Hilbert 空间中加权框架的扰动性及其应用

上海大学学报(自然科学版) ›› 2010, Vol. 16 ›› Issue (3): 277-280.

Hilbert 空间中加权框架的扰动性及其应用

马亚丽，叶万洲

(上海大学理学院，上海 200444)

出版日期:2010-06-28 发布日期:2010-06-28

Perturbation of Weighted Frames in Hilbert Space and Applications

MA Ya-li,YE Wan-zhou

(College of Sciences, Shanghai University, Shanghai 200444, China)

Online:2010-06-28 Published:2010-06-28

摘要/Abstract

摘要：

加权框架具有良好的冗余性，从而为信号重构和图像处理提供了非常有用的信息.借鉴对 Hibert 空间中 Riesz 框架扰动和摄动的研究，着重讨论加权框架也具有类似的扰动性结果.另外，讨论了加权框架在实际信号消噪中的应用，并初步提出加权阈值消噪法的主要思想.

关键词: 加权框架；Riesz 框架；扰动性；阈值消噪；Hilbert空间

Abstract:

Because the weighted frame possesses good redundancy, it supplies useful information for signal reconstruction and image processing. This paper borrows ideas from the research on the Riesz frame perturbation in the Hilbert space, and in particular, discusses the topic that a weighted frame has the similar perturbation result. Furthermore, application of weighted frames in the practical signal denoising is considered, and the idea of the framed threshold de-noising is proposed.

Key words: weighted frames; Riesz frames; perturbation; threshold de-noising; Hilbert space

马亚丽，叶万洲. Hilbert 空间中加权框架的扰动性及其应用[J]. 上海大学学报(自然科学版), 2010, 16(3): 277-280.

MA Ya-li,YE Wan-zhou. Perturbation of Weighted Frames in Hilbert Space and Applications[J]. Journal of Shanghai University（Natural Science Edition）, 2010, 16(3): 277-280.