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《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (3): 96-110.doi: 10.6040/j.issn.1671-9352.0.2025.338

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基于多重分形优化的图像超分辨率重建

姚勋祥1,刘培培2,徐英城3,范清兰1*,包芳勋4,张云峰1,3   

  1. 1.山东财经大学计算机科学与人工智能学院, 山东 济南 250014;2.山东女子学院人工智能学院, 山东 济南 250300;3.山东财经大学管理科学与工程学院, 山东 济南 250014;4.山东大学数学学院, 山东 济南 250100
  • 发布日期:2026-03-18
  • 通讯作者: 范清兰(1992— ),女,副教授,博士,研究方向为进化机器学习、计算机视觉、分类和特征学习. E-mail:qinglanfan@sdufe.edu.cn
  • 作者简介:姚勋祥(1989— ),男,讲师,博士,研究方向为图像超分辨及分形、目标检测. E-mail:Xunxiang.Yao@sdufe.edu.cn*通信作者:范清兰(1992— ),女,副教授,博士,研究方向为进化机器学习、计算机视觉、分类和特征学习. E-mail:qinglanfan@sdufe.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(62506209);山东省自然科学基金项目(ZR2024QF016,ZR2023QF161);山东省高等学校青年创新团队项目(2022KJ185)

  1. 1. School of Computer Science and Artificial Intelligence, Shandong University of Finance and Economics, Jinan 250014, Shandong, China;
    2. School of Artificial Intelligence, Shandong Womens University, Jinan 250300, Shandong, China;
    3. School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, Shandong, China;
    4. School of Mathematics, Shandong University, Jinan, 250100, Shandong, China
  • Published:2026-03-18

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摘要： 图像超分辨率旨在从低分辨率图像中重建包含丰富纹理细节的高分辨率图像。已有研究表明,精细结构主要对应于傅里叶域中的高频成分,但多数现有方法缺乏针对高频信息的自适应处理机制,容易导致边缘模糊或纹理紊乱。针对上述问题,本文在非下采样轮廓波变换(non-subsampled contourlet transform, NSCT)域内开展超分辨率研究,将图像分解为多个具有不同频率特性的子带。不同子带所包含的频率信息与图像细节程度密切相关,本文将其定义为图像粗糙度特征。此外,对各子带图像应用分形分析方法,利用分形对图像粗糙度的数学表征能力,描述图像信息的多种频率细节。在此基础上,构建多子带下的多重分形模型,并在各子带上自适应生成相应的分形表示,从而将超分辨率重建过程转化为一个多重分形优化问题。实验结果表明,本研究所提出的方法能够有效恢复图像高频细节。

关键词: 图像超分辨, 非下采样轮廓波变换, 分形插值函数, 图像粗糙度, 分形维度, 多重分形

Abstract: The goal of image super-resolution technique is to reconstruct high-resolution image with fine details and vivid texture details from its low-resolution version. On Fourier domain, such fine details are more related to the information in the high-frequency spectrum. Most of existing methods do not have specific modules to handle such high-frequency information adaptively. Thus, they cause edge blur or texture disorder. To tackle the problems, this work explores image super-resolution on multiple sub-bands of the corresponding image, which are generated by non-subsampled contourlet transform(NSCT). Different sub-bands hold the information of different frequency which is then related to the detailedness of information of the given low-resolution image. In this work, such image information detailedness is formulated as image roughness. Moreover, fractals analysis is applied to every single sub-band image. Since fractals can mathematically represent the image roughness, it then is able to represent the detailedness(i.e. various frequency of image information). Overall, a multi-fractals formulation is established based on multiple sub-bands image. On each sub-band image, different fractals representation is created adaptively according to image features. In this way, the image super-resolution process is transformed into a multifractal optimization problem. The experiment result demonstrates the effectiveness of the proposed method in recovering high-frequency details.

Key words: image super-resolution, nonsubsampled contourlet transform, fractal interpolation function, image roughness, fractal dimension, multifractal

中图分类号: 

  • TP391
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