Piecewise Scalable Frames in Hilbert Spaces

IF 0.9 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

International Journal of Wavelets Multiresolution and Information Processing Pub Date : 2023-11-04 DOI:10.1142/s0219691323500522

Amir Khosravi, Mohammad Reza Farmani

引用次数: 0

Abstract

Tight frames are extremely useful in applications. A scalable frame was recently introduced as a frame with the property of generating a tight frame by rescaling its frame vectors. In this paper, we consider piecewise scalable frames. We obtain some characterizations for them, and demonstrate that scalability is stable under unitary operators and isomorphisms between two Hilbert spaces. We further obtain a relation between the piecewise scalable frames in Hilbert spaces, and their tensor product

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Hilbert空间中的分段可伸缩帧

紧框架在应用程序中非常有用。可伸缩帧是最近引入的一种帧，它具有通过重新缩放其帧向量来生成紧帧的特性。在本文中，我们考虑分段可伸缩框架。得到了它们的一些特征，并证明了它们在幺正算子和两个Hilbert空间之间同构的条件下是稳定的。我们进一步得到了Hilbert空间中分段可伸缩框架及其张量积之间的关系

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

International Journal of Wavelets Multiresolution and Information Processing 工程技术-计算机：软件工程

CiteScore

2.60

自引率

7.10%

发文量

审稿时长

2.7 months

期刊介绍： International Journal of Wavelets, Multiresolution and Information Processing (hereafter referred to as IJWMIP) is a bi-monthly publication for theoretical and applied papers on the current state-of-the-art results of wavelet analysis, multiresolution and information processing. Papers related to the IJWMIP theme are especially solicited, including theories, methodologies, algorithms and emerging applications. Topics of interest of the IJWMIP include, but are not limited to: 1. Wavelets: Wavelets and operator theory Frame and applications Time-frequency analysis and applications Sparse representation and approximation Sampling theory and compressive sensing Wavelet based algorithms and applications 2. Multiresolution: Multiresolution analysis Multiscale approximation Multiresolution image processing and signal processing Multiresolution representations Deep learning and neural networks Machine learning theory, algorithms and applications High dimensional data analysis 3. Information Processing: Data sciences Big data and applications Information theory Information systems and technology Information security Information learning and processing Artificial intelligence and pattern recognition Image/signal processing.