Showing papers on "Continuous wavelet transform published in 1992"
TL;DR: The behavior of the continuous wavelet and Gabor coefficients in the asymptotic limit using stationary phase approximations are investigated and it is shown how, under some additional assumptions, these coefficients allow the extraction of some characteristics of the analyzed signal, such as frequency and amplitude modulation laws.
Abstract: The behavior of the continuous wavelet and Gabor coefficients in the asymptotic limit using stationary phase approximations are investigated. In particular, it is shown how, under some additional assumptions, these coefficients allow the extraction of some characteristics of the analyzed signal, such as frequency and amplitude modulation laws. Applications to spectral line estimations and matched filtering are briefly discussed. >
592 citations
TL;DR: The idea is introduced of a "super-wavelet," a linear combination of wavelets that itself is treated as a wavelet that allows the shape of the wavelet to adapt to a particular problem, which goes beyond adapting parameters of a fixed-shape wavelet.
Abstract: Methods are presented for adaptively generating wavelet templates for signal representation and classification using neural networks. Different network structures and energy functions are necessary and are given for representation and classification. The idea is introduced of a "super-wavelet," a linear combination of wavelets that itself is treated as a wavelet. The super-wavelet allows the shape of the wavelet to adapt to a particular problem, which goes beyond adapting parameters of a fixed-shape wavelet. Simulations are given for 1-D signals, with the concepts extendable to imagery. Ideas are discussed for applying the concepts in the paper to phoneme and speaker recognition.
389 citations
Book•
30 Sep 1992
TL;DR: Wavelet Theory Extentions and Ambiguity Functions, Linear Systems Modelling with Wavelet Theory, and Practical Resolution, Gain, and Processing Structures.
Abstract: Foreword. Preface. 1. Introduction/Background 2. The Wavelet Transform. 3. Practical Resolution, Gain, and Processing Structures. 4. Wavelet Theory Extentions and Ambiguity Functions. 5. Linear Systems Modelling with Wavelet Theory. 6. Wideband Scattering and Environmental Imaging. Related Research. References. Subject Index.
346 citations
TL;DR: The wavelet transform is described, which is particularly useful in those cases in which the shape of the mother wavelet is approximately known a priori and the bank of the VanderLugt matched filters is considered.
Abstract: The wavelet transform is a powerful tool for the analysis of short transient signals. We detail the advantages of the wavelet transform over the Fourier transform and the windowed Fourier transform and consider the wavelet as a bank of the VanderLugt matched filters. This methodology is particularly useful in those cases in which the shape of the mother wavelet is approximately known a priori. A two-dimensional optical correlator with a bank of the wavelet filters is implemented to yield the time-frequency joint representation of the wavelet transform of one-dimensional signals.
145 citations
TL;DR: In this paper, the wavelet transform is implemented using an optical multichannel correlator with a bank of wavelet filter filters, which provide a shift-invariant wavelet transformation with continuous translation and discrete dilation.
Abstract: The wavelet transform is implemented using an optical multichannel correlator with a bank of wavelet transform filters. This approach provides a shift-invariant wavelet transform with continuous translation and discrete dilation parameters. The wavelet transform filters can be in many cases simply optical transmittance masks. Experimental results show detection of the frequency transition of the input signal by the optical wavelet transform.
143 citations
TL;DR: It is shown that the best transforms for transform image coding, namely, the scrambled real discrete Fourier transform, the discrete cosine transform, and the discrete Cosine-III transform are also the best for image enhancement.
Abstract: Blockwise transform image enhancement techniques are discussed. Previously, transform image enhancement has usually been based on the discrete Fourier transform (DFT) applied to the whole image. Two major drawbacks with the DFT are high complexity of implementation involving complex multiplications and additions, with intermediate results being complex numbers, and the creation of severe block effects if image enhancement is done blockwise. In addition, the quality of enhancement is not very satisfactory. It is shown that the best transforms for transform image coding, namely, the scrambled real discrete Fourier transform, the discrete cosine transform, and the discrete cosine-III transform, are also the best for image enhancement. Three techniques of enhancement discussed in detail are alpha-rooting, modified unsharp masking, and filtering motivated by the human visual system response (HVS). With proper modifications, it is observed that unsharp masking and HVS-motivated filtering without nonlinearities are basically equivalent. Block effects are completely removed by using an overlap-save technique in addition to the best transform.
