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Partial Gabor frames and dual frames
International Journal of Wavelets, Multiresolution and Information Processing, 2021The theory of Gabor frames has been extensively investigated. This paper addresses partial Gabor systems. We introduce the concepts of partial Gabor system, frame and dual frame. We present some conditions for a partial Gabor system to be a partial Gabor frame, and using these conditions, we characterize partial dual frames. We also give some examples.
Hui-Fang Jia, Yu Tian, Guo-Liang He
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Journal of Pseudo-Differential Operators and Applications, 2020
The present study deals with the recently introduced concept of P-woven frames. Two frames $$\left\{ \varphi _{i}\right\} _{i\in I}$$ and $$\left\{ \psi _{i}\right\} _{i\in I}$$ for a Hilbert space H are called P-woven, if there exists a nontrivial subset $$\sigma $$ of I such that the family $$\left\{ g_{i}\right\} _{i\in I}$$ represented ...
Mohammad Ali Dehghan +1 more
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The present study deals with the recently introduced concept of P-woven frames. Two frames $$\left\{ \varphi _{i}\right\} _{i\in I}$$ and $$\left\{ \psi _{i}\right\} _{i\in I}$$ for a Hilbert space H are called P-woven, if there exists a nontrivial subset $$\sigma $$ of I such that the family $$\left\{ g_{i}\right\} _{i\in I}$$ represented ...
Mohammad Ali Dehghan +1 more
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Dual Frame and Multiple Frame Surveys
2020Practical issues in the design of a dual frame or multiple frame survey are highly related to the characteristics of the target population and the availability of sampling frames. This chapter focuses on issues with estimation using data from dual or multiple frame surveys.
Mary E. Thompson, Changbao Wu
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Acta Applicandae Mathematicae, 2008
Frames provide unconditional basis-like, but generally nonunique, representations of vectors in a Hilbert space H. The redundancy of frame expansions allows the flexibility of choosing different dual sequences to employ in frame representations. In particular, oblique duals, Type I duals, and Type II duals have been introduced in the literature because
Jae Kun Lim +2 more
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Frames provide unconditional basis-like, but generally nonunique, representations of vectors in a Hilbert space H. The redundancy of frame expansions allows the flexibility of choosing different dual sequences to employ in frame representations. In particular, oblique duals, Type I duals, and Type II duals have been introduced in the literature because
Jae Kun Lim +2 more
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Hilbert–Schmidt frames and their duals
International Journal of Wavelets, Multiresolution and Information Processing, 2021The concept of Hilbert–Schmidt frame (HS-frame) was first introduced by Sadeghi and Arefijamaal in 2012. It is more general than [Formula: see text]-frames, and thus, covers many generalizations of frames. This paper addresses the theory of HS-frames.
Ya-Nan Li, Yun-Zhang Li
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Optimal dual frames for uniform frames with erasures
2015 12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD), 2015Given a frame as a coder, its optimal dual as encoder can make the reconstruction error arising from erasure minimum. According to the eigenvalues of the frame operator, we give some sufficient conditions under which the unique optimal dual frame can be identified.
Qing Gao +3 more
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Equiangular Frames and Their Duals
2021Systems of m equiangular lines spanning \(\mathbb {R}^d\) or \(\mathbb {C}^d\) that satisfy the so-called Welch bound have recently gained a lot of attention due to various applications in signal processing. Such sets are called equiangular tight frames (ETFs).
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A Case of a Dual Frame of Reference
Perception, 1992It is demonstrated that observers may relate to two parts of the same object by using two different frames of reference. Subjects were asked to indicate directions within a model of a hallway in which signs were posted on a single prism. The majority of subjects interpreted a sign frontally facing them as indicating the direction which is ahead of ...
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International Journal of Wavelets, Multiresolution and Information Processing, 2019
This paper is devoted to the study of the dual [Formula: see text]-g-Bessel sequences of [Formula: see text]-g-frames. We firstly make use of the g-preframe operators of a g-Bessel sequence to investigate the constructions of [Formula: see text]-g-frames.
Shengnan Shi, Yongdong Huang
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This paper is devoted to the study of the dual [Formula: see text]-g-Bessel sequences of [Formula: see text]-g-frames. We firstly make use of the g-preframe operators of a g-Bessel sequence to investigate the constructions of [Formula: see text]-g-frames.
Shengnan Shi, Yongdong Huang
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Tight Frames and Dual Frame Pairs
2016We have already highlighted the frame decomposition, which shows that a frame \(\{f_{k}\}_{k=1}^{\infty }\) for a Hilbert space \(\mathcal{H}\) leads to the decomposition $$\displaystyle\begin{array}{rcl} f =\sum _{ k=1}^{\infty }\langle f,S^{-1}f_{ k}\rangle f_{k},\ \ \forall f \in \mathcal{H};& &{}\end{array}$$ (6.1) here \(S: \mathcal{H ...
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