Discrete wavelet transform is a powerful mathematical tool used for signal and image compression, nonlinear filtering or noise reduction, signal and biomedical imageprocessing and all kind of applications that implie...
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The key element in the design of fast algorithms in numerical analysis and signalprocessing is the selection of an efficient approximation for the functions and operators involved. In this talk we will consider appro...
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ISBN:
(纸本)0819441929
The key element in the design of fast algorithms in numerical analysis and signalprocessing is the selection of an efficient approximation for the functions and operators involved. In this talk we will consider approximations using wavelet and multiwavelet bases as well as a new type of approximation for bandlimited functions using exponentials obtained via Generalized Gaussian quadratures. Analytically, the latter approximation corresponds to using the basis of the Prolate Spheroidal Wave functions. We will briefly comment on the future development of approximation techniques and the corresponding fast algorithms.
It is well known that the image compression task can be effectively accomplished by means of the wavelet transform. A new method has been recently proposed for the computation of this transform, i.e. the Lifting Schem...
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ISBN:
(纸本)0819437646
It is well known that the image compression task can be effectively accomplished by means of the wavelet transform. A new method has been recently proposed for the computation of this transform, i.e. the Lifting Scheme (LS). Besides being computationally more efficient than the classical filter bank scheme, the LS also enables the computation of a wavelet transform which maps integers to integers, so allowing for the design of joint lossless and lossy compression schemes. The performance of this Integer wavelet Transform (IWT) has already been studied in the literature, and compared to that of the Discrete wavelet Transform (DWT) in the lossy case;it has been found that in most cases the DWT achieves slightly better performance with respect to the DWT. In this paper we show that this result does not hold in the case of lossy compression of smooth images, as the IWT has a much larger loss of performance, making it ineffective for the compression of such images. We first select measures of image smoothness;then we study the IWT lossy compression performance in the presence of different degrees of smoothness, on an set containing various kinds of images. Finally, we relate the IWT compression performance to the degree of image smoothness.
Multiscale statistical signal and image models resulted in major advances in many signalprocessing disciplines. This paper focuses on Bayesian image denoising. We discuss two important problems in specifying priors f...
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ISBN:
(纸本)0819451541
Multiscale statistical signal and image models resulted in major advances in many signalprocessing disciplines. This paper focuses on Bayesian image denoising. We discuss two important problems in specifying priors for imagewavelet coefficients. The first problem is the characterization of the marginal subband statistics. Different existing models include highly kurtotic heavy-tailed distributions, Gaussian scale mixture models and weighted sums of two different distributions. We discuss the choice of a particular prior and give some new insights in this problem. The second problem that we address is statistical modelling of inter- and intrascale dependencies between imagewavelet coefficients. Here we discuss the use of Hidden Markov Tree models, which are efficient in capturing inter-scale dependencies, as well as the use of Markov Random Field models, which are more efficient when it comes to spatial (intrascale) correlations. Apart from these relatively complex models, we review within a new unifying framework a class of low-complexity locally adaptive methods, which encounter the coefficient dependencies via local spatial activity indicators.
New techniques for developing more efficient noise reduction schemes are presented and implemented by applying the wavelet transform (WT) to a series of stationary and non- stationary signals. Their effectiveness is i...
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ISBN:
(纸本)0819422134
New techniques for developing more efficient noise reduction schemes are presented and implemented by applying the wavelet transform (WT) to a series of stationary and non- stationary signals. Their effectiveness is illustrated with specific applications to both real and synthetic seismic data, and the superiority over Fourier transform (FT) based methods is demonstrated. These methods aim at the efficient reduction of the effects that surface waves, airwaves, and direct waves can have on the interpretation of a seismic record. We first apply the WT on each trace in a common- depth-point gather and then perform stacking in the WT domain and compute both the mean and median transforms. Then, the signal-to-noise ratio of the stacked transforms is estimated and used as a criterion to improve the quality of the transformed data, and finally the total energy in the stacked WT plane is computed and redistributed in order to boost weak events. The advantage of stacking in the WT domain is that it allows for detection of weak reflections overpowered by high amplitude surface and air waves. Additionally, it is shown that by frequency modulating a mother wavelet, further attenuation of surface waves, airwaves, and first breaks may be achieved.
作者:
Schwarz, GDatcu, MDLR
German Remote Sensing Data Ctr German Aerosp Res Estab DFD D-82234 Oberpfaffenhofen Germany
During the last years, wavelets have become very popular in the fields of signalprocessing and pattern recognition and have led to a large number of publications. In the discipline of remote sensing several applicati...