129 citations
01 Jan 1992
TL;DR: In this paper, it was shown that the cross terms that exist in the energy distribution of the wavelet transform are comparable with those found in the Wigner dis- tribution (WD), a quadratic time-frequency representation, and the short time Fourier transform (STFT), of closely spaced signals.
Abstract: The wavelet transform (WT), a time-scale repre- sentation, is linear by definition. However, the nonlinear en- ergy distribution of this transform is often used to represent the signal; it contains ''cross terms" which could cause prob- lems while analyzing multicomponent signals. In this paper, we show that the cross terms that exist in the energy distribution of the WT are comparable with those found in the Wigner dis- tribution (WD), a quadratic time-frequency representation, and the energy distribution of the short time Fourier transform (STFT), of closely spaced signals. The cross terms of the WT and the STFT energy distributions occur at the intersection of their respective WT and STFT spaces, while for the WD they occur midtime and midfrequency. The parameters of the cross terms are a function of the difference in center frequencies and center times of the perpended signals. The amplitude of these cross terms can be as large as twice the product of the magni- tudes of the transforms of the two signals in question in all three cases. In this paper, we consider the significance of the effect of the cross terms on the analysis of a multicomponent signal in each of these three representations. We also compare the advantages and disadvantages of all of these methods in appli- cations to signal processing.
120 citations
TL;DR: The Hilbert transform is a commonly used technique for relating the real and imaginary parts of a causal spectral response as mentioned in this paper, which is found in both continuous and discrete forms and is widely used in circuit analysis, digital signal processing, image reconstruction and remote sensing.
Abstract: The Hilbert transform is a commonly used technique for relating the real and imaginary parts of a causal spectral response. It is found in both continuous and discrete forms and is widely used in circuit analysis, digital signal processing, image reconstruction and remote sensing. One useful application in the area of high-power microwave (HPM) technology is in correcting measured continuous wave (CW) transfer function data, so as to insure causality in reconstructed transient responses. Another application of the Hilbert transform is in the area of complex spectral estimation using magnitude-only data. Here, the applications of the transform to several specific spectral filtering and phase reconstruction problems are illustrated. >
77 citations
TL;DR: The optical experimental results are presented using the computer-generated transmittance masks as the wavelet transform filters in the Fourier domain.
Abstract: A two-dimensional wavelet transform is implemented by a bank of wavelet transform filters in the Fourier domain. An optical N 4 multichannel correlator architecture is proposed to perform parallel optical 2-D wavelet transforms. A holographic recording scheme is proposed to implement such a wavelet transform filter array. The optical experimental results are presented using the computer-generated transmittance masks as the wavelet transform filters.
37 citations
TL;DR: It is shown that a causal (i.e., zero valued before signal arrives) and analytical mother wavelet still guarantees completeness, which permits the selection of mother wavelets that better match causal analytical input signals.
Abstract: The causal analytical wavelet transform employs exponentially decaying nonsinusoidal wideband transient bases of compact support. The basis set h ab ( t ) = h [( t - b )/ a ]√ a is called daughter wavelets, which are constructed from a causal analytical mother wavelet h ( t ) by means of the dilation parameter a and the translation parameter b . We show that a causal (i.e., zero valued before signal arrives) and analytical mother wavelet still guarantees completeness. This permits the selection of mother wavelets that better match causal analytical input signals. An optical architecture is described for real-time implementation.
35 citations
TL;DR: It is shown that the optical implementations of both discrete and continuous wavelet transforms can be considered theoretically and shown that they can be stored and utilized in parallel large banks of wavelets to allow "instantaneous" DWT of functions of a single variable and (relatively) fast DWTs of two-dimensional functions.
Abstract: We consider theoretically the optical implementations of both discrete and continuous wavelet transforms. Discrete wavelet transforms (DWTs) require sums (or integrals) of the product of the input function with multiple stored functions (wavelets with various shifts and scales). The inverse DWT requires the same, exceptthe given function is replaced by the wavelet coefficients determined by the DWT. We show that we can store and utilize in parallel large banks of wavelets. This should allow "instantaneous" DWT of functions of a single variable and (relatively) fast DWTs of two-dimensional functions. Of course, the same applies to the inverse DWTs. A true continuous wavelet transform (CWT) must be continuous in both shift and scale. By means of a continuous anamorphic transformation of a one-dimensional signal and a suitable choice of kernel or filter, we can allow a normal two-dimensional optical Fourier transform image processor to perform a CWT.
