Regularity is a new filter property, brought by wavelet theory, for perfect reconstruction octave-band filter banks. Tools for investigating its role in coding applications are provided in this note. First, discrete-t...
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Regularity is a new filter property, brought by wavelet theory, for perfect reconstruction octave-band filter banks. Tools for investigating its role in coding applications are provided in this note. First, discrete-time interpretations an optimal estimates of regularity are reviewed. Then, a simple design procedure for paraunitary FIR filter banks with optimal trade-off between frequency selectivity and regularity is given. Finally, the obtained filters are used to measure the effect of regularity versus frequency selectivity in a still image compression scheme with optimized rate-distortion. In this case, regularity is shown to be more relevant than frequency selectivity, especially for short filters.
The classical Shannon sampling theorem has resulted in many applications and generalizations. From a multiresolution point of view, it provides the sine scaling function. In this case, for a band-limited signal, its w...
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The classical Shannon sampling theorem has resulted in many applications and generalizations. From a multiresolution point of view, it provides the sine scaling function. In this case, for a band-limited signal, its wavelet series transform (WST) coefficients below a certain resolution level can be exactly obtained from the samples with a sampling rate higher than the Nyquist rate. In this research, we study the properties of cardinal orthogonal scaling functions (COSF), which provide the standard sampling theorem in multiresolution spaces with scaling functions as interpolants. We show that COSF with compact support have and only have one possibility which is the Haar pulse. We present a family of COSF with exponential decay, which are generalizations of the Haar function. With these COSF, an application is the computation of WST coefficients of a signal by the Mallat algorithm. We present some numerical comparisons for different scaling functions to illustrate the advantage of COSF. For signals which are not in multiresolution spaces, we estimate the aliasing error in the sampling theorem by using uniform samples.
Interest in the discrete wavelet transform has grown explosively in the last five years, even though the underlying concepts are decades old and nearly identical transform techniques were being applied in industry 10 ...
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ISBN:
(纸本)0819413291
Interest in the discrete wavelet transform has grown explosively in the last five years, even though the underlying concepts are decades old and nearly identical transform techniques were being applied in industry 10 years ago. The most important aspect of the new work is the development of the underlying theory. Most if not all of the current applications of wavelets are software based, implying either slow execution times or very expensive computers. This paper shows the feasibility of using moderately-priced commercially-available imageprocessing boards to carry out multi-band 2-dimensional (2D) wavelet transforms at real-time (30 images/sec) or faster-than-real-time rates. Implementations for both real and complexwavelets are shown. Word length and kernel size limitations are discussed, along with methods to overcome them. One-dimensional wavelets are mentioned as a special case of 2D wavelets. Because of the high speed and moderate cost of these implementations, much wider application of wavelets to industrial problems is now possible.
M-band generalizations of the FIR wavelets of Daubechies have recently been introduced by several authors. We present here a set of explicit construction techniques for these M-band wavelet filters, and the results of...
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ISBN:
(纸本)0780309464
M-band generalizations of the FIR wavelets of Daubechies have recently been introduced by several authors. We present here a set of explicit construction techniques for these M-band wavelet filters, and the results of their application to image compression. Beginning with a characterization of several equivalent notions of N-th order regularity for M-band perfect reconstruction filters, we then use this characterization to devise a closed-form expression for N-th order regular wavelet lowpass filters. We complete the construction of a full M-band filter bank given a lowpass filter and a rank M unitary matrix. Finally, we apply several of these new wavelets to image coding.
This paper presents implementation of the wavelet transform on parallel computers. The time of computation of wavelet transform on classic computers limits its applications in several areas of signalprocessing and da...
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ISBN:
(纸本)0819411973
This paper presents implementation of the wavelet transform on parallel computers. The time of computation of wavelet transform on classic computers limits its applications in several areas of signalprocessing and data compression. We examine some problems encountered when parallelizing such a code and we compare three different SIMD computers on this basis: a Connection-Machine 2/200, a SYMPATI-2 Line Processor, and a MasPar MP-1.
We use the theory of the continuous wavelet transform to derive inversion formulas for the Radon transform. These inversion formulas are local in even dimensions in the following sense. In order to recover a function ...
