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On CosineModulated Wavelet Orthonormal Bases
 IEEE TRANS. ON IMAGE PROCESSING
, 1993
"... Recently multiplicity M , Kregular, orthonormal wavelet bases (that have implications in transform coding applications) have been constructed by several authors [1, 2, 3]. This paper describes and parameterizes the cosinemodulated class of multiplicity M wavelet tight frames (WTFs). In these WTFs ..."
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Cited by 12 (4 self)
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Recently multiplicity M , Kregular, orthonormal wavelet bases (that have implications in transform coding applications) have been constructed by several authors [1, 2, 3]. This paper describes and parameterizes the cosinemodulated class of multiplicity M wavelet tight frames (WTFs). In these WTFs
ADAPTIVE ORTHONORMAL BASES FOR VIDEO COMPRESSION
"... The paper describes the construction of a vector valued orthonormal basis adapted to an input sequence of video frames. The construction relies on an optimization step that singles out common discontinuities present in the input vector. This is achieved by constructing a sequence of partitions in t ..."
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Cited by 1 (1 self)
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The paper describes the construction of a vector valued orthonormal basis adapted to an input sequence of video frames. The construction relies on an optimization step that singles out common discontinuities present in the input vector. This is achieved by constructing a sequence of partitions
Proximal thresholding algorithm for minimization over orthonormal bases
 SIAM Journal on Optimization
, 2007
"... The notion of soft thresholding plays a central role in problems from various areas of applied mathematics, in which the ideal solution is known to possess a sparse decomposition in some orthonormal basis. Using convexanalytical tools, we extend this notion to that of proximal thresholding and inve ..."
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Cited by 62 (14 self)
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and investigate its properties, providing in particular several characterizations of such thresholders. We then propose a versatile convex variational formulation for optimization over orthonormal bases that covers a wide range of problems, and establish the strong convergence of a proximal thresholding algorithm
New Orthonormal Bases And Frames Using Chirp Functions
"... The proportionalbandwidth and constantbandwidth timefrequency signal decompositions of the wavelet, Gabor, and Wilson orthonormal bases have attracted substantial interest for representing nonstationary signals. However, these representations are limited in that they are based on rectangular tess ..."
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Cited by 1 (0 self)
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The proportionalbandwidth and constantbandwidth timefrequency signal decompositions of the wavelet, Gabor, and Wilson orthonormal bases have attracted substantial interest for representing nonstationary signals. However, these representations are limited in that they are based on rectangular
System Identification in Frequency Domain Using Orthonormal Bases
"... belongs among the most common tasks of system control. There are many methods to solve these tasks. This work deals with design of the algorithm for model construction and parameters estimation in frequency domain using a set of orthonormal base functions. The work presents the algorithm that uses t ..."
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belongs among the most common tasks of system control. There are many methods to solve these tasks. This work deals with design of the algorithm for model construction and parameters estimation in frequency domain using a set of orthonormal base functions. The work presents the algorithm that uses
The Fundamental Role of General Orthonormal Bases in System Identification
 IEEE Transactions on Automatic Control
, 1997
"... The purpose of this paper is threefold. Firstly, it is to establish that contrary to what might be expected, the accuracy of well known and frequently used asymptotic variance results can depend on choices of fixed poles or zeros in the model structure. Secondly, it is to derive new variance express ..."
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Cited by 22 (11 self)
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presented here encompass preexisting ones as special cases. Via this latter analysis a new perspective emerges on recent work pertaining to the use of orthonormal basis structures in system identification. Namely, that orthonormal bases are much more than an implementational option offering improved
Random orthonormal bases of spaces of high dimension
, 1210
"... Abstract. We consider a sequence HN of finite dimensional Hilbert spaces of dimensions dN →∞. Motivating examples are eigenspaces, or spaces of quasimodes, for a Laplace or Schrödinger operator on a compact Riemannian manifold. The set of Hermitian orthonormal bases of HN may be identified with U( ..."
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Cited by 4 (0 self)
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Abstract. We consider a sequence HN of finite dimensional Hilbert spaces of dimensions dN →∞. Motivating examples are eigenspaces, or spaces of quasimodes, for a Laplace or Schrödinger operator on a compact Riemannian manifold. The set of Hermitian orthonormal bases of HN may be identified with U
Frequency Domain Estimation Using Orthonormal Bases
 in Proceedings of the 13th IFAC World Congress
, 1996
"... . This paper examines the use of general orthonormal bases for system identification from frequency domain data. This idea has been studied in great depth for the particular case of the orthonormal trigonometric basis. Here we show that the accuracy of the estimate can be significantly improved by r ..."
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Cited by 7 (2 self)
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. This paper examines the use of general orthonormal bases for system identification from frequency domain data. This idea has been studied in great depth for the particular case of the orthonormal trigonometric basis. Here we show that the accuracy of the estimate can be significantly improved
Identification of Nonlinear Systems using Orthonormal Bases
, 2001
"... In this paper, non iterative algorithms for the identification of (multivariable) nonlinear systems consisting of the interconnection of LTI systems and static nonlinearities are presented. The proposed algorithms are numerically robust, since they are based only on least squares estimation and sing ..."
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Cited by 3 (0 self)
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noise, under weak assumptions on the persistency of excitation of the inputs. For the Wiener model and the Feedback BlockOriented model, consistency of the estimates can only be guaranteed in the noise free case. Key in the derivation of the results is the use of rational orthonormal bases
Results 11  20
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1,058