Data decorrelation and energy compaction are the two fundamental characteristics of wavelets that led to wavelet based image compression models. Wavelet transform is not a perfect whitening transform;but it is viewed ...
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ISBN:
(纸本)0819450804
Data decorrelation and energy compaction are the two fundamental characteristics of wavelets that led to wavelet based image compression models. Wavelet transform is not a perfect whitening transform;but it is viewed as an approximation to Karhunen-Loeve transform (KLT). In general, decorrelation does not imply statistical independence. Thus, a wavelet transform results in coefficients which exhibit inter and intra band dependencies. The energy compaction property of a wavelet is reflected in the coding performance, which can be measured by its coding gain. This paper investigates the above two important aspects of bi-orthogonal wavelets in the context of lossy compression. This investigation suggests that simple predictive models are sufficient to capture the dependencies exhibited by the wavelet coefficients. This paper also compares, the metrics that measure the performance of bi-orthogonal wavelets in lossy coding schemes.
Nonlinearities are often encountered in the analysis and processing of real-world signals. This paper develops new signal decompositions for nonlinear analysis and processing. The theory of tensor norms is employed to...
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ISBN:
(纸本)0819422134
Nonlinearities are often encountered in the analysis and processing of real-world signals. This paper develops new signal decompositions for nonlinear analysis and processing. The theory of tensor norms is employed to show that wavelets provide an optimal basis for the nonlinear signal decompositions. The nonlinear signal decompositions are also applied to signalprocessing problems.
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.
Integrated wavelets are a new method for discretizing the continuous wavelet transform (CWT). Independent of the choice of discrete scale and orientation parameters they yield tight families of convolution operators. ...
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ISBN:
(纸本)0819450804
Integrated wavelets are a new method for discretizing the continuous wavelet transform (CWT). Independent of the choice of discrete scale and orientation parameters they yield tight families of convolution operators. Thus these families can easily be adapted to specific problems. After presenting the fundamental ideas, we focus primarily on the construction of directional integrated wavelets and their application to medical images. We state an exact algorithm for implementing this transform and present applications from the field of digital mammography. The first application covers the enhancement of microcalcifications in digital mammograms. Further, we exploit the directional information provided by integrated wavelets for better separation of microcalcifications from similar structures.
signal decomposition techniques are an important tool for analyzing nonstationary signals. The proper selection of time-frequency basis functions for the decomposition is essential to a variety of signalprocessing ap...
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ISBN:
(纸本)0819418447
signal decomposition techniques are an important tool for analyzing nonstationary signals. The proper selection of time-frequency basis functions for the decomposition is essential to a variety of signalprocessingapplications. The discrete wavelet transform (DWT) is increasingly being used for signal analysis, but not until recently has attention been paid to the time-frequency resolution property of wavelets. This paper describes additional results on our procedure to design wavelets with better time-frequency resolution. In particular, our optimal duration-bandwidth product wavelets (ODBW) have better duration-bandwidth product, as a function of wavelet-defining filter length N, than Daubechies' minimum phase and least- asymmetric wavelets, and Dorize and Villemoes' optimum wavelets over the range N equals 8 to 64. Some examples and comparisons with these traditional wavelets are presented.
Battle-Lemarie's wavelet has a nice generalization in a bivariate setting. This generalization is called bivariate box spline wavelets. The magnitude of the filters associated with the bivariate box spline wavelet...
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Battle-Lemarie's wavelet has a nice generalization in a bivariate setting. This generalization is called bivariate box spline wavelets. The magnitude of the filters associated with the bivariate box spline wavelets is shown to converge to an ideal high-pass filter when the degree of the bivariate box spline functions increases to co. The passing and stopping bands of the ideal filter are dependent on the structure of the box spline function. Several possible idea! filters are shown. While these filters work for rectangularly sampled images, hexagonal box spline wavelets and filters are constructed to process hexagonally sampled images. The magnitude of the hexagonal filters converges to an ideal filter. Both convergences are shown to be exponentially fast. Finally, the computation and approximation of these filters are discussed. (C) 1997 SPIE and IS&T.
This work is devoted to the construction, the analysis and some applications of multiresolution analyses involving non translation invariant bases. It uses the very elementary tools of the Harten's multiresolution...
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ISBN:
(纸本)0819450804
This work is devoted to the construction, the analysis and some applications of multiresolution analyses involving non translation invariant bases. It uses the very elementary tools of the Harten's multiresolution framework(1) and its connections to non uniform, stationnary subdivision schemes described for instance by Dyn.(2) The applications deal with the analysis of the Gibbs phenomenon and the compression property of the corresponding multiscale process in one dimension as well as with compression of images.
Two-dimensional wavelet analysis with directional frames is well-adapted and efficient, for detecting oriented features in images. but, for (quasi-) isotropic components, it is unnecessarily redundant. Using wavelets ...
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ISBN:
(纸本)0819450804
Two-dimensional wavelet analysis with directional frames is well-adapted and efficient, for detecting oriented features in images. but, for (quasi-) isotropic components, it is unnecessarily redundant. Using wavelets with variable angular selectivity leads to a prohibitive computing cost in the continuous wavelet formalism. We propose here a solution based on a multiresolution analysis in the angular variable (transferred from a biorthogonal analysis on the line), in Addition to the usual multiresolution in scale. The resulting scheme is efficient and competitive with traditional methods. Some applications are given to image denoising.
In this contribution we present a steerable pyramid based on a particular set of complexwavelets named circular harmonic wavelets (CHW). The proposed CHWs set constitutes a generalization of the smoothed edge wavelet...
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ISBN:
(纸本)0819422134
In this contribution we present a steerable pyramid based on a particular set of complexwavelets named circular harmonic wavelets (CHW). The proposed CHWs set constitutes a generalization of the smoothed edge wavelets introduced by Mallat, consisting of extending the local differential representation of a signalimage from the first order to a generic n-th order. The key feature of the proposed representation is the use of complex operators leading to an expansion in series of polar separable complex functions, which are shown to possess the space-scale representability of the wavelets. The resulting tool is highly redundant, and for this reason is called hypercomplete circular harmonic pyramid (HCHP), but presents some interesting aspects in terms of flexibility, being suited for many imageprocessingapplications. In the present contribution the main theoretical aspects of the HCHPs are discussed along with some introductory applications.
The application of the wavelet transform in imageprocessing is most frequently based on a separable construction. Lines and columns in an image are treated independently and the basis functions are simply products of...
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ISBN:
(纸本)0819450804
The application of the wavelet transform in imageprocessing is most frequently based on a separable construction. Lines and columns in an image are treated independently and the basis functions are simply products of the corresponding one dimensional functions. Such method keeps simplicity in design and computation, but is not capable of capturing properly all the properties of an image. In this paper, a new truly separable discrete multi-directional transform is proposed with a subsampling method based on lattice theory. Alternatively, the subsampling can be omitted and this leads to a multi-directional frame. This transform can be applied in many areas like denoising, non-linear approximation and compression. The results on non-linear approximation and denoising show interesting gains compared to the standard two-dimensional analysis.
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