ISBN:
(纸本)081941283X
We use the theory of the continuous wavelet transform to derive inversion formulas for the Radon transform. These inversion formulas are local in even dimensions in the following sense. In order to recover a function f from its Radon transform in a ball of radius R gt;0 about a point x to within error ε gt;0, we can find α(ε) gt;0 such that this can be accomplished by knowing the projections of f only on lines passing through a ball of radius R + α(ε) about x. We give explicit a priori estimates on the error in the L2 and L infinity norms.
In this paper, a method using the wavelet transform and the multiresolution analysis to remove the speckle effect in Synthetic Aperture Radar imagery is proposed. This technique allows the filtering of the most speckl...
ISBN:
(纸本)081941283X
In this paper, a method using the wavelet transform and the multiresolution analysis to remove the speckle effect in Synthetic Aperture Radar imagery is proposed. This technique allows the filtering of the most speckled structures and the improvement of the performances of a classical Wiener filter. Results on one example are presented. They confirm the efficiency of the multiresolution approach, as described in Cauneau and Ranchin. The choice of the algorithm of wavelet transform and of the number of scales treated are discussed. The efficiency of the `a trous' algorithm is due to the isotropy of the wavelet used. This non-directional wavelet allows an improvement of the radiometric resolution without degrading significantly the geometrical resolution. Perspectives for an improvement of the quality of the speckle reduction are explored.
We present two methods for generating frames of a Hilbert space H. The first method uses bounded operators on H to transform a frame into another frame of H1 C H. The other method uses bounded linear operators on l2 t...
ISBN:
(纸本)081941283X
We present two methods for generating frames of a Hilbert space H. The first method uses bounded operators on H to transform a frame into another frame of H1 C H. The other method uses bounded linear operators on l2 to generate frames of H. We characterize all the mappings that transform frames into other frames. We also show how to construct all frames of a given Hilbert space H starting from any given frame. We show how to apply the theory to obtain shift-invariant tight frames, and shift-invariant tight multiresolution. We also show how to obtain scaling function and wavelets with prescribed properties. Finally, we discuss the noise reduction properties of frames.
The proceedings contain 39 papers. The topics discussed include: adapted waveform analysis, wavelet packets, and local cosine libraries as a tool for imageprocessing;irregular periodic sampling of images and their de...
The proceedings contain 39 papers. The topics discussed include: adapted waveform analysis, wavelet packets, and local cosine libraries as a tool for imageprocessing;irregular periodic sampling of images and their derivatives;extension of the karhunen-loeve transform for wavelets and perfect reconstruction filterbanks;multiscale method for tomographic reconstruction;fast updating in MRI via multiscale localization;local inversion of the radon transform in the plane using wavelets;edge localization in images by symmetrical wavelet transforms;recognition of 2D objects from the wavelet transform zero-crossing representation;selecting the projection functions used in an iterative Gabor expansion;multiresolution image registration procedure using spline pyramids;and hybrid technique using spline-wavelet packets and vector quantization for high-rate image compression.
In this paper, the wavelet transform is used for the purpose of noise reduction and signal enhancement in order to aid in the detection of randomly occurring short duration signals in noisy environments with signal to...
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ISBN:
(纸本)0819411973
In this paper, the wavelet transform is used for the purpose of noise reduction and signal enhancement in order to aid in the detection of randomly occurring short duration signals in noisy environments with signal to noise ratios of about -30 dB. The noise is characterized as being additive and consists of correlated interference as well as Gaussian noise. Such problems are encountered in many applications, such as health diagnostics (e.g. electrocardiograms, echo-cardiograms and electroencephalograms), underwater acoustics and geophysical applications where a signature signal passes through multiple media. The wavelet transform, with its basis functions localized both in time and frequency, provides the user with a signal representation suitable for detection purposes. Following the introduction, a brief description of the problem with the characteristics of the signal to be detected and the noise that is present in the environment is given. Then, background information on the wavelet transform is presented. Finally, our results obtained by applying the wavelet transform to signal detection are shown.
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