Approximation theory of wavelet frame based image restoration

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2024-09-27 DOI:10.1016/j.acha.2024.101712

Jian-Feng Cai , Jae Kyu Choi , Jianbin Yang

引用次数: 0

Abstract

In this paper, we analyze the error estimate of a wavelet frame based image restoration method from degraded and incomplete measurements. We present the error between the underlying original discrete image and the approximate solution which has the minimal

ℓ_{1}

-norm of the canonical wavelet frame coefficients among all possible solutions. Then we further connect the error estimate for the discrete model to the approximation to the underlying function from which the underlying image comes.

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基于小波帧的图像修复近似理论

本文分析了基于小波帧的图像复原方法从退化和不完整测量中得出的误差估计。我们提出了底层原始离散图像与近似解之间的误差，近似解在所有可能的解中具有最小的小波帧系数 ℓ1-norm 。然后，我们进一步将离散模型的误差估计与底层图像所来自的底层函数的近似值联系起来。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied and Computational Harmonic Analysis 物理-物理：数学物理

CiteScore

5.40

自引率

4.00%

发文量

审稿时长

22.9 weeks

期刊介绍： Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.