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Journal articles on the topic 'Tight frame wavelet'

Author: Grafiati

Published: 9 March 2023

Last updated: 31 July 2025

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1

Toda, Hiroshi, Zhong Zhang, and Takashi Imamura. "Practical design of perfect-translation-invariant real-valued discrete wavelet transform." International Journal of Wavelets, Multiresolution and Information Processing 12, no. 04 (2014): 1460005. http://dx.doi.org/10.1142/s0219691314600054.

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The real-valued tight wavelet frame having perfect translation invariance (PTI) has already proposed. However, due to the irrational-number distances between wavelets, its calculation amount is very large. In this paper, based on the real-valued tight wavelet frame, a practical design of a real-valued discrete wavelet transform (DWT) having PTI is proposed. In this transform, all the distances between wavelets are multiples of 1/4, and its transform and inverse transform are calculated fast by decomposition and reconstruction algorithms at the sacrifice of a tight wavelet frame. However, the r

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2

Gao, Jing Li, and Shi Hui Cheng. "The Traits of Canonical Banach Frames Generated by Multiple Scaling Functions and Applications in Applied Materials." Advanced Materials Research 684 (April 2013): 663–66. http://dx.doi.org/10.4028/www.scientific.net/amr.684.663.

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Frame theory has become a popular subject in scientific research during the past twenty years. In our study we use generalized multiresolution analyses in with dilation factor 4. We describe, in terms of the underlying multiresolution structure, all generalized multiresolution analyses Parseval frame wavelets all semi-orthogonal Parseval frame wavelets in . We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions. That is to say, the canonica

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3

Xu, Yong Fan. "The Characteristics of Orthogonal Wavelet Frames and Canonical Frames and Applications in Material Science." Advanced Materials Research 721 (July 2013): 741–44. http://dx.doi.org/10.4028/www.scientific.net/amr.721.741.

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Wavelet analysis has become a popular subject in scientific research during the past twenty years. We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions. That is to say, the canonical dual wavelet frame cannot be generated by the translations and dilations of a single function. Traits of tight wavelet frames are presented.

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Sun, Song Zhen, and Yi Guo. "Study of Periodic Frames and Trivariate Tight Wavelet Frames and Applications in Materials Engineering." Advanced Materials Research 1079-1080 (December 2014): 878–81. http://dx.doi.org/10.4028/www.scientific.net/amr.1079-1080.878.

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It is shown that there exists a frame wavelet with fast decay in the time domain and compact support in the frequency domain generating a wavelet system whose canonical dual frame cannot be generated by an arbitrary number of generators. We show that there exist wavelet frame generated by two functions which have good dual wavelet frames, but for which the canonical dual wavelet frame does not consist of wavelets, according to scaling functions.

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5

Ahmad, Owais. "Characterization of tight wavelet frames with composite dilations in L2(Rn)." Publications de l'Institut Math?matique (Belgrade) 113, no. 127 (2023): 121–29. http://dx.doi.org/10.2298/pim2327121a.

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Tight wavelet frames are different from the orthonormal wavelets because of redundancy. By sacrificing orthonormality and allowing redundancy, the tight wavelet frames become much easier to construct than the orthonormal wavelets. Guo, Labate, Lim, Weiss, and Wilson [Electron. Res. Announc. Am. Math. Soc. 10 (2004), 78-87] introduced the theory of wavelets with composite dilations in order to provide a framework for the construction of waveforms defined not only at various scales and locations but also at various orientations. In this paper, we provide the characterization of composite wavelet

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6

SHAH, FIRDOUS AHMAD. "TIGHT WAVELET FRAMES GENERATED BY THE WALSH POLYNOMIALS." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 06 (2013): 1350042. http://dx.doi.org/10.1142/s0219691313500422.

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Tight wavelet frames and their promising features in applications have attracted a great deal of interest and effort in recent years. In this paper, we give an explicit construction of tight wavelet frames generated by the Walsh polynomials on positive half-line ℝ+ using the extension principles. Finally, we derive the wavelet frame decomposition and reconstruction formulas which are similar to those of orthonormal wavelets on positive half-line ℝ+.

