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283
Matching pursuits with timefrequency dictionaries
 IEEE Transactions on Signal Processing
, 1993
"... AbstractWe introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions. These waveforms are chosen in order to best match the signal structures. Matching pursuits are general procedures t ..."
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Cited by 1147 (13 self)
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AbstractWe introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions. These waveforms are chosen in order to best match the signal structures. Matching pursuits are general procedures to compute adaptive signal representations. With a dictionary of Gabor functions a matching pursuit defines an adaptive timefrequency transform. We derive a signal energy distribution in the timefrequency plane, which does not include interference terms, unlike Wigner and Cohen class distributions. A matching pursuit isolates the signal structures that are coherent with respect to a given dictionary. An application to pattern extraction from noisy signals is described. We compare a matching pursuit decomposition with a signal expansion over an optimized wavepacket orthonormal basis, selected with the algorithm of Coifman and Wickerhauser. I.
Perceptual Coding of Digital Audio
 Proceedings of the IEEE
, 2000
"... During the last decade, CDquality digital audio has essentially replaced analog audio. Emerging digital audio applications for network, wireless, and multimedia computing systems face a series of constraints such as reduced channel bandwidth, limited storage capacity, and low cost. These new applic ..."
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Cited by 128 (3 self)
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During the last decade, CDquality digital audio has essentially replaced analog audio. Emerging digital audio applications for network, wireless, and multimedia computing systems face a series of constraints such as reduced channel bandwidth, limited storage capacity, and low cost. These new applications have created a demand for highquality digital audio delivery at low bit rates. In response to this need, considerable research has been devoted to the development of algorithms for perceptually transparent coding of highfidelity (CDquality) digital audio. As a result, many algorithms have been proposed, and several have now become international and/or commercial product standards. This paper reviews algorithms for perceptually transparent coding of CDquality digital audio, including both research and standardization activities. The paper is organized as follows. First, psychoacoustic principles are described with the MPEG psychoacoustic signal analysis model 1 discussed in some detail. Next, filter bank design issues and algorithms are addressed, with a particular emphasis placed on the Modified Discrete Cosine Transform (MDCT), a perfect reconstruction (PR) cosinemodulated filter bank that has become of central importance in perceptual audio coding. Then, we review methodologies that achieve perceptually transparent coding of FM and CDquality audio signals, including algorithms that manipulate transform components, subband signal decompositions, sinusoidal signal components, and linear prediction (LP) parameters, as well as hybrid algorithms that make use of more than one signal model. These discussions concentrate on architectures and applications of
On Tempo Tracking: Tempogram Representation and Kalman Filtering
, 2000
"... We formulate tempo tracking in a Bayesian framework where a tempo tracker is modeled as a stochastic dynamical system. The tempo is modeled as a hidden state variable of the system and is estimated by a Kalman filter. The Kalman filter operates on a Tempogram, a waveletlike multiscale expansion ..."
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Cited by 82 (8 self)
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We formulate tempo tracking in a Bayesian framework where a tempo tracker is modeled as a stochastic dynamical system. The tempo is modeled as a hidden state variable of the system and is estimated by a Kalman filter. The Kalman filter operates on a Tempogram, a waveletlike multiscale expansion of a real performance. An important advantage of our approach is that it is possible to formulate both offline or realtime algorithms. The simulation results on a systematically collected set of MIDI piano performances of Yesterday and Michelle by the Beatles shows accurate tracking of approximately %90 of the beats.
Efficient Iris Recognition through Improvement of Feature Vector and Classifier
 ETRI Journal
, 2001
"... In this paper, we propose an efficient method for personal identification by analyzing iris patterns that have a high level of stability and distinctiveness. To improve the efficiency and accuracy of the proposed system, we present a new approach to making a feature vector compact and efficient by u ..."
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Cited by 77 (0 self)
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In this paper, we propose an efficient method for personal identification by analyzing iris patterns that have a high level of stability and distinctiveness. To improve the efficiency and accuracy of the proposed system, we present a new approach to making a feature vector compact and efficient by using wavelet transform, and two straightforward but efficient mechanisms for a competitive learning method such as a weight vector initialization and the winner selection. With all of these novel mechanisms, the experimental results showed that the proposed system could be used for personal identification in an efficient and effective manner.
A Tutorial on Modern Lossy Wavelet Image Compression: Foundations of JPEG 2000
, 2001
"... The JPEG committee has recently released its new image coding standard, JPEG 2000, which will serve as a supplement for the original JPEG standard introduced in 1992. Rather than incrementally improving on the original standard, JPEG 2000 implements an entirely new way of compressing images based o ..."
