Reconstruction of sparse wavelet signals from partial Fourier measurements

In this paper, we show that high-dimensional sparse wavelet signals of finite levels can be constructed from their partial Fourier measurements on a deterministic sampling set with cardinality about a multiple of signal sparsity

A connection between multiresolution wavelet theory of scale N and representations of the Cuntz algebra O_N

In this paper we give a short survey of a connection between the theory of wavelets in L^2(R) and certain representations of the Cuntz algebra on L^2(T).Comment: 13 pages, AMS-TeX version 2.1, uses LaTeX circle font lcircle10. To appear in J. Roberts, ed., Proceedings of the Rome Conference on Operator Algebras and Quantum Field Theory. Survey article; for complete proofs see funct-an/9612002 and funct-an/9612003 by the same author

Multiresolution Analysis and Haar Wavelets on the Laguerre Hypergroup

Let ℍn be the Heisenberg group. The fundamental manifold of the radial function space for ℍn can be denoted by [0,+∞)×ℝ, which is just the Laguerre hypergroup. In this paper the multiresolution analysis on the Laguerre hypergroup 𝕂=[0,+∞)×ℝ is defined. Moreover the properties of Haar wavelet bases for La2(𝕂) are investigated

Мішана вейвлет-апроксимація Хаара функцій трьох змінних

Запропоновано метод побудови операторів мішаної вейвлет-апроксимації Хаара функцій трьох змінних. Доведені їх властивості, а також теорема про оцінку похибки наближення неперервних функцій цими операторами.The article suggests a method of creating Haar’s blending wavelet-approximation operators of functions of three variables. Proved their properties, as well as the theorem on error estimation of the approximation of continuous functions by these operators

Мішана вейвлет-апроксимація Хаара функцій трьох змінних

Запропоновано метод побудови операторів мішаної вейвлет-апроксимації Хаара функцій трьох змінних. Доведені їх властивості, а також теорема про оцінку похибки наближення неперервних функцій цими операторами.The article suggests a method of creating Haar’s blending wavelet-approximation operators of functions of three variables. Proved their properties, as well as the theorem on error estimation of the approximation of continuous functions by these operators

Decomposition of Integral Self-Affine Multi-Tiles

In this paper, we propose a method to decompose an integral self-affine ${\mathbb Z}^n$-tiling set $K$ into measure disjoint pieces $K_j$ satisfying $K=\displaystyle\bigcup K_j$ in such a way that the collection of sets $K_j$ forms an integral self-affine collection associated with the matrix $B$ and this with a minimum number of pieces $K_j$. When used on a given measurable $\mathbb{Z}^n$-tiling set $K\subset\mathbb{R}^n$, this decomposition terminates after finitely many steps if and only if the set $K$ is an integral self-affine multi-tile. Furthermore, we show that the minimal decomposition we provide is unique.Comment: 15pages, 5figures, added references, typo correction