TL;DR: In this paper, a noise reduction technique, developed recently for use in wavelet cluster analysis in cosmology and astronomy, is adapted here for time-series data, which is filtered using control surrogate data sets generated from randomized aspects of the original time series.
Abstract: Wavelet transforms are powerful techniques that can decompose time series into both time and frequency components. Their application to experimental data has been hindered by the lack of a straightforward method to handle noise. A noise reduction technique, developed recently for use in wavelet cluster analysis in cosmology and astronomy, is adapted here for time-series data. Noise is filtered using control surrogate data sets generated from randomized aspects of the original time series. The method is a powerful extension of the wavelet transform that is readily applied to the detection of structure in stationary and nonstationary time series.
TL;DR: In this article, the integrated wavelet transform of a measure on a set J and, using the thermodynamic formalism, rigorously show that, for a large class of dynamical systems, it gives the correlation dimension of J. They recover qualitatively the same result analyzing the Mellin transform of the wavelet.
Abstract: The authors define the integrated wavelet transform of a measure on a set J and, using the thermodynamic formalism, they rigorously show that, for a large class of dynamical systems, it gives the correlation dimension of J. They recover qualitatively the same result analysing the Mellin transform of the wavelet. They apply this method to the numerical analysis of some hyperbolic and nonhyperbolic invariant sets.
TL;DR: An optical Haar mother wavelet is created with a Semetex 128 x 128 magneto-optic spatial light modulator and two techniques for dilating it are explored: aperture stopping and operating the SLM in ternary phase-amplitude mode.
Abstract: An optical Haar mother wavelet is created with a Semetex 128 x 128 magneto-optic spatial light modulator. Two techniques for dilating the mother wavelet are explored: (1) aperture stopping and (2) operating the SLM in ternary phase-amplitude mode. Discrete resolution levels of a continuous wavelet transform are obtained by optically correlating a binarized image with multiple dilations ofthe mother wavelet. Frequency-plane masks for the correlation process are generated using thermoplastic holography. Experimental results are compared with a digital simulation of the wavelet transform.
01 Jan 1992
TL;DR: In this paper, an efficient algorithm for the estimation of the 2-d disparity between a pair of stereo images is presented, where phase-based methods are extended to the case of 2-D disparities and shown to correspond to computing local correlation fields.
Abstract: An efficient algorithm for the estimation of the 2-d disparity between a pair of stereo images is presented. Phase based methods are extended to the case of 2-d disparities and shown to correspond to computing local correlation fields. These are derived at multiple scales via the frequency domain and a coarse-to-fine 'focusing' strategy determines the final disparity estimate. Fast implementation is achieved by using a generalised form of wavelet transform, the multiresolution Fourier transform (MFT), which enables efficient calculation of the local correlations. Results from initial experiments on random noise stereo pairs containing both 1-d and 2-d disparities, illustrate the potential of the approach.
TL;DR: The utility of wavelet analysis as a tool for geophysical research is examined using both continuous and discrete versions of the wavelet transform, and the effects of filtering in wavelet phase space using the discrete case are also examined.
Abstract: The utility of wavelet analysis as a tool for geophysical research is examined using both continuous and discrete versions of the wavelet transform. In both cases, waveform decomposition and reconstruction is possible using somewhat different computational procedures. The theoretical background of each procedure is briefly described and applied using a specific 'wavelet'. The wavelet used is based on a Gaussian function, and provides simultaneous time-frequency (or space-wavenumber) localization that meets the lower limit of the uncertainty principle. A representation of this type is ideally suited for the analysis of waveforms that arise from nonstationary processes. The properties of wavelet analysis are examined by expanding an FM-chirp waveform and azimuth cuts taken from two different SAR ocean images. The performance and ease of implementation are compared for the continuous and discrete formulations, and the effects of filtering in wavelet phase space using the discrete case are also examined. >
TL;DR: In this article, the theory of compactly supported wavelets is placed in its historical context, and a multirate digital filter interpretation is provided, and adaptive trees of wavelet filters are described.