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FU, ZUOXIAN, CAIXIA DENG, and YUANYAN TANG. "A METHOD FOR CONSTRUCTION OF BIVARIATE N-BAND WAVELET TIGHT FRAMES." International Journal of Wavelets, Multiresolution and Information Processing 11, no. 03 (2013): 1350023. http://dx.doi.org/10.1142/s0219691313500239.

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This paper presents a construction method of bivariate N-band wavelet tight frames. First, we discuss the properties of N-band scaling functions, and the construction of the corresponding wavelet tight frame as well as the explication of the formula of the wavelet tight frame. Thereafter, the decomposition and reconstruction formulas of the bivariate N-band wavelet tight frames are provided. Finally, the numerical example is given.

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8

LI, DENG-FENG, and JUN-FANG CHENG. "CONSTRUCTION OF MRA E-TIGHT FRAME WAVELETS, MULTIPLIERS AND CONNECTIVITY PROPERTIES." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 05 (2011): 713–29. http://dx.doi.org/10.1142/s0219691311004274.

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A method that constructs an MRA E-tight frame wavelet by using a generalized low pass E-filter is given, and it is showed that all of MRA E-tight frame wavelets can be obtained via the method, where the dilation matrix E is the quincunx matrix or the matrix consists of (0, 1)T and (2, 0)T. Furthermore, the properties of MRA E-tight frame wavelet multipliers as well as E-pseudoscaling function multipliers and generalized low pass E-filter multipliers are characterized. In addition, as an application of these multipliers, we discuss the connectivity of the set of all MRA E-tight frame wavelets i

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9

Farkov, Yuri, Elena Lebedeva, and Maria Skopina. "Wavelet frames on Vilenkin groups and their approximation properties." International Journal of Wavelets, Multiresolution and Information Processing 13, no. 05 (2015): 1550036. http://dx.doi.org/10.1142/s0219691315500368.

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An explicit description of all Walsh polynomials generating tight wavelet frames is given. An algorithm for finding the corresponding wavelet functions is suggested, and a general form for all wavelet frames generated by an appropriate Walsh polynomial is described. Approximation properties of tight wavelet frames are also studied. In contrast to the real setting, it appeared that a wavelet tight frame decomposition has an arbitrary large approximation order whenever all wavelet functions are compactly supported.

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10

JEONG, BYEONGSEON, MYUNGJIN CHOI, and HONG OH KIM. "CONSTRUCTION OF SYMMETRIC TIGHT WAVELET FRAMES FROM QUASI-INTERPOLATORY SUBDIVISION MASKS AND THEIR APPLICATIONS." International Journal of Wavelets, Multiresolution and Information Processing 06, no. 01 (2008): 97–120. http://dx.doi.org/10.1142/s0219691308002240.

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This paper presents tight wavelet frames with two compactly supported symmetric generators of more than one vanishing moments in the Unitary Extension Principle. We determine all possible free tension parameters of the quasi-interpolatory subdivision masks whose corresponding refinable functions guarantee our wavelet frame. In order to reduce shift variance of the standard discrete wavelet transform, we use the three times oversampling filter bank and eventually obtain a ternary (low, middle, high) frequency scale. In applications to signal/image denoising and erasure recovery, the results dem

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11

Zhou, Jie, and Zeze Zhang. "A Brief Survey of the Graph Wavelet Frame." Complexity 2022 (October 3, 2022): 1–12. http://dx.doi.org/10.1155/2022/8153249.

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In recent years, the research of wavelet frames on the graph has become a hot topic in harmonic analysis. In this paper, we mainly introduce the relevant knowledge of the wavelet frames on the graph, including relevant concepts, construction methods, and related theory. Meanwhile, because the construction of graph tight framelets is closely related to the classical wavelet framelets on ℝ , we give a new construction of tight frames on ℝ . Based on the pseudosplines of type II, we derive an MRA tight wavelet frame with three generators ψ 1 , ψ 2 , and ψ 3 using the oblique extension principle (

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12

Chen, Qing Jiang, Yu Zhou Chai, and Chuan Li Cai. "The Study of Tight Periodic Wavelet Frames and Wavelet Frame Packets and Applications." Advanced Materials Research 977 (June 2014): 532–35. http://dx.doi.org/10.4028/www.scientific.net/amr.977.532.

