A method for deriving Divergence-free wavelets is presented. The approach, in 2D, produces the same wavelets as mentioned by Battle. However, Battle claims that to produce the 3D equivalent construct is still an open ...
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ISBN:
(纸本)0819419281
A method for deriving Divergence-free wavelets is presented. The approach, in 2D, produces the same wavelets as mentioned by Battle. However, Battle claims that to produce the 3D equivalent construct is still an open problem. Our method solves this problem in a simple and intuitive manner. We discuss potential applications for 2D and 3D divergence-free vector wavelets in imageprocessing problems: particularly using volumetric CT or MRI data.
In this paper, we compare for image coding applications a low-complexity IIR wavelet based on an allpass polyphase decomposition to a pair of linear phase biorthogonal wavelets. To code the wavelet coefficients, we us...
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In this paper, we compare for image coding applications a low-complexity IIR wavelet based on an allpass polyphase decomposition to a pair of linear phase biorthogonal wavelets. To code the wavelet coefficients, we use Shapiro's zerotree algorithm which has the virtues of being both efficient and delivering excellent performance (in a rate-distortion sense). We consider a variety of methods for eliminating filter transients at the image boundaries including circular convolution, symmetric extension (for the biorthogonal wavelets), and direct transmission (for the IIR wavelet). By also coding the filter states in a zerotree form, we find that direct transmission generally performs better than circular convolution. Finally, we show that the use of this IIR wavelet provides equivalent performance to the biorthogonal wavelets at greatly reduced computational complexity.
We used morphological filters to approximate wavelet scaling functions for multiresolution processing of an image. Because some spatial light modulators (SLMs) can only display binary data, wavelet processing of binar...
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ISBN:
(纸本)081941834X
We used morphological filters to approximate wavelet scaling functions for multiresolution processing of an image. Because some spatial light modulators (SLMs) can only display binary data, wavelet processing of binary images is inhibited. Therefore, we considered an alternative way - morphological processing - to generate a wavelet representation that consists entirely of binary elements. The effects of these filters are dependent on the input signal and cannot be generalized. Therefore, we used a statistical approach to approximate the scaling functions or various wavelets using morphological filters.
The wavelet transform (WT) can be used for pattern recognition. One scheme is to extract the wavelet features in the 4-D space-scale joint representation of the 2-D pattern for statistical pattern recognition. Another...
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ISBN:
(纸本)0819418447
The wavelet transform (WT) can be used for pattern recognition. One scheme is to extract the wavelet features in the 4-D space-scale joint representation of the 2-D pattern for statistical pattern recognition. Another scheme is the wavelet matched filters (WMF), that uses the WT to enhance the edge features and make correlation between the WT of the input image and the WT of the reference image. This approach uses the optical shift invariant continuous WT and implements the WT and the matching of two WTs in a single step of the correlation. Several adaptive WTs and the matching pursuits have been proposed that use the best basis functions to the signal decomposition. The basis is selected from a library of dictionary waveforms to minimize an energy or an entropy in such a way that the signal expansion with those bases is the best for signal representation or classification. Pattern recognition emphasizes the classification. Fast numerical algorithms are given for the signal expansion with the best adaptive discrete orthogonal bases. Most approaches use a fixed shape basic wavelet with varying shift and dilation parameters. Szu et al., proposed adaptive wavelets that are linear combination of wavelets, called the `super-wavelet.' The super-wavelets can be continuous and redundant. The shape of the super-wavelets can be adaptively changed for the particular applications. They show the adaptive WT of the 1-D speech signals. In this paper we show the adaptive WT with continuous 2-D wavelets, whose shape is adaptively changed to achieve the pattern recognition invariant to continuous shift and scale changes. We show why such an adaptive WT is needed and how to construct the composite wavelet matched filter (CWMF) with the adaptive super-wavelet for the continuous scale invariant pattern recognition. The real-time complex valued optical filters implementation is reported in this paper.
Wavelet transforms applied to multiresolution analyses of images produce outputs similar in theory to those of matched filters. In order to maximize the output at the location and scale of a signal of interest, it is ...