Abstract: Compactly supported wavelet bases are sets of compactly supported functions that are orthonormal bases for a wide variety of function spaces, including signals that have finite energy or finite power. The theory of compactly supported wavelets is placed in its historical context. Wavelet matrices and wavelet functions of one and two variables are defined. The continuous, discrete, and finite wavelet transforms are contrasted with the corresponding Fourier transforms. A multirate digital filter interpretation is provided, and adaptive trees of wavelet filters are described.
30 Aug 1992
TL;DR: The authors present a processor-time optimal algorithm to implement wavelet transforms on a VLSI implementable parallel digital architecture.
Abstract: Both from a mathematical as well as a biological perspective, wavelet transforms present a themselves as an attractive means for extracting low-level information from an image. The authors present a processor-time optimal algorithm to implement wavelet transforms on a VLSI implementable parallel digital architecture. >
23 Mar 1992
TL;DR: High-quality speech successfully generated by time-scale modification shows that the reconstruction method is suitable for various applications as well as making experimental auditory stimuli.
Abstract: A novel method of signal reconstruction from a modified auditory representation is presented. This consists of three parts: (1) an algorithm to reconstruct a signal from its modified wavelet transform with a general wavelet; (2) obtaining an auditory representation using an auditory wavelet transform whose analyzing wavelet is the impulse response of an auditory peripheral model; and (3) estimating the reconstruction algorithm both with and without data reduction. An example of its application to the time-scale modification of speech is presented. High-quality speech successfully generated by time-scale modification shows that the reconstruction method is suitable for various applications as well as making experimental auditory stimuli. >
01 Oct 1992
TL;DR: Besides filtering and detection problems, a comparison of wavelet functions is proposed and new-schemes directed to pattern recognition and multiscale mapping are introduced.
Abstract: This paper presents some applications of the wavelet transforms to EEG and ECG signals. Besides filtering and detection problems, a comparison of wavelet functions is proposed and new-schemes directed to pattern recognition and multiscale mapping are introduced.
04 Oct 1992
TL;DR: In this article, the ridge and skeleton leading to a simplified representation of a given signal have been defined, which allows the estimation of the frequency and the amplitude modulation laws associated with each elementary contribution.
Abstract: By studying the wavelet transform behavior of asymptotic signals, the so-called ridge and skeleton leading to a simplified representation of a given signal have been defined. This skeleton allows the estimation of the frequency and the amplitude modulation laws associated with each elementary contribution. In the particular case of signals composed of spectral lines (monochromatic signals modulated in amplitude), the ridges can be set to the horizontal by disentangling the components, which allows the estimation of the frequency and the amplitude modulation law of each spectral line. This technique permits a complete modeling of a sound signal, leading to various transformations such as transposition, cross synthesis, and time stretching. This mathematical formalism cannot be applied to signals containing fast transitions or isolated transients. The problem of the detection and characterization of such signals is addressed by means of vertical ridges. Locally homogeneous signals are emphasized in order to model transients corresponding to a discontinuity of a given derivative. >
19 May 1992
TL;DR: Extremely efficient surface interpolation can be obtained by use of a wavelet transform, which requires only O(n) computer operations, and often only a single iteration is required.
Abstract: Extremely efficient surface interpolation can be obtained by use of a wavelet transform. This can be accomplished using biologicallyplausible filters, requires only O(n) computer operations, and often only a single iteration is required.
07 Oct 1992
TL;DR: In this paper, the authors discussed the application of the wavelet transform and derived the theoretical performance of the joint maximum likelihood estimation and the Cramer-Rao lower bound (CRLB) obtained.
Abstract: The authors discuss the application of the wavelet transform. The theoretical performance is derived. The joint maximum likelihood estimation is presented and the Cramer-Rao lower bound (CRLB) obtained. The joint estimation using the wavelet transform is shown to be more robust, and under high signal to noise ratio it is unbiased and the estimation variance is close to the CRLB for a large variety of signals. All these results are verified by computer simulations. It is demonstrated that the estimation accuracy depends on the signal structure, and the optimum signal structure is strongly related to the form of its wavelet transform. >
04 Oct 1992
TL;DR: In this article, the analytic-signal transform is used to extend electromagnetic waves from real space-time to complex space time, which leads naturally to a family of elementary conformal wavelets, which can all be obtained by applying conformal transformations of space time to a basic wavelet.
