基于条纹相干的卷积稀疏编码改进理论分析

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-03-24 DOI:10.1016/j.cam.2025.116631

Haifeng Li , Wengu Chen

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引用次数: 0

摘要

卷积稀疏编码在广泛的应用中被证明是非常有效的。最近的工作解决了使用条纹相干的全局正交匹配追踪（OMP）的理论性能，条纹相干是卷积字典的一个更强的特征。本文进一步对卷积稀疏模型进行了理论分析。我们的结果改进了基于卷积稀疏模型的全局OMP的保证条件。本文还为基于卷积稀疏模型的条纹相干寻基提供了理论保障，这是现有研究成果中所缺乏的。

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An improved theoretical analysis of convolutional sparse coding using stripe coherence

Convolutional sparse coding has proven to be very effective in a wide range of applications. Recent work addressed the theoretical performance of global orthogonal matching pursuit (OMP) using the stripe coherence that is a stronger characterization of the convolutional dictionary. In this paper, we further provide the theoretical analysis of convolutional sparse model. Our result improves the guarantee condition for global OMP based on convolutional sparse model. We also provide the theoretical guarantee for basis pursuit using stripe coherence based on convolutional sparse model, which is absent in the existing results.

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.