JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (3): 96-110.doi: 10.6040/j.issn.1671-9352.0.2025.338

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  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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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

CLC Number: 

  • TP391
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