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Updated: May 31, 2026
07:05
Applying Hyperspectral Reflectance Imaging to Investigate the Palettes and the Techniques of Painters
Published on: June 18, 2021
A primal-dual method for total-variation-based wavelet domain inpainting.
You-Wei Wen1, Raymond H Chan, Andy M Yip
1Faculty of Science, Kunming University of Science and Technology, Kunming, China. wenyouwei@gmail.com
Summary
Image information loss in wavelet domains necessitates inpainting. This study introduces an efficient variational method for optimal wavelet image reconstruction, proving its convergence and demonstrating strong performance.
Area of Science:
- Digital Image Processing
- Wavelet Theory
- Computational Mathematics
Background:
- Information loss during image storage and transmission in wavelet domains is a significant challenge.
- Wavelet-based image representations are susceptible to data corruption or loss.
- Effective image inpainting techniques are crucial for restoring lost wavelet coefficients.
Purpose of the Study:
- To develop and analyze a variational approach for image inpainting in the wavelet domain.
- To propose an efficient iterative algorithm for solving the proposed variational model.
- To demonstrate the convergence and performance of the developed inpainting method.
Main Methods:
- Formulation of the image reconstruction problem using a variational approach.
- Development of a simple and efficient iterative scheme for optimal solution calculation.
- Mathematical proof of the convergence of the proposed iterative algorithm.
Main Results:
- The proposed variational method effectively reconstructs images with lost wavelet coefficients.
- The iterative scheme converges to an optimal solution for the inpainting problem.
- Numerical results validate the superior performance of the proposed algorithm.
Conclusions:
- The variational approach provides a robust framework for wavelet domain image inpainting.
- The proposed iterative scheme is efficient and guarantees convergence.
- This method offers a valuable solution for restoring corrupted or incomplete wavelet-transformed images.
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