Recent Developments on Dual Wavelet Frames

Han, Bin

doi:10.1007/978-0-8176-4683-7_6

Cited by 2 publications

(3 citation statements)

References 31 publications

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“…Theorem 14. If a given set of masks { : 0 ≤ ≤ } and {̃: 0 ≤ ≤ } in ℓ 1 (Z) satisfy (20), then, the discrete dual wavelet frame transforms and defined on = { , , } satisfy = : → .…”

Section: Algorithm 13 Given a Signalmentioning

confidence: 99%

“…Then, this group of masks satisfy (20). Hence, the system pair ( (Ψ), (Ψ)) defined in (8) and (10) associated with the masks {̂0,̂1,̂2,̂3}, {̂0,̂1,̂2,̂3} is a dual wavelet frame for In our simulations, we choose the dual wavelet frame system given in Example 17.…”

Section: Numerical Simulations Of Dwftgmentioning

confidence: 99%

“…Jiang and Pounds studied sixfold symmetric biframes with four framelets (frame generators) for triangular-mesh-based surface multiresolution processing in [18]. Readers can refer to [19][20][21][22] for more construction methods and properties regarding dual wavelet frameworks in 2 (R ).…”

Section: And Van De Ville Introducedmentioning

confidence: 99%

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Dual Wavelet Frame Transforms on Manifolds and Graphs

Cui

Liu

et al. 2019

Journal of Mathematics

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In this paper, we consider the dual wavelet frames in both continuum setting, i.e., on manifolds, and discrete setting, i.e., on graphs. Firstly, we give sufficient conditions for the existence of dual wavelet frames on manifolds by their corresponding masks. Then, we present the formula of the decomposition and reconstruction for the dual wavelet frame transforms on graphs. Finally, we give a numerical example to illustrate the validity of the dual wavelet frame transformation applied to the graph data.

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Section: Algorithm 13 Given a Signalmentioning

confidence: 99%