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Information science focuses on understanding problems from the perspective of the stake holders involved and then applying information and other technologies as needed. A necessary and sufficient condition is identified in term of refinement masks for applying the unitary extension principle for periodic functions to construct tight wavelet frames. Then a theory on the approxi-mation order of truncated tight frame series is established, which facilitates construction of tight periodic wavelet frames with desirable approximation order. The pyramid decomposition scheme is derived based on the ge

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Li, Baobin. "Constructing totally interpolating wavelet frame systems." International Journal of Wavelets, Multiresolution and Information Processing 13, no. 03 (2015): 1550017. http://dx.doi.org/10.1142/s0219691315500174.

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The system of totally interpolating wavelet frames is discussed in this paper, in which both the scaling function and one of wavelet functions are interpolating. It will be shown that corresponding filter banks possess the special structure, and the parametrization of filter banks is present. Moreover, we show that when considering tight frame systems with two generators, the Ron–Shen's continuous-linear-spline-based tight frame is the only one with totally interpolating property and symmetry. But in the dual frame context, more good examples of bi-frames with symmetric/antisymmetric property

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14

YANG, SHOUZHI, and YANMEI XUE. "CONSTRUCTION OF COMPACTLY SUPPORTED CONJUGATE SYMMETRIC COMPLEX TIGHT WAVELET FRAMES." International Journal of Wavelets, Multiresolution and Information Processing 08, no. 06 (2010): 861–74. http://dx.doi.org/10.1142/s0219691310003857.

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Two algorithms for constructing a class of compactly supported complex tight wavelet frames with conjugate symmetry are provided. Firstly, based on a given complex refinable function ϕ, an explicit formula for constructing complex tight wavelet frames is presented. If the given complex refinable function ϕ is compactly supported conjugate symmetric, then we prove that there exists a compactly supported conjugate symmetric/anti-symmetric complex tight wavelet frame Ψ = {ψ1, ψ2, ψ3} associated with ϕ. Secondly, under the conditions that both the low-pass filters and high-pass filters are unknown

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15

KROMMWEH, JENS. "TIGHT FRAME CHARACTERIZATION OF MULTIWAVELET VECTOR FUNCTIONS IN TERMS OF THE POLYPHASE MATRIX." International Journal of Wavelets, Multiresolution and Information Processing 07, no. 01 (2009): 9–21. http://dx.doi.org/10.1142/s0219691309002751.

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The extension principles play an important role in characterizing and constructing of wavelet frames. The common extension principles, the unitary extension principle (UEP) or the oblique extension principle (OEP), are based on the unitarity of the modulation matrix. In this paper, we state the UEP and OEP for refinable function vectors in the polyphase representation. Finally, we apply our results to directional wavelets on triangles which we have constructed in a previous work. We will show that the wavelet system generates a tight frame for L2(ℝ2).

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16

Borup, L., R. Gribonval, and M. Nielsen. "Tight wavelet frames in Lebesgue and Sobolev spaces." Journal of Function Spaces and Applications 2, no. 3 (2004): 227–52. http://dx.doi.org/10.1155/2004/792493.

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We study tight wavelet frame systems inLp(ℝd)and prove that such systems (under mild hypotheses) give atomic decompositions ofLp(ℝd)for1≺p≺∞. We also characterizeLp(ℝd)and Sobolev space norms by the analysis coefficients for the frame. We consider Jackson inequalities for bestm-term approximation with the systems inLp(ℝd)and prove that such inequalities exist. Moreover, it is proved that the approximation rate given by the Jackson inequality can be realized by thresholding the frame coefficients. Finally, we show that in certain restricted cases, the approximation spaces, for bestm-term approx

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17

Chen, Qing Jiang, Xiao Ting Lei, and Jian Feng Zhou. "The Description and Characterization of Symmetric Frames and Gabor Frames and Applications in Material Engineering." Advanced Materials Research 712-715 (June 2013): 2458–63. http://dx.doi.org/10.4028/www.scientific.net/amr.712-715.2458.

