross triangulations and we propose a method based on weighted essentially non-oscillatory techniques and obtained by modifying classical spline quasi-interpolants in order to approximate piecewise smooth functions avoiding Gibbs phenomenon near discontinuities and, at the same time, maintaining the high-order accuracy in smooth regions. We analyse the convergence properties of the proposed quasi-interpolants and we provide some numerical and graphical tests confirming the theoretical results.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0168927424001247/pdfft?md5=e7d005a097a5af6e0af8dd8a4781cd17&pid=1-s2.0-S0168927424001247-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141138020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mixed virtual element methods for elliptic optimal control problems with boundary observations in L2(Γ) L2(Γ) 中具有边界观测的椭圆最优控制问题的混合虚拟元素方法
IF 2.8 2区 数学
Applied Numerical Mathematics Pub Date : 2024-05-24 DOI: 10.1016/j.apnum.2024.05.019
Minghui Yang, Zhaojie Zhou
{"title":"Mixed virtual element methods for elliptic optimal control problems with boundary observations in L2(Γ)","authors":"Minghui Yang,&nbsp;Zhaojie Zhou","doi":"10.1016/j.apnum.2024.05.019","DOIUrl":"10.1016/j.apnum.2024.05.019","url":null,"abstract":"<div><p>In this paper, we study the mixed virtual element approximation to an elliptic optimal control problem with boundary observations. The objective functional of this type of optimal control problem contains the outward normal derivatives of the state variable on the boundary, which reduces the regularity of solutions to the optimal control problems. We construct the mixed virtual element discrete scheme and derive an a priori error estimate for the optimal control problem based on the variational discretization for the control variable. Numerical experiments are carried out on different meshes to support our theoretical findings.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141134269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Weighted least squares collocation methods 加权最小二乘法定位方法
IF 2.8 2区 数学
Applied Numerical Mathematics Pub Date : 2024-05-24 DOI: 10.1016/j.apnum.2024.05.017
Luigi Brugnano , Felice Iavernaro , Ewa B. Weinmüller
{"title":"Weighted least squares collocation methods","authors":"Luigi Brugnano ,&nbsp;Felice Iavernaro ,&nbsp;Ewa B. Weinmüller","doi":"10.1016/j.apnum.2024.05.017","DOIUrl":"10.1016/j.apnum.2024.05.017","url":null,"abstract":"<div><p>We consider overdetermined collocation methods and propose a weighted least squares approach to derive a numerical solution. The discrete problem requires the evaluation of the Jacobian of the vector field which, however, appears in a <span><math><mi>O</mi><mo>(</mo><mi>h</mi><mo>)</mo></math></span> term, <em>h</em> being the stepsize. We show that, by neglecting this infinitesimal term, the resulting scheme becomes a low-rank Runge–Kutta method. Among the possible choices of the weights distribution, we analyze the one based on the quadrature formula underlying the collocation conditions. A few numerical illustrations are included to better elucidate the potential of the method.</p></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":null,"pages":null},"PeriodicalIF":2.8,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0168927424001235/pdfft?md5=55c77be155705bdd999f3cc3fb7b73c2&pid=1-s2.0-S0168927424001235-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141130534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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