✦ LIBER ✦

Minimality of the Data in Wavelet Filters

✍ Scribed by Palle E.T Jorgensen

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 974 KB
Volume: 159
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.2000.1958

No coin nor oath required. For personal study only.

✦ Synopsis

Orthogonal wavelets, or wavelet frames, for L 2 (R) are associated with quadrature mirror filters (QMF), a set of complex numbers which relate the dyadic scaling of functions on R to the Z-translates. In this paper, we show that generically, the data in the QMF-systems of wavelets are minimal, in the sense that the data cannot be nontrivially reduced. The minimality property is given a geometric formulation in the Hilbert space l 2 (Z), and it is then shown that minimality corresponds to irreducibility of a wavelet representation of the algebra O 2 ; and so our result is that this family of representations of O 2 on the Hilbert space l 2 (Z) is irreducible for a generic set of values of the parameters which label the wavelet representations.

📜 SIMILAR VOLUMES

Wavelet transform-based Wiener filtering

Wavelet transform-based Wiener filtering of event-related fMRI data

✍ Stephen M. LaConte; Shing-Chung Ngan; Xiaoping Hu 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 400 KB

On a Family of Filters Arising in Wavele

On a Family of Filters Arising in Wavelet Construction

✍ Charles A. Micchelli 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 254 KB

Wavelet reconstruction almost always reduces to the study of certain algebraic identities for polynomials. Typically, one polynomial is chosen and another is found which satisfies an identity appropriate for the desired wavelet construction. In this paper we explore one such equation and give applic

Quantification of MRS data in the freque

Quantification of MRS data in the frequency domain using a wavelet filter, an approximated Voigt lineshape model and prior knowledge

✍ P. Gillies; I. Marshall; M. Asplund; P. Winkler; J. Higinbotham 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 188 KB

Design of orthonormal wavelet filter ban

Design of orthonormal wavelet filter banks using the Remez exchange algorithm

✍ Xi Zhang; Toshinori Yoshikawa 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 209 KB 👁 1 views

This paper presents a new method for designing orthonormal wavelet filter banks using the Remez exchange algorithm. It is well known that orthonormal wavelet bases can be generated by paraunitary filter banks. Thus, synthesis of orthonormal wavelet bases can be reduced to the design of paraunitary f

Denoising of complex MRI data by wavelet

Denoising of complex MRI data by wavelet-domain filtering: Application to high-b-value diffusion-weighted imaging

✍ Ronnie Wirestam; Adnan Bibic; Jimmy Lätt; Sara Brockstedt; Freddy Ståhlberg 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 814 KB

## Abstract The Rician distribution of noise in magnitude magnetic resonance (MR) images is particularly problematic in low signal‐to‐noise ratio (SNR) regions. The Rician noise distribution causes a nonzero minimum signal in the image, which is often referred to as the rectified noise floor. True

Exponential data weighting in the Kalman

Exponential data weighting in the Kalman-Bucy filter

✍ Brian D.O. Anderson 📂 Article 📅 1973 🏛 Elsevier Science 🌐 English ⚖ 788 KB