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ISBN:
(纸本)0819426490
During the last years, wavelets have become very popular in the fields of signalprocessing and pattern recognition and have led to a large number of publications. In the discipline of remote sensing several applications of wavelets have emerged, too. Among them are such diverse topics as image data compression, image enhancement, feature extraction, and detailed data analysis. On the other hand, the processing of remote sensing image data-both for optical and radar data-follows a well-known systematic sequence of correction and data management steps supplemented by dedicated image enhancement and data analysis activities. In the following we will demonstrate where wavelets and wavelet transformed data can be used advantageously within the standard processing chain usually applied to remote sensing image data. Summarizing potential waveletapplications for remote sensing image data, we conclude that wavelets offer a variety of new perspectives especially for image coding, analysis, classification, archiving, and enhancement. However, applications requiring geometrical corrections and separate dedicated representation bases will probably remain a stronghold of classical image domain processing techniques.
Traditional cepstral analysis methods are often used as part of feature extraction process in speech recognition. However the cepstral analysis method uses the Discrete Fourier Transform (DFT) in one of its computatio...
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ISBN:
(纸本)9781479902699;9781479902675
Traditional cepstral analysis methods are often used as part of feature extraction process in speech recognition. However the cepstral analysis method uses the Discrete Fourier Transform (DFT) in one of its computation process. The DFT uses fixed frame resolution to analyze frames of signal thus it will result in an analysis that would not accurately analyze localized events. This paper investigates the use of the Discrete wavelet Transform (DWT) for calculating the cepstrum coefficients. Two wavelet types with different decomposition level are experimented to yield the cepstrum which is called the wavelet Cepstral Coefficient (WCC). To test the WCC speech recognizing task of recognizing 26 English alphabets were conducted. Under same number of feature dimension the WCC outperformed the MFCC with about 20% in terms of recognition rate under both speaker dependent and speaker independent task.
This paper describes different methodologies for noise reduction or denoising with applications in the field of microscopy. An in depth study on wavelet- and polynomial based denoising has been performed by considerin...
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ISBN:
(纸本)0819422134
This paper describes different methodologies for noise reduction or denoising with applications in the field of microscopy. An in depth study on wavelet- and polynomial based denoising has been performed by considering standard test images and phantom tests with moderate and high levels of Gaussian noise. Different thresholding methods have been tested and evaluated and in particular a novel sigmoidal- type thresholding method has been proposed. In real applications, noise variance estimation problem becomes crucial because most of the thresholding estimators tends to overestimate this value. A comparison with the Hermite polynomial transform (HPT) and a modification of the HPT based in detecting the position and orientation of relevant edges has been accomplished. From this study one can conclude that both wavelet-based and polynomial-based denoising methods perform better than any other nonlinear filtering method both in terms of perceptual quality and edge-preserving characteristics.
We present new quantitative results for the characterization of the L-2-error of wavelet-like expansions as a function of the scale a. This yields an extension as well as a simplification of the asymptotic error formu...
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ISBN:
(纸本)0819429139
We present new quantitative results for the characterization of the L-2-error of wavelet-like expansions as a function of the scale a. This yields an extension as well as a simplification of the asymptotic error formulas that have been published previously. We use our bound determinations to compare the approximation power of various families of wavelet transforms. We present explicit formulas for the leading asymptotic constant for both splines and Daubechies wavelets. For a specified approximation error, this allows us to predict the sampling rate reduction that can obtained by using splines instead Daubechies wavelets. In particular, we prove that the gain in sampling density (splines vs. Daubechies) converges to pi as the order goes to infinity.
The multitude of visual media-based applications demands sophisticated compression and indexing techniques for efficient storage, transmission and retrieval of images and video. Compressed domain techniques are becomi...
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ISBN:
(纸本)0818688211
The multitude of visual media-based applications demands sophisticated compression and indexing techniques for efficient storage, transmission and retrieval of images and video. Compressed domain techniques are becoming popular due its inherent advantages of efficiency and reduced complexity. wavelet transform is emerging as a powerful tool for efficient compression of visual information. A variety of wavelet based video compression techniques have been reported in the literature. However, there has been little work done in the area of video indexing in the wavelet domain. This is crucial for consideration of wavelets as a potential candidate for multimedia applications, including standards such as MPEG-7. In this paper we first present a brief review of wavelet-based indexing techniques. We then propose a video indexing system in a wavelet compression framework. Simulation results show that the proposed system provides a good indexing performance at a low complexity.
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