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Texture analysis and classification with treestructured wavelet transform
 IEEE Trans. Image Processing
, 1993
"... AbstractOne difficulty of texture analysis in the past was the lack of adequate tools to characterize different scales of textures effectively. Recent developments in multiresolution analysis such as the Gabor and wavelet transforms help to overcome this difficulty. In this research, we propose a m ..."
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Cited by 314 (1 self)
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AbstractOne difficulty of texture analysis in the past was the lack of adequate tools to characterize different scales of textures effectively. Recent developments in multiresolution analysis such as the Gabor and wavelet transforms help to overcome this difficulty. In this research, we propose a multiresolution approach based on a modified wavelet transform called the treestructured wavelet transform or wavelet packets for texture analysis and classification. The development of this new transform is motivated by the observation that a large class of natural textures can be modeled as quasiperiodic signals whose dominant frequencies are located in the middle frequency channels. With the transform, we are able to zoom into any desired frequency channels for further decomposition. In contrast, the conventional pyramidstructured wavelet transform performs further decomposition only in low frequency channels. We develop a progressive texture classification algorithm which is not only computationally attractive but also has excellent performance. The performance of our new method is compared with that of several other methods using the DCT, DST, DHT, pyramidstructured wavelet transforms, Gabor filters, and Laws filters.
Using phaseretrieval to measure the intensity and phase of ultrashort pulses:frequencyresolved optical gating
 J. Opt. Soc. Amer
, 1993
"... We recently introduced a new technique, frequencyresolved optical gating (FROG), for directly determining the full intensity I(t) and phase p(t) of a single femtosecond pulse. By using almost any instantaneous nonlinearoptical interaction of two replicas of the ultrashort pulse to be measured, FRO ..."
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Cited by 41 (6 self)
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We recently introduced a new technique, frequencyresolved optical gating (FROG), for directly determining the full intensity I(t) and phase p(t) of a single femtosecond pulse. By using almost any instantaneous nonlinearoptical interaction of two replicas of the ultrashort pulse to be measured, FROG involves measuring the spectrum of the signal pulse as a function of the delay between the replicas. The resulting trace of intensity versus frequency and delay yields an intuitive display of the pulse that is similar to the pulse spectrogram, except that the gate is a function of the pulse to be measured. The problem of inverting the FROG trace to obtain the pulse intensity and phase can also be considered a complex twodimensional phaseretrieval problem. As a result, the FROG trace yields, in principle, an essentially unique pulse intensity and phase. We show that this is also the case in practice. We present an iterativeFouriertransform algorithm for inverting the FROG trace. The algorithm is unusual in its use of a novel constraint: the mathematical form of the signal field. Without the use of a support constraint, the algorithm performs quite well in practice, even for pulses with serious phase distortions and for experimental data with noise, although it occasionally stagnates when pulses with large intensity fluctuations are used. 1.
Introduction to the fractional Fourier transform and its applications
 in Advances in Imaging and Electron Physics
, 1999
"... ..."
Shift Covariant TimeFrequency Distributions of Discrete Signals
 IEEE Trans. on Signal Processing
, 1997
"... Many commonly used timefrequency distributions are members of the Cohen class. This class is defined for continuous signals and since timefrequency distributions in the Cohen class are quadratic, the formulation for discrete signals is not straightforward. The Cohen class can be derived as the cla ..."
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Cited by 18 (6 self)
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Many commonly used timefrequency distributions are members of the Cohen class. This class is defined for continuous signals and since timefrequency distributions in the Cohen class are quadratic, the formulation for discrete signals is not straightforward. The Cohen class can be derived as the class of all quadratic timefrequency distributions that are covariant to time shifts and frequency shifts. In this paper we extend this method to three types of discrete signals to derive what we will call the discrete Cohen classes. The properties of the discrete Cohen classes differ from those of the original Cohen class. To illustrate these properties we also provide explicit relationships between the classical Wigner distribution and the discrete Cohen classes. I. Introduction I N signal analysis there are four types of signals commonly used. These four types are based on whether the signal is continuous or discrete, and whether the signal is aperiodic or periodic. The four signal types ...
Extraction and Analysis of Multiple Periodic Motions in Video Sequences
"... Abstract—The analysis of periodic or repetitive motions is useful in many applications, such as the recognition and classification of human and animal activities. Existing methods for the analysis of periodic motions first extract motion trajectories using spatial information and then determine if t ..."
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Cited by 13 (2 self)
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Abstract—The analysis of periodic or repetitive motions is useful in many applications, such as the recognition and classification of human and animal activities. Existing methods for the analysis of periodic motions first extract motion trajectories using spatial information and then determine if they are periodic. These approaches are mostly based on feature matching or spatial correlation, which are often infeasible, unreliable, or computationally demanding. In this paper, we present a new approach, based on the timefrequency analysis of the video sequence as a whole. Multiple periodic trajectories are extracted and their periods are estimated simultaneously. The objects that are moving in a periodic manner are extracted using the spatial domain information. Experiments with synthetic and real sequences display the capabilities of this approach. Index Terms—Periodic motion analysis, timefrequency distributions, short term Fourier transform. 1
Regularity and unitarity of bilinear timefrequency signal representations
 IEEE Trans. Inform. Theory
, 1992
"... AbstractTwo structural properties of bilinear timefrequency representations (BTFR’s) of signals are introduced and studied. The definition of these properties is based on a linearoperator description of BTFR’s. The first property, termed regularity, has important implications with respect to the r ..."
