We study a certain nonlinear operator T from L2(R, C N) to itself under which every refinable function vector is a fixed point. The iterations Tnf of T on any f ε L2(R, CN) with the Riesz basis property are investiga...
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We present a unified image compressor with spline biorthogonal wavelets and dyadic rational filter coefficients which gives high computational speed and excellent compression performance. Convolutions with these filte...
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Wavelet transform technique is applied to the analysis of data collected in experiments on the characterization of nonlinear optical materials which may be in the form of liquid, thin film or crystal. Many characteriz...
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ISBN:
(纸本)0819422134
Wavelet transform technique is applied to the analysis of data collected in experiments on the characterization of nonlinear optical materials which may be in the form of liquid, thin film or crystal. Many characterization techniques are based on nonlinear optical processes such as higher harmonic generation in which second harmonic or third harmonic signals may be generated by the nonlinear material. When the optical path length of the material is changed, the interference between bound and free waves forms a fringe pattern. Conventional Fourier transform techniques are not suitable for analyzing such fringes when they have a variable periodicity and a low signal-to-noise ratio. However, the wavelet transform method is best suited for such signals because it provides a better resolution in both space and frequency domains. In this study, optical properties of materials are extracted from these fringe patterns by decomposing them into coefficients which are inner products of the signal and a family of wavelets generated from a mother wavelet by dilation and shift operations.
Application of fast discrete orthogonal transforms with various basis functions for data compression and efficient signal coding occupies a special place in the evolution of spectral representations. This has become m...
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ISBN:
(纸本)0819422134
Application of fast discrete orthogonal transforms with various basis functions for data compression and efficient signal coding occupies a special place in the evolution of spectral representations. This has become more apparent with the development of different wavelet and wavelet-packet transforms. Two basic compression procedures, known as zonal and threshold coding, are commonly being applied to the spectral vector. The optimal zonal coding method provides a minimum error of reconstruction for certain compression ratio. In order to determine optimal zonal coding method for the chosen transform one has to obtain the estimates of its spectra on a given class of signals. This task was considered on a general class of input vectors for classical discrete orthogonal transforms, including Fourier, Hartley, cosine, sine, as well as Walsh and Haar transforms. In this paper, we expand those results on various wavelet transforms by evaluating the upper bounds of their spectra. These estimates allow not only to a priori select the wavelet coefficient packets that have minimum input in signal reconstruction, but also to compute the maximum mean-square errors of reconstruction for a particular compression ratio and to analyze efficacy of different wavelets based on that criterion.
We present an approach to off-line optical character recognition for hand-written or printed characters using for feature extraction and classification biorthogonal discrete wavelet transform. Our aim is to optimize c...
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ISBN:
(纸本)0819422134
We present an approach to off-line optical character recognition for hand-written or printed characters using for feature extraction and classification biorthogonal discrete wavelet transform. Our aim is to optimize character recognition methods independently of printing styles, writing styles and fonts used. Characters are identified with their contours, thus characterized from their curvature function. Curvature function is used for feature extraction while classification is accomplished by LVQ algorithms. This method achieves great recognition accuracy and font insensitivity requiring only a small training set of characters.
In this paper, a high-quality, space-frequency adaptive, trellis coded wavelet image codec is presented. The algorithm seeks jointly optimal space and frequency segmentation of an image. For this, first, wavelet packe...
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ISBN:
(纸本)0819422134
In this paper, a high-quality, space-frequency adaptive, trellis coded wavelet image codec is presented. The algorithm seeks jointly optimal space and frequency segmentation of an image. For this, first, wavelet packets are formed to localize the high-energy frequency bands. Then, the wavelet coefficients are further classified to maximize the coding gain. Design target is set to minimize Lagrangian cost functions which are formed with distortion in l2 norm being the cost and coding rate as constraint. Resultant mapping is used to quantize the wavelet coefficients with trellis code quantization. This is followed by adaptive arithmetic coding producing the final compressed bitstream. Described approach is tested on several ISO standard images and results are compared to other compression techniques. Representative examples are included.
The energy cascade found in fully developed fluid turbulence is known to originate as large-scale organized motions called coherent structures. The process of detecting, locating, and tracking these coherent structure...
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ISBN:
(纸本)0819422134
The energy cascade found in fully developed fluid turbulence is known to originate as large-scale organized motions called coherent structures. The process of detecting, locating, and tracking these coherent structures is therefore of central importance to the continued study of turbulence. For certain types of flow, these structures can be associated with quadrature events between the streamwise- and transverse-instantaneous velocities. A number of researchers have begun applying wavelet-based methods to the problem of coherent structure detection. Significant performance improvements over other existing methods have already been reported. In this paper, we describe several variations of the standard wavelet cross-transform suitable for use as quadrature detectors. One adaptation simultaneously employs two different analyzing wavelets: one with odd symmetry and one with even symmetry. With these wavelets, the resulting cross-transform can be made to detect quadrature events in the time-scale plane, and thus isolate coherent structures very effectively. The method is described, and demonstrated for cylinder wake flow data. Its performance is then quantitatively compared to some of the popular alternative techniques for detecting coherent structures.
In speckled radar images, filtering must achieve a tradeoff between smoothing of homogeneous areas and edge and texture preservation. Multiscale analysis splits up the image information content, such as edges and text...
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ISBN:
(纸本)0819422134
In speckled radar images, filtering must achieve a tradeoff between smoothing of homogeneous areas and edge and texture preservation. Multiscale analysis splits up the image information content, such as edges and texture, according to a scale factor by successive lowpass and highpass filterings followed by downsampling. The speckle noise is present on each downsampled image. Each image level is then filtered in order to reduce the speckle noise. High frequency images are processed by median filtering or spatial filtering, or by using a threshold. On low frequency images a distinction is made between homogeneous areas, textural areas and areas including edges according to the values of the variation coefficient. Each class is processed differently. A Wiener filter including a multiplicative noise hypothesis for the speckle is used for textured areas. For homogeneous areas the pixel value is simply replaced by the mean value. For areas containing edges, the pixel value is let unchanged. The filtered image is finally obtained y synthesis from these images. This algorithm has been applied to an ERS1 image.
Using a three-dimensional formulation of inverse synthetic aperture (ISAR), we show how the arbitrary formatting capability of a time-integrating opto-electronic processor can be used to format the data in such a way ...
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ISBN:
(纸本)0819422339
Using a three-dimensional formulation of inverse synthetic aperture (ISAR), we show how the arbitrary formatting capability of a time-integrating opto-electronic processor can be used to format the data in such a way as to focus the image. The focusing parameters are found from prominent points in the radar data itself assuming a rigid body object. The opto-electronic processor is particularly suited for generated image data such as found with ISAR since it can arbitrarily place data points as needed depending on the object motion without need of interpolations. The processor is a time-integrating architecture that uses direct laser diode intensity modulation for signal insertion, acousto-optic scanners for arbitrary formatting, and a Modified Kosters Interferometer for stable two dimensional Fourier transformation. The processor also automatically generates multi-resolution imagery as a by-product of its generation of the final fine resolution image. Thus, there is a sequence of values available for each image pixel that are available for enhanced multi-resolution imageprocessing. This research is funded by the Office of Naval Research.
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