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Materials science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. In this paper, we discuss a new set of symmetric tight frame wave-lets with the associated filterbanks outputs downsampled by several generators. The frames consist of several generators obtained from the lowpass filter using spectral factorization, with lowpass fil-ter via a simple approach using Legendre polynomials. The filters are feasible to be designed and offer smooth scaling functions and frame wavelets. We shall give an example to demonstrste that so -me examp

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18

Srivastava, Swati. "On Normalized Tight Frame Wavelet Sets." Kyungpook mathematical journal 55, no. 1 (2015): 127–35. http://dx.doi.org/10.5666/kmj.2015.55.1.127.

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19

Maury, Saurabh Chandra. "Complete Invariance Property with respect to Homeomorphism over Frame Multiwavelet and Super-Wavelet Spaces." Journal of Mathematics 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/528342.

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We discuss the complete invariance property with respect to homeomorphism (CIPH) over various sets of wavelets containing all orthonormal multiwavelets, all tight frame multiwavelets, all super-wavelets of lengthn, and all normalized tight super frame wavelets of lengthn.

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20

Zhao, Ping, and Chun Zhao. "Three-channel Symmetric Tight Frame Wavelet Design Method." Information Technology Journal 12, no. 4 (2013): 623–31. http://dx.doi.org/10.3923/itj.2013.623.631.

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21

Iosevich, Alex, Chun-Kit Lai, and Azita Mayeli. "Tight wavelet frame sets in finite vector spaces." Applied and Computational Harmonic Analysis 46, no. 1 (2019): 192–205. http://dx.doi.org/10.1016/j.acha.2017.10.005.

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22

WANG, HAIHUI, and XIAO KONG. "A MULTISCALE TIGHT FRAME-INSPIRED SCHEME FOR NONLINEAR DIFFUSION." International Journal of Wavelets, Multiresolution and Information Processing 10, no. 05 (2012): 1250041. http://dx.doi.org/10.1142/s0219691312500415.

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Nonlinear diffusion and wavelet shrinkage are two successfully applied methods for discontinuity preserving denoising of signals and images. Recently, relations between both methods have been established taking into account wavelet shrinkage at one or multiscale. In this paper we show that one step of (stabilized) explicit discretization of nonlinear diffusion can be expressed in terms of tight frame shrinkage on a single spatial level or multiscale. We prove that our scheme permits larger steps while having more choices of shrinkage functions. Numerical examples demonstrate the behavior of ou

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23

Shen, Jian Guo. "The Bivariate Minimum-Energy Tight Wavelet Frames and Applications in Economics and Management." Advanced Materials Research 915-916 (April 2014): 1412–17. http://dx.doi.org/10.4028/www.scientific.net/amr.915-916.1412.

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Material science is an interdisciplinary field applying the properties of matter to various areas of science and engineering. Frames have become the focus of active research field, both in the-ory and in applications. In the article, the binary minimum-energy wavelet frames and frame multi-resolution resolution are introduced. A precise existence criterion for minimum-energy frames in terms of an ineqity condition on the Laurent poly-nomial symbols of the filter functions is provided. An explicit formula for designing minimum-energy frames is also established. The sufficient condi tion for the

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Yadav, G. C. S., and Amita Dwivedi. "Construction of three interval frame scaling sets." International Journal of Wavelets, Multiresolution and Information Processing 18, no. 04 (2020): 2050029. http://dx.doi.org/10.1142/s0219691320500290.

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In this paper, a construction of three interval frame scaling sets is described and certain classes of normalized tight frame wavelet sets are also constructed with the help of these three interval frame scaling sets. We also generalize this construction to obtain [Formula: see text]-interval frame scaling sets.

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25

李, 晨. "Wavelet Tight Frame Construction Based on Multi-Resolution Analysis." Pure Mathematics 10, no. 11 (2020): 1106–14. http://dx.doi.org/10.12677/pm.2020.1011132.

