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779
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 384 (40 self)
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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
Blind Source Separation by Sparse Decomposition in a Signal Dictionary
, 2000
"... Introduction In blind source separation an Nchannel sensor signal x(t) arises from M unknown scalar source signals s i (t), linearly mixed together by an unknown N M matrix A, and possibly corrupted by additive noise (t) x(t) = As(t) + (t) (1.1) We wish to estimate the mixing matrix A and the M ..."
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Cited by 274 (34 self)
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Introduction In blind source separation an Nchannel sensor signal x(t) arises from M unknown scalar source signals s i (t), linearly mixed together by an unknown N M matrix A, and possibly corrupted by additive noise (t) x(t) = As(t) + (t) (1.1) We wish to estimate the mixing matrix A and the Mdimensional
Bayesian Compressive Sensing
, 2007
"... The data of interest are assumed to be represented as Ndimensional real vectors, and these vectors are compressible in some linear basis B, implying that the signal can be reconstructed accurately using only a small number M ≪ N of basisfunction coefficients associated with B. Compressive sensing ..."
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Cited by 330 (24 self)
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The data of interest are assumed to be represented as Ndimensional real vectors, and these vectors are compressible in some linear basis B, implying that the signal can be reconstructed accurately using only a small number M ≪ N of basisfunction coefficients associated with B. Compressive sensing
On the Realizability of BiOrthogonal, MDimensional 2Band Filter Banks
, 1995
"... In this paper we show an algebraic approach for the design of ladder structures for causal biorthogonal filter banks. The key ingredient of the approach is known in literature as Euclid's algorithm. Using this algorithm we derive some strong result on the design freedom for ladder structures. ..."
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Cited by 11 (0 self)
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. In particular we show that the dimensionality of the problem plays an important role. We end by with some conjectures concerning the extensions to multichannel and noncausal filter banks. Keywords Digital signal processing, biorthogonal filter bank, multidimensional, ladder structure, Euclid
The DualTree Complex Wavelet Transform  A coherent framework for multiscale signal and image processing
, 2005
"... The dualtree complex wavelet transform (CWT) is a relatively recent enhancement to the discrete wavelet transform (DWT), with important additional properties: It is nearly shift invariant and directionally selective in two and higher dimensions. It achieves this with a redundancy factor of only 2 ..."
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Cited by 270 (29 self)
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d for ddimensional signals, which is substantially lower than the undecimated DWT. The multidimensional (MD) dualtree CWT is nonseparable but is based on a computationally efficient, separable filter bank (FB). This tutorial discusses the theory behind the dualtree transform, shows how complex
Phase retrieval from very few measurements
, 2013
"... In many applications, signals are measured according to a linear process, but the phases of these measurements are often unreliable or not available. To reconstruct the signal, one must perform a process known as phase retrieval. This paper focuses on completely determining signals with as few inte ..."
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Cited by 4 (1 self)
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intensity measurements as possible, and on efficient phase retrieval algorithms from such measurements. For the case of complex Mdimensional signals, we construct a measurement ensemble of size 4M − 4 which yields injective intensity measurements; this is conjectured to be the smallest such ensemble
In Situ Compressive Sensing
"... Compressive sensing (CS) is a framework that exploits the compressible character of most natural signals, allowing the accurate measurement of an mdimensional signal u in terms of n ≪ m measurements v. The CS measurements may be represented in terms of an n×m matrix that defines the linear relation ..."
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Cited by 1 (1 self)
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Compressive sensing (CS) is a framework that exploits the compressible character of most natural signals, allowing the accurate measurement of an mdimensional signal u in terms of n ≪ m measurements v. The CS measurements may be represented in terms of an n×m matrix that defines the linear
Shift Invariant Properties Of The DualTree Complex Wavelet Transform
 In Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing (ICASSP
, 1999
"... We discuss the shift invariant properties of a new implementation of the Discrete Wavelet Transform, which employs a dual tree of wavelet filters to obtain the real and imaginary parts of complex wavelet coefficients. This introduces limited redundancy (2 m :1 for mdimensional signals) and allows ..."
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Cited by 41 (6 self)
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We discuss the shift invariant properties of a new implementation of the Discrete Wavelet Transform, which employs a dual tree of wavelet filters to obtain the real and imaginary parts of complex wavelet coefficients. This introduces limited redundancy (2 m :1 for mdimensional signals
Complex Wavelets For Shift Invariant . . .
 JOURNAL OF 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 (2^m:1 for mdimensional signals) and allows the transform to provide approximate shift ..."
Abstract

Cited by 6 (0 self)
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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 (2^m:1 for mdimensional signals) and allows the transform to provide approximate
Systolic arrays for multidimensional discrete transforms
 J. Supercomputing
, 1990
"... An active area of research in supercomputing is concerned with mapping certain finite sums, such as discrete Fourier transforms, onto arrays of processors. This paper presents systolic mapping techniques that exploit the parallelism inherent in discrete Fourier transforms. It is established that, fo ..."
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Cited by 1 (0 self)
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, for an Mdimensional signal, parallel executions of such transforms are closely related to mappings of an (M+1)dimensional finite vector space into itself. Three examples of such parallel schemes are then described for the discrete Fourier transform of a twodimensional finite extent sequence of size N1×N
Results 1  10
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