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A class of tight framelet packets

Da-Yong Lu, Qi-Bin Fan (2011)

Czechoslovak Mathematical Journal

This paper obtains a class of tight framelet packets on L 2 ( ℝ d ) from the extension principles and constructs the relationships between the basic framelet packets and the associated filters.

A cryptography using lifting scheme integer wavelet transform over min-max-plus algebra

Mahmud Yunus, Mohamad Ilham Dwi Firmansyah, Kistosil Fahim Subiono (2024)

Kybernetika

We propose a cryptographic algorithm utilizing integer wavelet transform via a lifting scheme. In this research, we construct some predict and update operators within the lifting scheme of wavelet transforms employing operations in min-max-plus algebra, termed as lifting scheme integer wavelet transform over min-max-plus algebra (MMPLS-IWavelet). The analysis and synthesis process on MMPLS-IWavelet is implemented for both encryption and decryption processes. The encryption key comprises a sequence...

A general construction of nonseparable multivariate orthonormal wavelet bases

Abderrazek Karoui (2008)

Open Mathematics

The construction of nonseparable and compactly supported orthonormal wavelet bases of L 2(R n); n ≥ 2, is still a challenging and an open research problem. In this paper, we provide a special method for the construction of such wavelet bases. The wavelets constructed by this method are dyadic wavelets. Also, we show that our proposed method can be adapted for an eventual construction of multidimensional orthogonal multiwavelet matrix masks, candidates for generating multidimensional multiwavelet...

A geometrical solution of a problem on wavelets

Antoine Ayaghe (2000)

Studia Mathematica

We prove the existence of nonseparable, orthonormal, compactly supported wavelet bases for L 2 ( ℝ 2 ) of arbitrarily high regularity by using some basic techniques of algebraic and differential geometry. We even obtain a much stronger result: “most” of the orthonormal compactly supported wavelet bases for L 2 ( ℝ 2 ) , of any regularity, are nonseparable

A gradient-projective basis of compactly supported wavelets in dimension n > 1

Guy Battle (2013)

Open Mathematics

A given set W = W X of n-variable class C 1 functions is a gradient-projective basis if for every tempered distribution f whose gradient is square-integrable, the sum ∑ χ ( ∫ ℝ n ∇ f · ∇ W χ * ) W χ converges to f with respect to the norm ∇ ( · ) L 2 ( ℝ n ) . The set is not necessarily an orthonormal set; the orthonormal expansion formula is just an element of the convex set of valid expansions of the given function f over W. We construct a gradient-projective basis W = W x of compactly supported class C 2−ɛ functions on ℝn such that [...]...

A note on integer translates of a square integrable function on ℝ

Maciej Paluszyński (2010)

Colloquium Mathematicae

We consider the subspace of L²(ℝ) spanned by the integer shifts of one function ψ, and formulate a condition on the family ψ ( · - n ) n = - ∞ ∞ , which is equivalent to the weight function ∑ n = - ∞ ∞ | ψ ̂ ( · + n ) | ² being > 0 a.e.

A survey on wavelet methods for (geo) applications.

Willi Freeden, Thorsten Maier, Steffen Zimmermann (2003)

Revista Matemática Complutense

Wavelets originated in 1980's for the analysis of (seismic) signals and have seen an explosion of applications. However, almost all the material is based on wavelets over Euclidean spaces. This paper deals with an approach to the theory and algorithmic aspects of wavelets in a general separable Hilbert space framework. As examples Legendre wavelets on the interval [-1,+1] and scalar and vector spherical wavelets on the unit sphere 'Omega' are discussed in more detail.

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