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ISBN:
(纸本)0819418447
Wavelet transforms applied to multiresolution analyses of images produce outputs similar in theory to those of matched filters. In order to maximize the output at the location and scale of a signal of interest, it is necessary for the wavelet used in the multiresolution analysis to `match' the signal of interest. Current techniques match a signal to one of several predefined wavelets in a library, which requires wavelets to be designed in advance. Here, we present an alternative by developing a technique for deriving the wavelet directly from the desired signal spectrum in such a way that the mean squared error between their spectra is a minimum. Furthermore, the matched wavelet is designed such that its associated scaling function generates an orthonormal multiresolution analysis. The technique includes an algorithm for finding the scaling function from an orthonormal wavelet, and algorithms for finding the optimal wavelet magnitude and phase from a given input signal. Several examples are shown to demonstrate the performance of the technique for both known orthonormal wavelets and arbitrary signals.
This wavelet based data compression algorithm addresses a growing need to handle large quantities of image data quickly and efficiently. This wavelet technique has been coded based on the assumption that small coeffic...
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ISBN:
(纸本)0819418447
This wavelet based data compression algorithm addresses a growing need to handle large quantities of image data quickly and efficiently. This wavelet technique has been coded based on the assumption that small coefficients computed by the two-dimensional orthogonal wavelet transform are principally associated with image noise, and only the largest values are required to capture the information content of the respective source image. The approach has been successfully applied to one-dimensional signals in the design of signal classifiers. This particular algorithm for wavelet-based image compression has been designed and compared to the Joint Photographic Expert Group (JPEG) still picture image compression standard. Examples are shown of side scan sonar images, x rays, and laser line scan images.
We develop an algorithm to reconstruct the wavelet coefficients of an image from the Radon transform data. The proposed method uses the properties of wavelets to localize the Radon transform and can be used to reconst...
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ISBN:
(纸本)0780331222
We develop an algorithm to reconstruct the wavelet coefficients of an image from the Radon transform data. The proposed method uses the properties of wavelets to localize the Radon transform and can be used to reconstruct a local region of the cross section of a body, using almost completely local data which significantly reduces the amount of exposure and computations in x-ray tomography. For example, for a local region of radius 20 pixels in a 256/spl times/256 image the proposed method can reduce the exposure to 12.5% of the conventional filtered backprojection method. Compared to the existing schemes, which can only reduce to 40%.
In this contribution we introduce a new family of wavelets named Circular Harmonic wavelets (CHW), suited for multiscale feature-based representations, that constitute a basis for general steerable wavelets. The famil...
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ISBN:
(纸本)0819419281
In this contribution we introduce a new family of wavelets named Circular Harmonic wavelets (CHW), suited for multiscale feature-based representations, that constitute a basis for general steerable wavelets. The family is based on Circular Harmonic Functions (CHF) derived by the Fourier expansion of local Radial Tomographic Projections. A multiscale general feature analysis can be performed by linearly combining the outputs of CHW operators of different order. After a survey on the general properties of the CHFs, we investigate the relationship between CHF and the wavelet expansion, stating the basic admissibility and stability conditions with reference to the Hankel transform of the radial profiles and describing some fundamental mathematical properties. Finally some applications are illustrated through examples.
It is shown that analyses based on Symmetric Daubechies wavelets (SDW) lead to a multiresolution form of the Laplacian operator. This property, which is related to the complex values of the SDWs, gives a way to new me...
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ISBN:
(纸本)0819419281
It is shown that analyses based on Symmetric Daubechies wavelets (SDW) lead to a multiresolution form of the Laplacian operator. This property, which is related to the complex values of the SDWs, gives a way to new methods of image enhancement applications. After a brief recall of the construction and main properties of the SDW, we propose a representation of the sharpening operator at different scales and we discuss the `importance of the phase' of the complex wavelet coefficients.
We demonstrate some wavelet-based imageprocessingapplications of a class of simplicial grids arising in finite element computations and computer graphics. The cells of a triangular grid form the set of leaves of a b...
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ISBN:
(纸本)0819419281
We demonstrate some wavelet-based imageprocessingapplications of a class of simplicial grids arising in finite element computations and computer graphics. The cells of a triangular grid form the set of leaves of a binary tree and the nodes of a directed graph consisting of a single cycle. The leaf cycle of a uniform grid forms a pattern for pixel image scanning and for coherent computation of coefficients of splines and wavelets. A simple form of image encoding is accomplished with a 1D quadrature mirror filter whose coefficients represent an expansion of the image in terms of 2D Haar wavelets with triangular support. A combination the leaf cycle and an inherent quadtree structure allow efficient neighbor finding, grid refinement, tree pruning and storage. Pruning of the simplex tree yields a partially compressed image which requires no decoding, but rather may be rendered as a shaded triangulation. This structure and its generalization to n-dimensions form a convenient setting for wavelet analysis and computations based on simplicial grids.
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