We present complex rotation-covariant multiresolution families aimed for image analysis. Since they are complex-valued functions, they provide the important phase information, which is missing in the discrete wavelet ...
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ISBN:
(纸本)0819450804
We present complex rotation-covariant multiresolution families aimed for image analysis. Since they are complex-valued functions, they provide the important phase information, which is missing in the discrete wavelet transform with real wavelets. Our basis elements have nice properties in Hilbert space such as smoothness of fractional order alpha is an element of R+. The corresponding filters allow a FFT-based implementation and thus provide a fast algorithm for the wavelet transform.
The Lifting Scheme (LS) is a very efficient implementation of the Discrete Wavelet transform (DWT). In this work we compute the arithmetic gain realized when the LS is used instead of conventional filter banks. It is ...
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ISBN:
(纸本)0819441929
The Lifting Scheme (LS) is a very efficient implementation of the Discrete Wavelet transform (DWT). In this work we compute the arithmetic gain realized when the LS is used instead of conventional filter banks. It is shown that contrary to was was presented in the original work from Sweldens again of four is possible. However the LS should be used with care as it can increase the memory bandwidth. Some implementations are presented together with their impact on the bandwidth.
Recently, the contourlet transform(1) has been developed as a true two-dimensional representation that can capture the geometrical structure in pictorial information. Unlike other transforms that were initially constr...
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ISBN:
(纸本)0819450804
Recently, the contourlet transform(1) has been developed as a true two-dimensional representation that can capture the geometrical structure in pictorial information. Unlike other transforms that were initially constructed in the continuous-domain and then discretized for sampled data, the contourlet construction starts from the discrete-domain using filter banks, and then convergences to a continuous-domain expansion via a multiresolution analysis framework. In this paper we study the approximation behavior of the contourlet expansion for two-dimensional piecewise smooth functions resembling natural images. Inspired by the vanishing moment property which is the key for the good approximation behavior of wavelets, we introduce the directional vanishing moment condition for contourlets. We show that with anisotropic scaling and sufficient directional vanishing moments, contourlets essentially achieve the optimal approximation rate, O((log M)M-3(-2)) square error with a best M-term approximation, for 2-D piecewise smooth functions with C-2 contours. Finally, we-show some numerical experiments demonstrating the potential of contourlets in several imageprocessingapplications.
Wavelet image denoising practice has shown that the performance of simple estimators may be substantially improved by averaging these estimators over a collection of transformations such as translations or rotations. ...
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ISBN:
(纸本)0819450804
Wavelet image denoising practice has shown that the performance of simple estimators may be substantially improved by averaging these estimators over a collection of transformations such as translations or rotations. In this paper, we explain and quantify these empirical findings using estimation theory. We consider a general nonlinear observation model, analyze the estimation risk of transformation-averaged estimators, and derive an upper bound on the risk reduction due to transformation averaging. The bound is evaluated for several estimators, using different averaging strategies (including a randomized strategy) and different wavelet bases. The practical usefulness of the bound is established for standard image denoising examples.
This paper introduces a class of wavelet packets based upon a set of biorthogonal basis functions. Using a Kronecker product formulation, we develop a self-similar factorization that obeys a set of perfect reconstruct...
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ISBN:
(纸本)0819450804
This paper introduces a class of wavelet packets based upon a set of biorthogonal basis functions. Using a Kronecker product formulation, we develop a self-similar factorization that obeys a set of perfect reconstruction conditions. This construction is then identified as a wavelet packet decomposition and is applied to the finite field case. Finally, it is demonstrated that the proposed wavelet packets can be applied as a well-known class of error control codes.
This paper provides an overview of subband and wavelet theories. It emphasizes their strong relations. The practical merits of these decomposition techniques in signalprocessing are examined. The current status of th...
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ISBN:
(纸本)0819412236
This paper provides an overview of subband and wavelet theories. It emphasizes their strong relations. The practical merits of these decomposition techniques in signalprocessing are examined. The current status of this active research field is summarized and it concludes with the discussion of potential extensions for future study.
The use of wavelets has grown enormously since their original inception in the mid-1980s. Since the wavelet data representation combines spatial, frequency, and scale information in a sparse data representation, they ...
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The use of wavelets has grown enormously since their original inception in the mid-1980s. Since the wavelet data representation combines spatial, frequency, and scale information in a sparse data representation, they are very useful in a number of imageprocessingapplications. This paper discusses current work in applying wavelets to object and pattern recognition. Feature extraction methods and search algorithms for matching images are discussed. Some important issues are the search for invariant representations, similarities between existing applications and the human visual system, and the derivation of wavelets that match specific targets. Results from several existing systems and areas for future research are presented. (C) 2001 SPIE and IS&T.
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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