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Cited by 73 (0 self)
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The JPEG committee has recently released its new image coding standard, JPEG 2000, which will serve as a supplement for the original JPEG standard introduced in 1992. Rather than incrementally improving on the original standard, JPEG 2000 implements an entirely new way of compressing images based on the wavelet transform, in contrast to the discrete cosine transform (DCT) used in the original JPEG standard. The significant change in coding methods between the two standards leads one to ask: What prompted the JPEG committee to adopt such a dramatic change? The answer to this question comes from considering the state of image coding at the time the original JPEG standard was being formed. At that time wavelet analysis and wavelet coding were still
Wavelet transforms versus Fourier transforms
 Department of Mathematics, MIT, Cambridge MA
, 213
"... Abstract. This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The "wavelet transform " maps each f(x) to its coefficients with respect to this basis. The mathematics is simple and t ..."
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Cited by 73 (2 self)
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Abstract. This note is a very basic introduction to wavelets. It starts with an orthogonal basis of piecewise constant functions, constructed by dilation and translation. The "wavelet transform " maps each f(x) to its coefficients with respect to this basis. The mathematics is simple and the transform is fast (faster than the Fast Fourier Transform, which we briefly explain), but approximation by piecewise constants is poor. To improve this first wavelet, we are led to dilation equations and their unusual solutions. Higherorder wavelets are constructed, and it is surprisingly quick to compute with them — always indirectly and recursively. We comment informally on the contest between these transforms in signal processing, especially for video and image compression (including highdefinition television). So far the Fourier Transform — or its 8 by 8 windowed version, the Discrete Cosine Transform — is often chosen. But wavelets are already competitive, and they are ahead for fingerprints. We present a sample of this developing theory. 1. The Haar wavelet To explain wavelets we start with an example. It has every property we hope for, except one. If that one defect is accepted, the construction is simple and the computations are fast. By trying to remove the defect, we are led to dilation equations and recursively defined functions and a small world of fascinating new problems — many still unsolved. A sensible person would stop after the first wavelet, but fortunately mathematics goes on. The basic example is easier to draw than to describe: W(x)
Short Wavelets and Matrix Dilation Equations
, 1995
"... Scaling functions and orthogonal wavelets are created from the coefficients of a lowpass and highpass filter (in a twoband orthogonal filter bank). For "multifilters" those coefficients are matrices. This gives a new block structure for the filter bank, and leads to multiple scaling funct ..."
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Cited by 72 (10 self)
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Scaling functions and orthogonal wavelets are created from the coefficients of a lowpass and highpass filter (in a twoband orthogonal filter bank). For "multifilters" those coefficients are matrices. This gives a new block structure for the filter bank, and leads to multiple scaling functions and wavelets. Geronimo, Hardin, and Massopust constructed two scaling functions that have extra properties not previously achieved. The functions \Phi 1 and \Phi 2 are symmetric (linear phase) and they have short support (two intervals or less), while their translates form an orthogonal family. For any single function \Phi, apart from Haar's piecewise constants, those extra properties are known to be impossible. The novelty is to introduce 2 by 2 matrix coefficients while retaining orthogonality. This note derives the properties of \Phi 1 and \Phi 2 from the matrix dilation equation that they satisfy. Then our main step is to construct associated wavelets: two wavelets for two scaling functions....
Simultaneous Noise Suppression and Signal Compression using a Library of Orthonormal Bases and the Minimum Description Length Criterion
 WAVELETS IN GEOPHYSICS
, 1994
"... We describe an algorithm to estimate a discrete signal from its noisy observation, using a library of orthonormal bases (consisting of various wavelets, wavelet packets, and local trigonometric bases) and the informationtheoretic criterion called minimum description length (MDL). The key to effecti ..."
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Cited by 71 (4 self)
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We describe an algorithm to estimate a discrete signal from its noisy observation, using a library of orthonormal bases (consisting of various wavelets, wavelet packets, and local trigonometric bases) and the informationtheoretic criterion called minimum description length (MDL). The key to effective random noise suppression is that the signal component in the data may be represented efficiently by one or more of the bases in the library, whereas the noise component cannot be represented efficiently by any basis in the library. The MDL criterion gives the best compromise between the fidelity of the estimation result to the data (noise suppression) and the efficiency of the representation of the estimated signal (signal compression): it selects the "best" basis and the "best" number of terms to be retained out of various bases in the library in an objective manner. Because of the use of the MDL criterion, our algorithm is free from any parameter setting or subjective judgments. This ...