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Advanced signal-processing framework for remote photoplethysmography-based heart rate measurement: Integrating adaptive Kalman filtering with discrete wavelet transformation. [PDF]

PLoS One
Debnath U, Kim S.
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Hybrid wavelet transform, K-means singular value decomposition and Spatial memory guided cat swarm optimization technique for watermark embedding. [PDF]

Sci Rep
Sharma C, Dhillon A, Prashar D, Khan AA, Ali F, AlZubi AA.   +5 more
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Head direction cells use a head-referenced dual-axis updating rule in 3D space

Williams M, Street J, Burgess N, Jeffery K.   +3 more
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Partial Gabor frames and dual frames

International Journal of Wavelets, Multiresolution and Information Processing, 2021
The 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.
Tian, Yu, Jia, Hui-Fang, He, Guo-Liang
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GP-woven dual frames

Journal of Pseudo-Differential Operators and Applications, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bibak Hafshejani, Akram, Dehghan, Mohammad Ali   +1 more
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Tensor Product K-Dual Frames

Bulletin of the Malaysian Mathematical Sciences Society, 2023
\textit{R. J. Duffin} and \textit{A. C. Schaeffer} [Trans. Am. Math. Soc. 72, 341--366 (1952; Zbl 0049.32401)] introduced the concept of frame in the context of nonharmonic Fourier series. Later, \textit{I. Daubechies} et al. [J. Math. Phys. 27, 1271--1283 (1986; Zbl 0608.46014)] reintroduced and investigated frames, as a generalization of orthonormal ...
Keyshams, Z., Ghasemi, B., Abtahi, F.
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Duals of Frame Sequences

Acta Applicandae Mathematicae, 2008
Let \(\mathcal{H}\) be a separable Hilbert space and \(J\) a countable index set. A sequence \(\{ y_j\}_{j\in J}\) is called a {\textit{Bessel sequence}} in \(\mathcal{H}\) if the bound \(\sum_{j\in J} |\langle x,\, y_j\rangle|^2\leq C\|x\|_{\mathcal{H}}\) holds for all \(x\in \mathcal{H}\), and \(\{ x_j\}_{j\in J}\) is called a {\textit{frame sequence}
Heil, Christopher, Koo, Yoo Young, Lim, Jae Kun   +2 more
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Dual Frame and Multiple Frame Surveys

2020
Practical 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.
Changbao Wu, Mary E. Thompson
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Hilbert–Schmidt frames and their duals

International Journal of Wavelets, Multiresolution and Information Processing, 2021
The 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.
Li, Ya-Nan, Li, Yun-Zhang
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Partial affine system–based frames and dual frames

Mathematical Methods in the Applied Sciences, 2017
In this paper, we introduce the notion of partial affine system that is a subset of an affine system. It has potential applications in signal analysis. A general affine system has been extensively studied; however, the partial one has not. The main focus of this paper is on partial affine system–based frames and dual frames.
Yun‐Zhang Li, Yu Tian
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