Abstract: The previously defined analytic-signal transform is used to extend electromagnetic waves from real space-time to complex space-time. This leads naturally to a family of elementary conformal wavelets, which can all be obtained by applying conformal transformations of space-time to a basic wavelet. The basic wavelet, is uniquely determined by analyticity considerations. These wavelets are parametrized by location x, time t, scale s and velocity v. An arbitrary wave can be decomposed into either stationary or moving wavelets. Such decompositions may be useful in the analysis of waves emitted by a moving source. There also exist decompositions suitable for accelerating sources. >
TL;DR: This paper describes matrix based algorithms for computing wavelet transform representations with application to multiresolution analysis and its structure is well suited for programming purpose and also for the implementation on VLSI processors.
Abstract: This paper describes matrix based algorithms for computing wavelet transform representations with application to multiresolution analysis. Structure of the algorithm presented is well suited for programming purpose and also for the implementation on VLSI processors. By using overlap-add or overlap-save techniques, constant matrix size can be used to accommodate arbitrary data lengths. Performance of the algorithm described in this paper is illustrated by decomposing an image into details and smoothed components.
TL;DR: It is demonstrated that the smoothing obtained by data compression, by omitting low frequency components of the wavelet transform, can enhance interpolation, thus producing improved classification on testing data sets.
Abstract: Preprocessing is beneficial before classification with neural networks because eliminating irrelevant data produces faster learning due to smaller datasets and due to a reduction of confusion caused by irrelevant data. In this paper we demonstrate a further benefit due to smoothing that may be accomplished at the same time. A common trade off with neural networks is between accuracy of classification of training sets versus accuracy of classification of testing sets not used for training. Classification of testing sets requires the network to interpolate. We show that the smoothing obtained by data compression, by omitting low frequency components of the wavelet transform, can enhance interpolation, thus producing improved classification on testing data sets. A wavelet transform decomposes a signal obtained from a radar simulator into frequency and spatial domains using a Mexican hat wavelet. Varying cut-off frequencies are used in omitting higher frequency components of the wavelet transform. An inverse wavelet transform shows the lest square degradation in signal due to smoothing. We demonstrate that omitting high frequency terms results in faster computation in neural network learning and provides better interpolation, that is increases classification performance with testing data sets. The reasons are explained. The wavelet compression results are compared with using low pass filtering.
Dissertation•
01 Jan 1992
TL;DR: It is shown, that the dyadic wavelet maxima (zero-crossings) representation is, in general, nonunique, and using the idea of the inherently bounded AQLR, two stability results are proven.
Abstract: The analysis of a discrete multiscale edge representation is considered. A general signal description, called an inherently bounded adaptive quasi linear representation (AQLR), motivated by two important examples, namely, the wavelet maxima representation, and the wavelet zero-crossings representation, is introduced. This paper mainly addresses the questions of uniqueness and stability. It is shown, that the dyadic wavelet maxima (zero-crossings) representation is, in general, nonunique. Nevertheless, using the idea of the inherently bounded AQLR, two stability results are proven. For a general perturbation, a global BIBO stability is shown. For a special case, where perturbations are limited to the continuous part of the representation, a Lipschitz condition is satisfied. >
TL;DR: Butterworth wavelets are introduced and it is shown that they constitute a large class of orthonormal wavelets which gives rise to fast wavelet transform algorithms.
Abstract: Butterworth wavelets are introduced and it is shown that they constitute a large class of orthonormal wavelets. Advantages of this approach are the simplicity of the analyzing wavelet design, connections with the digital filter design techniques, FIR and IIR type of implementations and computational savings in the IIR case which gives rise to fast wavelet transform algorithms. A mirror representation and nonorthogonal wavelet expansion are discussed in this context.© (1992) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
01 Jan 1992
TL;DR: A video codec based on a fast adaptive wavelet transform is proposed for low bitrate applications with good performance at very low bitrates without disturbing artifacts, such as the blocking effect which is typical in block transform based codecs.
Abstract: A video codec based on a fast adaptive wavelet transform is proposed for low bitrate applications. The filter bank used to perform the biorthogonal wavelet decomposition consists of very short linear phase filters with coefficients in powers-of-two and a polyphase structure. A different frequency decomposition is performed for each frame in the sequence in order to improve the energy compaction of the transform. The same motion vector field is used for consecutive interpolated and predicted frames. The amount of transmitted side information is then reduced by a factor of two while maintaining a good estimation. Simulations on different typical sequences show good performance at very low bitrates without disturbing artifacts, such as the blocking effect which is typical in block transform based codecs.