Results 1  10
of
244,078
Complex wavelets for shift invariant analysis and filtering of signals
 J. Applied and Computational Harmonic Analysis
, 2001
"... This paper describes a form of discrete wavelet transform, which generates complex coefficients by using a dual tree of wavelet filters to obtain their real and imaginary parts. This introduces limited redundancy (2m: 1 for mdimensional signals) and allows the transform to provide approximate shift ..."
Abstract

Cited by 379 (40 self)
 Add to MetaCart
to be shift invariant and describe how to estimate the accuracy of this approximation and design suitable filters to achieve this. We discuss two different variants of the new transform, based on odd/even and quartersample shift (Qshift) filters, respectively. We then describe briefly how the dual tree may
The phaselet transform  an integral redundancy nearly shiftinvariant wavelet transform
 IEEE Trans. on Signal Proc
, 2003
"... This paper introduces an approximately shift invariant redundant dyadic wavelet transform the phaselet transform that includes the popular dualtree complex wavelet transform of Kingsbury [1] as a special case. The main idea is to use a finite set of wavelets that are related to each other in a sp ..."
Abstract

Cited by 15 (1 self)
 Add to MetaCart
This paper introduces an approximately shift invariant redundant dyadic wavelet transform the phaselet transform that includes the popular dualtree complex wavelet transform of Kingsbury [1] as a special case. The main idea is to use a finite set of wavelets that are related to each other in a
Nonuniform Sampling and Reconstruction in ShiftInvariant Spaces
, 2001
"... This article discusses modern techniques for nonuniform sampling and reconstruction of functions in shiftinvariant spaces. It is a survey as well as a research paper and provides a unied framework for uniform and nonuniform sampling and reconstruction in shiftinvariant spaces by bringing together ..."
Abstract

Cited by 219 (13 self)
 Add to MetaCart
This article discusses modern techniques for nonuniform sampling and reconstruction of functions in shiftinvariant spaces. It is a survey as well as a research paper and provides a unied framework for uniform and nonuniform sampling and reconstruction in shiftinvariant spaces by bringing
The Structure of Finitely Generated ShiftInvariant Spaces in ...
, 1992
"... : A simple characterization is given of finitely generated subspaces of L 2 (IR d ) which are invariant under translation by any (multi)integer, and used to give conditions under which such a space has a particularly nice generating set, namely a basis, and, more than that, a basis with desirable ..."
Abstract

Cited by 160 (20 self)
 Add to MetaCart
that the approximation order provided by a given local space is already provided by the shiftinvariant space generated by just one function, with this function constructible as a finite linear combination of the finite generating set for the whole space, hence compactly supported. This settles a question of some 20
On ShiftInvariant Sparse Coding
 PRIETO (EDS.), INDEPENDENT COMPONENT ANALYSIS AND BLIND SIGNAL SEPARATION: PROC. FIFTH INTL. CONF., ICA 2004
, 2004
"... The goals of this paper are: 1) the introduction of a shiftinvariant sparse coding model together with learning rules for this model; 2) the comparison of this model to the traditional sparse coding model; and 3) the analysis of some limitations of the newly proposed approach. To evaluate ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
The goals of this paper are: 1) the introduction of a shiftinvariant sparse coding model together with learning rules for this model; 2) the comparison of this model to the traditional sparse coding model; and 3) the analysis of some limitations of the newly proposed approach. To evaluate
Frames and Stable Bases for ShiftInvariant Subspaces of . . .
, 1994
"... Let X be a countable fundamental set in a Hilbert space H, and let T be the operator T : ` 2 (X) ! H : c 7! X x2X c(x)x: Whenever T is welldefined and bounded, X is said to be a Bessel sequence. If, in addition, ran T is closed, then X is a frame. Finally, a frame whose corresponding T is inje ..."
Abstract

Cited by 131 (30 self)
 Add to MetaCart
Let X be a countable fundamental set in a Hilbert space H, and let T be the operator T : ` 2 (X) ! H : c 7! X x2X c(x)x: Whenever T is welldefined and bounded, X is said to be a Bessel sequence. If, in addition, ran T is closed, then X is a frame. Finally, a frame whose corresponding T is injective is a stable basis (also known as a Riesz basis). This paper considers the above three properties for subspaces H of L 2 (IR d ), and for sets X of the form X = fOE(\Delta \Gamma ff) : OE 2 \Phi; ff 2 ZZ d g; with \Phi either a singleton, a finite set, or, more generally, a countable set. The analysis is performed on the Fourier domain, where the two operators TT and T T are decomposed into a collection of simpler "fiber" operators. The main theme of the entire analysis is the characterization of each of the above three properties in terms of the analogous property of these simpler operators. AMS (MOS) Subject Classifications: 42C15 Key Words: Riesz bases, stable bases, shif...
Shiftinvariant spaces on the real line
 Proc. Amer. Math. Soc
, 1997
"... (Communicated by J. Marshall Ash) Abstract. We investigate the structure of shiftinvariant spaces generated by a finite number of compactly supported functions in Lp(R) (1≤p≤∞). Based on a study of linear independence of the shifts of the generators, we characterize such shiftinvariant spaces in t ..."
Abstract

Cited by 35 (7 self)
 Add to MetaCart
(Communicated by J. Marshall Ash) Abstract. We investigate the structure of shiftinvariant spaces generated by a finite number of compactly supported functions in Lp(R) (1≤p≤∞). Based on a study of linear independence of the shifts of the generators, we characterize such shiftinvariant spaces
Results 1  10
of
244,078