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Shen, Jian Guo. "The Presentation of the Quarternary Super-Wavelet Wraps and Applications in Material Science." Advanced Materials Research 684 (April 2013): 469–72. http://dx.doi.org/10.4028/www.scientific.net/amr.684.469.

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Our goal is to obtain a character -ization of normalized tight frame super-wavelets The basis of materials science involves relating the desired properties and relative performance of a material in a certain application to the structure of the atoms and phases in that material through characterization. An approach for designing a sort of biorthogonal vector-valued wavelet wraps in four-dimensional space is presented and their biorthogonality traits are characterized by virtue of iteration method and time-frequency analysis method. The biorthogonality formulas concerning these wavelet wraps are

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Yunus, Mahmud, and Hendra Gunawan. "Tight Wavelet Frame Decomposition and Its Application in Image Processing." ITB Journal of Sciences 40, no. 2 (2008): 151–65. http://dx.doi.org/10.5614/itbj.sci.2008.40.2.5.

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PENG, LIZHONG, and WEITAO YUAN. "HIGHER-DENSITY DUAL TREE DISCRETE WAVELET TRANSFORM." International Journal of Wavelets, Multiresolution and Information Processing 05, no. 05 (2007): 815–41. http://dx.doi.org/10.1142/s0219691307002063.

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This paper introduces the higher-density dual-tree (HDDT) discrete wavelet transform (DWT). A new MRA is introduced to describe higher-density DWT and used to obtain the sufficient condition for the HDDT Hilbert transform pair. In designing HDDT filters we use the extended common-factor method which not only includes the common-factor method but also provides exact linear phase bi-frame filters. Both HDDT tight frame and bi-frame (anti)symmetric filter design methods are given. At last, the results of denoising experiments by our newly designed HDDT filters in this paper prove the effectivenes

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Yang, Xiaocheng, Xiang You, Lin Wu, et al. "A Radio-interferometric Imaging Method Based on the Wavelet Tight Frame." Astronomical Journal 169, no. 3 (2025): 130. https://doi.org/10.3847/1538-3881/ada28d.

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Abstract Reconstructing the signal from measured visibilities in radio interferometry is an ill-posed inverse problem. In this paper, we present a novel radio-interferometric imaging method based on the wavelet tight frame aimed at efficiently obtaining an accurate solution. In our approach, the signal is sparsely represented by the directional tensor product complex tight framelets, which can effectively capture the texture and shape features of the images. To enhance computational efficiency, we employ the projected fast iterative soft-thresholding algorithm for solving the l 1-norm minimiza

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Ji, Hui, Zuowei Shen, and Yuhong Xu. "Wavelet Based Restoration of Images with Missing or Damaged Pixels." East Asian Journal on Applied Mathematics 1, no. 2 (2011): 108–31. http://dx.doi.org/10.4208/eajam.020310.240610a.

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AbstractThis paper addresses the problem of how to restore degraded images where the pixels have been partly lost during transmission or damaged by impulsive noise. A wide range of image restoration tasks is covered in the mathematical model considered in this paper - e.g. image deblurring, image inpainting and super-resolution imaging. Based on the assumption that natural images are likely to have a sparse representation in a wavelet tight frame domain, we propose a regularization-based approach to recover degraded images, by enforcing the analysis-based sparsity prior of images in a tight fr

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31

Fomel, Sergey, and Yang Liu. "Seislet transform and seislet frame." GEOPHYSICS 75, no. 3 (2010): V25—V38. http://dx.doi.org/10.1190/1.3380591.

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We introduce a digital waveletlike transform, which is tailored specifically for representing seismic data. The transform provides a multiscale orthogonal basis with basis functions aligned along seismic events in the input data. It is defined with the help of the wavelet-lifting scheme combined with local plane-wave destruction. In the 1D case, the seislet transform is designed to follow locally sinusoidal components. In the 2D case, it is designed to follow local plane-wave components with smoothly variable slopes. If more than one component is present, the transform turns into an overcomple

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Liang, Jingwei, Jianwei Ma, and Xiaoqun Zhang. "Seismic data restoration via data-driven tight frame." GEOPHYSICS 79, no. 3 (2014): V65—V74. http://dx.doi.org/10.1190/geo2013-0252.1.