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Cited by 13 (3 self)
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AbstractTwo structural properties of bilinear timefrequency representations (BTFR’s) of signals are introduced and studied. The definition of these properties is based on a linearoperator description of BTFR’s. The first property, termed regularity, has important implications with respect to the recovery of signals from their BTFR outcome, the derivation of other bilinear signal representations from a BTFR, the BTFR’s reaction to linear signal transformations, and the construction of bases of induced BTFRdomain spaces. The second property, called uniturity, is equivalent to validity of Moyal’s formula. Unitarity is thus necessary and sufficient for a closedform solution of optimal signal synthesis and for a BTFR formulation of optimal detection/estimation methods. Besides, unitarity also allows the systematic construction of BTFR “product relations’’ like Wigner distribution’s interference formula and ambiguity
If the Independent Components of Natural Images are Edges, What are the Independent Components of Natural Sounds?
, 2001
"... Previous work has shown that various flavours of Independent Component Analysis, when applied to natural images, all result in broadly similar localised, oriented bandpass feature detectors, which have been likened to wavelets or edge detectors. ..."
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Cited by 11 (1 self)
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Previous work has shown that various flavours of Independent Component Analysis, when applied to natural images, all result in broadly similar localised, oriented bandpass feature detectors, which have been likened to wavelets or edge detectors.
Asymptotic singular value decay of timefrequency localization operators
 Wavelet Applications in Signal and Image Processing II
, 1994
"... The Weyl correspondence is a convenient way to define a broad class of timefrequency localization operators. Given a region Ω in the timefrequency plane R 2 and given an appropriate µ, the Weyl correspondence can be used to construct an operator L(Ω, µ) which essentially localizes the timefrequen ..."
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Cited by 10 (1 self)
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The Weyl correspondence is a convenient way to define a broad class of timefrequency localization operators. Given a region Ω in the timefrequency plane R 2 and given an appropriate µ, the Weyl correspondence can be used to construct an operator L(Ω, µ) which essentially localizes the timefrequency content of a signal on Ω. Different choices of µ provide different interpretations of localization. Empirically, each such localization operator has the following singular value structure: there are several singular values close to 1, followed by a sharp plunge in values, with a final asymptotic decay to zero. The exact quantification of these qualitative observations is known only for a few specific choices of Ω and µ. In this paper we announce a general result which bounds the asymptotic decay rate of the singular values of any L(Ω, µ) in terms of integrals of χ Ω ∗ ˜µ  2 and (χ Ω ∗ ˜µ) ∧  2 outside squares of increasing radius, where ˜µ(a, b) = µ(−a, −b). More generally, this result applies to all operators L(σ, µ) allowing window functions σ in place of the characteristic functions χ Ω. We discuss the motivation and implications of this result. We also sketch the philosophy of proof, which involves the construction of an approximating operator through the technology of Gabor frames—overcomplete systems which allow basislike expansions and Plancherellike formulas, but which are not bases and are not orthogonal systems.
On subbigroup and its applications
 Pure Appl. Math Sci
, 1996
"... The most renowned strategy utilized for perusing mind movement is electroencephalography (EEG). Electroencephalography is the neurophysiologic estimation of the electrical action of the cerebrum by recording from anodes put on the scalp, or in the exceptional cases on the cortex. The ensuing follows ..."
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Cited by 9 (0 self)
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The most renowned strategy utilized for perusing mind movement is electroencephalography (EEG). Electroencephalography is the neurophysiologic estimation of the electrical action of the cerebrum by recording from anodes put on the scalp, or in the exceptional cases on the cortex. The ensuing follows are known as an electroencephalogram (EEG) and speak to alleged brainwaves. This system is picking up prevalence as it is a nonintrusive interface and is giving a methodology to controlling machines through contemplations. The proposed linking and familiarity rating method classifies the music, video assessment responses of EEGSignal. The metrics namely true positive, true negative, false positive, false negative, sensitivity, specificity and classification accuracy are chosen for evaluating the performance of the proposed classifier. The simulation result shows that the proposed classifier achieves 95.4 % accuracy which is better than other methods.
Signal Detection in Underwater Sound Using Wavelets
 J. Am. Statist. Ass
, 1998
"... This paper considers the use of wavelet methods in relation to a common signal processing problem, that of detecting transient features in sound recordings which contain interference or distortion. In this particular case, the data are various types of underwater sounds, and the objective is to dete ..."
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Cited by 9 (1 self)
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This paper considers the use of wavelet methods in relation to a common signal processing problem, that of detecting transient features in sound recordings which contain interference or distortion. In this particular case, the data are various types of underwater sounds, and the objective is to detect intermittent departures (potential `signals') from the background sound environment in the data (`noise'), where the latter may itself be evolving and changing over time. We develop an adaptive model of the background interference, using recursive density estimation of the joint distribution of certain summary features of its wavelet decomposition. Observations which are considered to be outliers from this density estimate at any time are then flagged as potential `signals'. The performance of our method is illustrated on artificial data, where a known `signal' is contaminated with simulated underwater `noise' using a range of different signaltonoise ratios, and a `baseline' comparison is made with results obtained from a relatively unsophisticated, but commonly used, timefrequency approach. A similar comparison is then reported in relation to the more significant problem of detecting various types of dolphin sound in real conditions. KEY WORDS: Multivariate Density Estimation; Short Time Fourier Transform; Segmentation; Signal Detection; Signal Processing; Thresholding; Underwater Sounds; Wavelet Decomposition 1. INTRODUCTION For present purposes, underwater sounds can be considered as comprising acoustic events of interest superimposed on a background underwater sound environment. Throughout this paper, we shall refer to the former as `signals', and the latter as `noise'; although it should be appreciated that in doing so, we use the terms rather loosely. In the searc...