In this paper, we propose an image restoration algorithm based on state-of-the-art wavelet domain statistical models. We present an efficient method to estimate the model parameters from the observations, and solve th...
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ISBN:
(纸本)0819441929
In this paper, we propose an image restoration algorithm based on state-of-the-art wavelet domain statistical models. We present an efficient method to estimate the model parameters from the observations, and solve the restoration problem in orthonormal and translation-invariant (TI) wavelet domains. Substantial improvements over previous wavelet-based restoration methods are obtained. The use of a TI wavelet transform further enhances the restoration performance. We study the improvement from the viewpoint of Bayesian estimation theory and show that replacing an estimator with its TI version will reduce the expected risk if the signal and the degradation model are stationary.
Compact support is undoubtedly one of the wavelet properties that is given the greatest weight both in theory and applications. It is usually believed to be essential for two main reasons : (1) to have fast numerical ...
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ISBN:
(纸本)0819441929
Compact support is undoubtedly one of the wavelet properties that is given the greatest weight both in theory and applications. It is usually believed to be essential for two main reasons : (1) to have fast numerical algorithms, and (2) to have good time or space localization properties. Here, we argue that this constraint is unnecessarily restrictive and that fast algorithms and good localization can also be achieved with non-compactly supported basis functions. By dropping the compact support requirement, one gains in flexibility. This opens up new perspectives such as fractional wavelets whose key parameters (order, regularity, etc...) are tunable in a continuous fashion. To make our point, we draw an analogy with the closely related task of image interpolation. This is an area where it was believed until very recently that interpolators should be designed to be compactly supported for best results. Today, there is compelling evidence that non-compactly supported interpolators (such as splines, and others) provide the best cost/performance tradeoff.
Fast algorithms performing time-scale analysis of multivariate functions are discussed. The algorithms employ univariate wavelets and involve a directional parameter, namely the angle of rotation. Both the rotation st...
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ISBN:
(纸本)0819429139
Fast algorithms performing time-scale analysis of multivariate functions are discussed. The algorithms employ univariate wavelets and involve a directional parameter, namely the angle of rotation. Both the rotation steps and the wavelet analysis/synthesis steps in the algorithms require a number of computations proportional to the number of data involved. The rotation and wavelet techniques are used for the segregation of wanted and unwanted components in a seismic signal. As an illustration, the rotation and wavelet methods are applied to a synthetic shot record.
In this paper, we propose a statistical modeling of images based on a decomposition with complex-valued Daubechies wavelets. These wavelets possess interesting properties that can be turn into account in the modeling ...
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ISBN:
(纸本)0819437646
In this paper, we propose a statistical modeling of images based on a decomposition with complex-valued Daubechies wavelets. These wavelets possess interesting properties that can be turn into account in the modeling to obtain a better characterization of the images. This characterization is achieved by statistically modeling the wavelet coefficient distribution via a hidden Markov tree model. The wavelet coefficients in an image are organized into three tree structures and this type of model has already been used successfully in this context by independently modeling each of these trees. We propose a further refinement by considering the joint modeling of the three trees with a so-called mixed memory hidden Markov tree model. The model is based on a memory mixture, a general approach to obtain an approximation of the joint distribution in the presence of factorial Markov models. The utilization of such model is quite general and can be applied to various signal-processing problems. To illustrate the interest of this model as well as the relevance of using complex Daubechies wavelets, we evaluate their performance for a classification and a denoising application.
In the given paper a method for resolving two overlapping signals is described for the case, when both signals are Gaussians with equal half-width. Using wavelet transform of the original signal, which contains such a...
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ISBN:
(纸本)0819422355
In the given paper a method for resolving two overlapping signals is described for the case, when both signals are Gaussians with equal half-width. Using wavelet transform of the original signal, which contains such a superposition of two Gaussians, we express the shift between peaks in terms of wavelet image maxima. This enables us to develop a fast method to determine positions and amplitudes of the gaussian sources with a satisfactory accuracy. A comparison with Fourier method often applied to this problem is presented.
wavelets are mathematical functions that cut up data into different frequency components, and then study each component with a resolution matched to its scale. They have advantages over traditional Fourier methods in ...