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Restoration/interpolation of missing traces plays a crucial role in the seismic data processing pipeline. Efficient restoration methods have been proposed based on sparse signal representation in a transform domain such as Fourier, wavelet, curvelet, and shearlet transforms. Most existing methods are based on transforms with a fixed basis. We considered an adaptive sparse transform for restoration of data with complex structures. In particular, we evaluated a data-driven tight-frame-based sparse regularization method for seismic data restoration. The main idea of the data-driven tight frame (T

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Zhang, Le Juan, Lu Zhang, Zhi Ming LI, and Shi Yao Cui. "Study of Gabor Features and Heart Sound Signal Recognition by the Principal Component Analysis." Applied Mechanics and Materials 644-650 (September 2014): 4452–54. http://dx.doi.org/10.4028/www.scientific.net/amm.644-650.4452.

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Simple cells Gabor wavelet transform and human visual system in the visual stimulus response very similar. It has the good characteristics of the local space in the extraction of target and frequency domain information. Although the Gabor wavelet does not of itself constitute orthogonal basis, but in the specific parameters can form a tight frame. Gabor wavelet is sensitive to the image edge, can provide good direction and scale selection characteristics, but also insensitive to illumination changes, can provide the illumination change good adaptability. These features make Gabor wavelet is wi

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Chen, Zhen, Yuli Fu, Youjun Xiang, Junwei Xu, and Rong Rong. "A novel low-rank model for MRI using the redundant wavelet tight frame." Neurocomputing 289 (May 2018): 180–87. http://dx.doi.org/10.1016/j.neucom.2018.02.002.

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Wang, Chengxiang, Li Zeng, Yumeng Guo, and Lingli Zhang. "Wavelet tight frame and prior image-based image reconstruction from limited-angle projection data." Inverse Problems & Imaging 11, no. 6 (2017): 917–48. http://dx.doi.org/10.3934/ipi.2017043.

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Luo, Xiaoqiang, Wei Yu, and Chengxiang Wang. "An Image Reconstruction Method Based on Total Variation and Wavelet Tight Frame for Limited-Angle CT." IEEE Access 6 (2018): 1461–70. http://dx.doi.org/10.1109/access.2017.2779148.

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Zhang, Liang, and Jingtian Tang. "AMT denoising via double sparse dictionary learning." Journal of Physics: Conference Series 2895, no. 1 (2024): 012047. https://doi.org/10.1088/1742-6596/2895/1/012047.

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Abstract Audio magnetotellurics (AMT) is commonly employed in the exploration of resources. However, the energy of AMT signals is relatively weak, making them susceptible to various artificial sources of interference, thus being submerged in intense noise. This poses a significant disadvantage for the identification of various resources. Sparse representation is a commonly used method for AMT denoising, but under strong noise interference, conventional sparse representation methods often fail to effectively remove noise due to the inadequate performance of the sparse basis. To enhance the perf

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38

He, Mi, Yongjian Nian, Luping Xu, Lihong Qiao, and Wenwu Wang. "Adaptive Separation of Respiratory and Heartbeat Signals among Multiple People Based on Empirical Wavelet Transform Using UWB Radar." Sensors 20, no. 17 (2020): 4913. http://dx.doi.org/10.3390/s20174913.

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The non-contact monitoring of vital signs by radar has great prospects in clinical monitoring. However, the accuracy of separated respiratory and heartbeat signals has not satisfied the clinical limits of agreement. This paper presents a study for automated separation of respiratory and heartbeat signals based on empirical wavelet transform (EWT) for multiple people. The initial boundary of the EWT was set according to the limited prior information of vital signs. Using the initial boundary, empirical wavelets with a tight frame were constructed to adaptively separate the respiratory signal, t

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Xu, Na, Huiling Hou, Zhiyong Cheng, Mingquan Wang, Yu Wang, and Guogang Wang. "Nonlocal Low-Rank and Prior Image-Based Reconstruction in a Wavelet Tight Frame Using Limited-Angle Projection Data." IEEE Access 9 (2021): 24616–28. http://dx.doi.org/10.1109/access.2021.3057489.

