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.
image coding using multirate filter banks and wavelets is evaluated in this paper. The coding systems considered are based on the M-channel general lapped biorthogonal transform (GLBT) and the embedded zerotree wavele...
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ISBN:
(纸本)0780374029
image coding using multirate filter banks and wavelets is evaluated in this paper. The coding systems considered are based on the M-channel general lapped biorthogonal transform (GLBT) and the embedded zerotree wavelet (EZW) coding methods, as well as the baseline JPEG standard. The study concentrates on both coding efficiency and complexity. The tradeoff between efficiency and complexity of each coding system has been analyzed. The coding results show that the choice of a coding scheme depends mainly on the applications at hand.
Deconvolution in blind digital images is a common issue in image enhancement techniques, which basically was a notion of many researches. In this study, spatial varying blind deconvloution is stated and implemented. I...
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ISBN:
(纸本)9781728133775
Deconvolution in blind digital images is a common issue in image enhancement techniques, which basically was a notion of many researches. In this study, spatial varying blind deconvloution is stated and implemented. In addition, image noise removal approach which utilizes the normalized platform of second-generation wavelet transform is applied as pre-processing step. The low and high frequencies are decomposed in this step in order to be extracted. Practically, the main merit of wavelet transform is its efficiency in reduction of data redundancy in digital images. This feature helps a lot in terms of data classification where it is easy to distinguish the signal from its noisy counterpart. The second step, a recursive deep convolutional neural network (R-DbCNN) is implemented to suppress any image blur affected by second-generation wavelet transform to further remove the blur of noisy image. The experimental results depict that the suggested method outperforms recent blur removal techniques for different bluer image types in terms of image quality and time consumption.
In this paper a denoising technique for multispectral images exploiting interband correlations is proposed. A redundant wavelet transform is applied and denoising is applied by thresholding wavelet coefficients. A sca...
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ISBN:
(纸本)0819451215
In this paper a denoising technique for multispectral images exploiting interband correlations is proposed. A redundant wavelet transform is applied and denoising is applied by thresholding wavelet coefficients. A scale adaptive threshold value is obtained by exploiting the interband correlation of the signal. First, the coefficients from different bands are multiplied. For these products, the signal and noise probability density functions (pdf) become more separated. The high signal correlation between bands is exploited further by summing these products over all bands, in this way separating noise and signal pdfs even more. The noise pdf of the proposed quantities is derived analytically and from this, a wavelet threshold is derived. The technique is demonstrated to outperform single band wavelet thresholding on multispectral remote sensing images.
First, a general procedure for constructing a variety of orthogonal wavelets which are compactly supported in frequency domain is presented. These orthogonal wavelets, as a result of the method of Multiresolution Anal...
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ISBN:
(纸本)0780336798;0780336801
First, a general procedure for constructing a variety of orthogonal wavelets which are compactly supported in frequency domain is presented. These orthogonal wavelets, as a result of the method of Multiresolution Analysis(MRA), share the same space structure. This property makes it possible to construct a ''combined'' orthonormal base of L-2(R) which contains more than one wavelet functions. This kind of combined orthonormal wavelet bases are more flexible and are expected to be more efficient than the conventional wavelet bases in data compression, speech coding and image coding.
Spherical filters have recently been introduced in order to avoid the spherical harmonic transform. Spherical filtering can be used in a variety of applications, such as climate modelling, electromagnetic and acoustic...
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ISBN:
(纸本)0819450804
Spherical filters have recently been introduced in order to avoid the spherical harmonic transform. Spherical filtering can be used in a variety of applications, such as climate modelling, electromagnetic and acoustic scattering, and several other areas. However, up to now these methods have been restricted to special grids on the sphere. The main reason for this was to enable the use of FFT techniques. In this paper we extend the spherical filter to arbitrary grids by using the the Nonequispaced Fast Fourier Transform (NFFT).(1) The new algorithm can be applied to a variety of different distributions on the sphere, equidistributions on the sphere being an important example. The algorithm's performance is illustrated with several numerical examples.
We are reviewing scalar quantizers with deadzone and overload in the high-bitrate approximation, give sharp bounds on the quality of this approximation and present results on the optimal quantizer in this setting. Som...
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ISBN:
(纸本)0819450804
We are reviewing scalar quantizers with deadzone and overload in the high-bitrate approximation, give sharp bounds on the quality of this approximation and present results on the optimal quantizer in this setting. Some recent results by Hui and Neuhoff(1) are reproduced under weaker conditions. We conclude by comparing the mathematical results with experimental data. For details about the results of this article we refer to an article in prepeparation.
In this paper, an in depth investigation and comparison of the performance obtainable with short wavelet filters for low bit rate perceptual audio coding is presented. This a priori knowledge of the short wavelet filt...
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ISBN:
(纸本)0819425915
In this paper, an in depth investigation and comparison of the performance obtainable with short wavelet filters for low bit rate perceptual audio coding is presented. This a priori knowledge of the short wavelet filters performance evaluation open new horizons in their usage, especially, when combined with the Moving Pictures Expert Group (MPEG-4) requirements for segmental signal to noise ratio (SSNR) scalable audio coding.
In this work we display a multiresolution analysis scheme restricted on the interval [0,N]. This scheme is developed for the case of Hermite spline functions but it can be implemented in more general cases. Embedded i...
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ISBN:
(纸本)0819432997
In this work we display a multiresolution analysis scheme restricted on the interval [0,N]. This scheme is developed for the case of Hermite spline functions but it can be implemented in more general cases. Embedded in this scheme we construct semiorthogonal multiwavelets. Also we expose several methods and algorithms for signalprocessingapplications.
Using the time-frequency (or -scale) diversity of the source processes allows the blind source separation problem to be tackled within Gaussian models. In this work, we show that this approach amounts to minimizing a ...
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ISBN:
(纸本)0819450804
Using the time-frequency (or -scale) diversity of the source processes allows the blind source separation problem to be tackled within Gaussian models. In this work, we show that this approach amounts to minimizing a certain sparseness criterion for the energy distribution of the source over the time-frequency (or -scale) plane. We also explore the link between independence and sparsity and shows that other sparsity criteria (some examples of which are provided) can be used. Further, we introduce an adaptive method which tries to find the best sparse representation of the. source energy in order to exploit the sparsity in a most efficient way. An algorithm, adapted from that of Coifman and Wickerhauser has been developed for this end. Finally a simulation example has been given.
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