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wavelets are mathematical functions that cut up data into different frequency components, and then study each component with a resolution matched to its scale. They have advantages over traditional Fourier methods in analyzing physical situations where the signal contains discontinuities and sharp spikes. wavelets were developed independently in the fields of mathematics, quantum physics, electrical engineering, and seismic geology. Interchanges between these fields during the last ten years have led to many new wavelet applications such as image compression, turbulence, human vision, radar, and earthquake prediction. This article introduces wavelets to the interested technical person outside of the digital signalprocessing field. I describe the history of wavelets beginning with Fourier, compare wavelet transforms with Fourier transforms, state properties and other special aspects of wavelets, and finish with some interesting applications such as image compression, musical tones, and denoising noisy data. Readers may contact Amara Graps at the Bay Area Environmental Research Institute and Intergalactic Reality, 22724 Majestic Oak Way, Cupertino, CA 95014, e-mail agraps@***, http://***/~agraps/***
The Continuous Wavelet Transform (CWT) is an effective way to analyze nonstationary signals and to localize and characterize singularities. Fast algorithms have already been developed to compute the CWT at integer tim...
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ISBN:
(纸本)0819441929
The Continuous Wavelet Transform (CWT) is an effective way to analyze nonstationary signals and to localize and characterize singularities. Fast algorithms have already been developed to compute the CWT at integer time points and dyadic or integer scales. We propose here a new method that is based on a B-spline expansion of both the signal and the analysis wavelet and that allows the CWT computation at arbitrary scales. Its complexity is O(N), where N represents the size of the input signal;in other words, the cost is independent of the scale factor. Moreover;the algorithm lends itself well to a parallel implementation.
One of the main advantages of the discrete wavelet representation is the near-optimal estimation of signals corrupted with noise. After the seminal work of De Vore and Lucier (1992) and Donoho and Johnstone (1995), ne...
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ISBN:
(纸本)0819425915
One of the main advantages of the discrete wavelet representation is the near-optimal estimation of signals corrupted with noise. After the seminal work of De Vore and Lucier (1992) and Donoho and Johnstone (1995), new techniques for choosing appropriate threshold and/or shrinkage functions have recently been explored by Bayesian and likelihood methods. This work is motivated by a Bayesian approach and is based on the complex representation of signals by the Symmetric Daubechies wavelets. applications for two dimensional signals are discussed.
Functional (time-dependent) Magnetic Resonance Imaging can be used to determine which parts of the brain are active during various limited activities;these parts of the brain are called activation regions. In this pre...
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ISBN:
(纸本)0819450804
Functional (time-dependent) Magnetic Resonance Imaging can be used to determine which parts of the brain are active during various limited activities;these parts of the brain are called activation regions. In this preliminary study we describe some experiments that are suggested, from the following questions: Does one get improved results by analyzing the compleximage data rather than just the real magnitude image data? Does wavelet shrinkage smoothing improve images? Should one smooth in time as well as within and between slices? If so, how should one model the relationship between time smoothness (or correlations) and spatial smoothness (or correlations). The measured data is really the Fourier coefficients of the compleximage-should we remove noise in the Fourier domain before computing the compleximages? In this preliminary study we describe some experiments related to these questions.
We propose a novel approach for scattered data smoothing based on second generation wavelets. This wavelet transform automatically adapts to the irregularity of the grid. Our implementation also pays attention to nume...
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ISBN:
(纸本)0819441929
We propose a novel approach for scattered data smoothing based on second generation wavelets. This wavelet transform automatically adapts to the irregularity of the grid. Our implementation also pays attention to numerical stability, a crucial property in estimation procedures. The wavelet coefficients are shrunk either with simple soft-thresholding or with an empirical Bayesian estimation.
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