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40

Abraham Sundar, K. Joseph, V. Vaithiyanathan, G. Raja Singh Thangadurai, and Naveen Namdeo. "Design and Analysis of Fusion Algorithm for Multi-Frame Super-Resolution Image Reconstruction using Framelet." Defence Science Journal 65, no. 4 (2015): 292. http://dx.doi.org/10.14429/dsj.65.8265.

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<p>A enhanced fusion algorithm for generating a super resolution image from a sequence of low-resolution images captured from identical scene apparently a video, based on framelet have been designed and analyzed. In this paper an improved analytical method of image registration is used which integrates nearest neighbor method and gradient method. Comparing to Discrete Wavelet Transform (DWT) the Framelet Transform (FrT) have tight frame filter bank that offers symmetry and permits shift in invariance. Therefore using framelet this paper also present a framelet based enhanced fusion for c

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Skopina, M. A. "Tight wavelet frames." Doklady Mathematics 77, no. 2 (2008): 182–85. http://dx.doi.org/10.1134/s1064562408020063.

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Charina, Maria, and Joachim Stöckler. "Tight wavelet frames for subdivision." Journal of Computational and Applied Mathematics 221, no. 2 (2008): 293–301. http://dx.doi.org/10.1016/j.cam.2007.10.033.

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43

Han, Bin. "On Dual Wavelet Tight Frames." Applied and Computational Harmonic Analysis 4, no. 4 (1997): 380–413. http://dx.doi.org/10.1006/acha.1997.0217.

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Sun, Jianjun, Bin Huang, Xiaodong Chen, and Lihong Cui. "Symmetry Feature and Construction for the 3-Band Tight Framelets with Prescribed Properties." Journal of Applied Mathematics 2012 (2012): 1–20. http://dx.doi.org/10.1155/2012/907175.

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A construction approach for the 3-band tight wavelet frames by factorization of paraunitary matrix is developed. Several necessary constraints on the filter lengths and symmetric features of wavelet frames are investigated starting at the constructed paraunitary matrix. The matrix is a symmetric extension of the polyphase matrix corresponding to 3-band tight wavelet frames. Further, the parameterizations of 3-band tight wavelet frames with3N+1filter lengths are established. Examples of framelets with symmetry/antisymmetry and Sobolev exponent are computed by appropriately choosing the paramete

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Leonardi, Nora, and Dimitri Van De Ville. "Tight Wavelet Frames on Multislice Graphs." IEEE Transactions on Signal Processing 61, no. 13 (2013): 3357–67. http://dx.doi.org/10.1109/tsp.2013.2259825.

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Goh, Say Song, Zhi Yuan Lim, and Zuowei Shen. "Symmetric and antisymmetric tight wavelet frames." Applied and Computational Harmonic Analysis 20, no. 3 (2006): 411–21. http://dx.doi.org/10.1016/j.acha.2005.09.006.

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Farkov, Yuri A. "Wavelet tight frames in Walsh analysis." Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae. Sectio computatorica, no. 49 (2019): 161–77. https://doi.org/10.71352/ac.49.161.

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Ştefănoiu, Dan. "Parametric Wavelets: Tight Frames Class." IFAC Proceedings Volumes 30, no. 27 (1997): 135–41. http://dx.doi.org/10.1016/s1474-6670(17)41170-0.

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Bownik, Marcin. "Tight frames of multidimensional wavelets." Journal of Fourier Analysis and Applications 3, no. 5 (1997): 525–42. http://dx.doi.org/10.1007/bf02648882.

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Shirasuna, Miyori, Zhong Zhang, Hiroshi Toda, and Tetsuo Miyake. "Design of Approximate Tight Wavelet Frames Using Gabor Wavelet." Journal of Signal Processing 20, no. 1 (2016): 41–53. http://dx.doi.org/10.2299/jsp.20.41.

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