Research on Two-Dimensional Linear Canonical Transformation Series and Its Applications
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| Veröffentlicht in: | Fractal and Fractional vol. 9, no. 9 (2025), p. 596-617 |
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| 022 | |a 2504-3110 | ||
| 024 | 7 | |a 10.3390/fractalfract9090596 |2 doi | |
| 035 | |a 3254516230 | ||
| 045 | 2 | |b d20250101 |b d20251231 | |
| 100 | 1 | |a Zhao Weikang |u School of Information and Electrical Engineering, Hebei University of Engineering, Handan 056038, China; zhaowk0903@163.com | |
| 245 | 1 | |a Research on Two-Dimensional Linear Canonical Transformation Series and Its Applications | |
| 260 | |b MDPI AG |c 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a In light of the computational efficiency bottleneck and inadequate regional feature representation in traditional global data approximation methods, this paper introduces the concept of non-uniform partition to transform global continuous approximation into multi-region piecewise approximation. Additionally, we propose an image representation algorithm based on linear canonical transformation and non-uniform partitioning, which enables the regional representation of sub-signal features while reducing computational complexity. The algorithm first demonstrates that the two-dimensional linear canonical transformation series has a least squares solution within each region. Then, it adopts the maximum likelihood estimation method and the scale transformation characteristics to achieve conversion between the nonlinear and linear expressions of the two-dimensional linear canonical transformation series. It then uses the least squares method and the recursive method to convert the image information into mathematical expressions, realize image vectorization, and solve the approximation coefficients in each region more quickly. The proposed algorithm better represents complex image texture areas while reducing image quality loss, effectively retains high-frequency details, and improves the quality of reconstructed images. | |
| 653 | |a Transformations (mathematics) | ||
| 653 | |a Principles | ||
| 653 | |a Mathematical analysis | ||
| 653 | |a Image reconstruction | ||
| 653 | |a Fourier transforms | ||
| 653 | |a Signal processing | ||
| 653 | |a Least squares method | ||
| 653 | |a Decomposition | ||
| 653 | |a Approximation | ||
| 653 | |a Algorithms | ||
| 653 | |a Maximum likelihood estimation | ||
| 653 | |a Algebra | ||
| 653 | |a Image quality | ||
| 653 | |a Complexity | ||
| 653 | |a Data compression | ||
| 653 | |a Cognition & reasoning | ||
| 653 | |a Representations | ||
| 653 | |a Recursive methods | ||
| 700 | 1 | |a Luo Huibin |u Greater Bay Area Innovation Institute, Beijing Institute of Technology, Zhuhai 519088, China; zhbitluo@163.com | |
| 700 | 1 | |a Zhang, Guifang |u School of Computing and Artificial Intelligence, Jiangxi University of Finance and Economics, Nanchang 330013, China | |
| 700 | 1 | |a KinTak, U |u School of Computer Science and Engineering, Faculty of Innovation Engineering, Macau University of Science and Technology, Macau 999078, China | |
| 773 | 0 | |t Fractal and Fractional |g vol. 9, no. 9 (2025), p. 596-617 | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3254516230/abstract/embedded/6A8EOT78XXH2IG52?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text + Graphics |u https://www.proquest.com/docview/3254516230/fulltextwithgraphics/embedded/6A8EOT78XXH2IG52?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3254516230/fulltextPDF/embedded/6A8EOT78XXH2IG52?source=fedsrch |