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79
On the Stability of the Basis Pursuit
 in the Presence of Noise,” EURASIP Signal Processing J
, 2006
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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 146 (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
Waveletbased image coding: An overview
 Applied and Computational Control, Signals, and Circuits
, 1998
"... ABSTRACT This paper presents an overview of waveletbased image coding. We develop the basics of image coding with a discussion of vector quantization. We motivate the use of transform coding in practical settings,and describe the properties of various decorrelating transforms. We motivate the use o ..."
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Cited by 46 (3 self)
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ABSTRACT This paper presents an overview of waveletbased image coding. We develop the basics of image coding with a discussion of vector quantization. We motivate the use of transform coding in practical settings,and describe the properties of various decorrelating transforms. We motivate the use of the wavelet transform in coding using ratedistortion considerations as well as approximationtheoretic considerations. Finally,we give an overview of current coders in the literature. 1
Matching Pursuit and Atomic Signal Models Based on Recursive Filter Banks
 IEEE Transactions on Signal Processing
, 1902
"... The matching pursuit algorithm can be used to derive signal decompositions in terms of the elements of a dictionary of timefrequency atoms. Using a structured overcomplete dictionary yields a signal model that is both parametric and signaladaptive. In this paper, we apply matching pursuit to the d ..."
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Cited by 45 (1 self)
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The matching pursuit algorithm can be used to derive signal decompositions in terms of the elements of a dictionary of timefrequency atoms. Using a structured overcomplete dictionary yields a signal model that is both parametric and signaladaptive. In this paper, we apply matching pursuit to the derivation of signal expansions based on damped sinusoids. It is shown that expansions in terms of complex damped sinusoids can be efficiently derived using simple recursive filter banks. We discuss a subspace extension of the pursuit algorithm which provides a framework for deriving realvalued expansions of real signals based on such complex atoms. Furthermore, we consider symmetric and asymmetric twosided atoms constructed from underlying onesided damped sinusoids. The primary concern is the application of this approach to the modeling of signals with transient behavior such as music; it is shown that timefrequency atoms based on damped sinusoids are more suitable for representing trans...
Boundary filters for finitelength signals and timevarying filterbanks
 IEEE Trans. Circuits Syst. II
, 1995
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Joint spacefrequency segmentation using balanced wavelet packet tree for leastcost image representation
 IEEE Trans. Im. Proc
, 1997
"... Abstract—We examine the question of how to choose a spacevarying filterbank tree representation that minimizes some additive cost function for an image. The idea is that for a particular cost function, e.g., energy compaction or quantization distortion, some tree structures perform better than oth ..."
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Cited by 29 (5 self)
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Abstract—We examine the question of how to choose a spacevarying filterbank tree representation that minimizes some additive cost function for an image. The idea is that for a particular cost function, e.g., energy compaction or quantization distortion, some tree structures perform better than others. While the wavelet tree represents a good choice for many signals, it is generally outperformed by the best tree from the library of wavelet packet frequencyselective trees. The recently introduced doubletree library of bases performs better still, by allowing different wavelet packet trees over all binary spatial segments of the image. We build on this foundation and present efficient new pruning algorithms for both one and twodimensional (1D and 2D) trees that will find the best basis from a library that is many times larger than the library of the singletree or doubletree algorithms. The augmentation of the library of bases overcomes the constrained nature of the spatial variation in the doubletree bases, and is a significant enhancement in practice. Use of these algorithms to select the leastcost expansion for images with a ratedistortion cost function gives a very effective signal adaptive compression scheme. This scheme is universal in the sense that, without assuming a model for the signal or making use of training data, it performs very well over a large class of signal types. In experiments it achieves compression rates that are competitive with the best trainingbased schemes. I.
Orthonormal ShiftInvariant Wavelet Packet Decomposition and Representation
 Signal Processing
, 1995
"... In this work, a shifted wavelet packet (SWP) library, containing all the time shifted wavelet packet bases, is defined. A corresponding shiftinvariant wavelet packet decomposition (SIWPD) search algorithm for a "best basis" is introduced. The search algorithm is representable by a binar ..."
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Cited by 29 (8 self)
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In this work, a shifted wavelet packet (SWP) library, containing all the time shifted wavelet packet bases, is defined. A corresponding shiftinvariant wavelet packet decomposition (SIWPD) search algorithm for a "best basis" is introduced. The search algorithm is representable by a binary tree, in which a node symbolizes an appropriate subspace of the original signal. We prove that the resultant "best basis" is orthonormal and the associated expansion, characterized by the lowest information cost, is shiftinvariant. The shiftinvariance stems from an additional degree of freedom, generated at the decomposition stage and incorporated into the search algorithm. The added dimension is a relative shift between a given parentnode and its respective childrennodes. We prove that for any subspace it suffices to consider one of two alternative decompositions, made feasible by the SWP library. These decompositions correspond to a zero shift and a 2  relative shift where denotes the resolution level.
Flexible Treestructured Signal Expansions Using Timevarying Wavelet Packets
, 1997
"... In this paper we address the problem of finding the best timevarying filter bank treestructured representation for a signal. The tree is allowed to vary at regular intervals, and the spacing of these changes can be arbitrarily short. The question of how to choose treestructured representations of ..."
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Cited by 22 (4 self)
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In this paper we address the problem of finding the best timevarying filter bank treestructured representation for a signal. The tree is allowed to vary at regular intervals, and the spacing of these changes can be arbitrarily short. The question of how to choose treestructured representations of signals based on filter banks has attracted considerable attention. Wavelets, and their adaptive versions, known as wavelet packets, represent one approach that has proved very popular. Wavelet packets are subband trees where the tree is chosen to match the characteristics of the signal. Variations where the tree varies over time have been proposed as the double tree, and the timefrequency tree algorithms. Timevariation adds a further level of adaptivity. In all of the approaches proposed so far the tree must be either fixed for the whole duration of the signal, or fixed for its dyadic subintervals (i.e. halves, quarters, etc). The solution that we propose, since it allows much more flexib...
Orthonormal ShiftInvariant Adaptive Local Trigonometric Decomposition
 Signal Processing
"... In this paper, an extended library of smooth local trigonometric bases is defined, and an appropriate fast "bestbasis" search algorithm is introduced. When compared with the standard local cosine decomposition (LCD), the proposed algorithm is advantageous in three respects. First, it le ..."
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Cited by 19 (5 self)
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In this paper, an extended library of smooth local trigonometric bases is defined, and an appropriate fast "bestbasis" search algorithm is introduced. When compared with the standard local cosine decomposition (LCD), the proposed algorithm is advantageous in three respects. First, it leads to a bestbasis expansion that is shiftinvariant. Second, the resulting representation is characterized by a lower information cost. Third, the polarity of the folding operator is adapted to the parity properties of the segmented signal at the endpoints. The shiftinvariance stems from an adaptive relative shift of expansions in distinct resolution levels. We show that at any resolution level it suffices to examine and select one of two relative shift options a zero shift or a 2  shift. A variable folding operator, whose polarity is locally adapted to the parity properties of the signal, further enhances the representation. The computational complexity is manageable and comparable to that of the LCD.