We show how periodized wavelet packet transforms and periodized wavelet transforms can be implemented on a quantum computer. Surprisingly, we find that the implementation of wavelet packet transforms is less costly th...
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ISBN:
(纸本)0819432997
We show how periodized wavelet packet transforms and periodized wavelet transforms can be implemented on a quantum computer. Surprisingly, we find that the implementation of wavelet packet transforms is less costly than the implementation of wavelet transforms on a quantum computer.
The developments in wavelet theory have given rise to the wavelet thresholding method, for extracting a signal from noisy data [1,2]. Multiwavelets, wavelets with several scaling functions, have recently been introduc...
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ISBN:
(纸本)0780376226
The developments in wavelet theory have given rise to the wavelet thresholding method, for extracting a signal from noisy data [1,2]. Multiwavelets, wavelets with several scaling functions, have recently been introduced and they offer simultaneous orthogonality, symmetry and short support;which is not possible with ordinary wavelets, also called scalar wavelets [3]. This property makes multiwavelets more suitable for various signalprocessingapplications, especially compression and denoising. Like scalar wavelets, multiwavelets can be realized as filterbanks, however the filterbanks are now matrix-valued;requiring two or more input streams, which can be accomplished by prefiltering. In this paper, several thresholding methods to be used with different multiwavelets for image denoising are presented. The performances of multiwavelets are compared with those of scalar wavelets. Simulations reveal that multiwavelet based image denoising schemes outperform wavelet based methods both subjectively and objectively.
This paper deals with a restoration (both denoising and deblurring) method. For instance in the case of denoising, this latter is only a small modification from the usual wavelet thresholding. However, it has the sign...
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ISBN:
(纸本)0819441929
This paper deals with a restoration (both denoising and deblurring) method. For instance in the case of denoising, this latter is only a small modification from the usual wavelet thresholding. However, it has the significant advantage to allow the use of several bases in such a way that we select what is considered as information by a basis or another basis or another basis, and so on for as many bases as we want. The computational cost of the method is mainly the computation of the coordinates of the signal (or image) in the bases.
We propose to model satellite and aerial images using a probabilistic approach. We show how the properties of these images, such as scale invariance, rotational invariance and spatial adaptivity lead to a new general ...
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ISBN:
(纸本)0819450804
We propose to model satellite and aerial images using a probabilistic approach. We show how the properties of these images, such as scale invariance, rotational invariance and spatial adaptivity lead to a new general model which aims to describe a broad range of natural images. The complex wavelet transform initially proposed by Kingsbury is a simple way of taking into account all these characteristics. We build a statistical model around this transform, by defining an adaptive Gaussian model with interscale dependencies, global parameters, and hyperpriors controlling the behavior of these parameters. This model has been successfully applied to denoising and deconvolution, for real images and simulations provided by the French Space Agency.
Very low bit rate image coding is an important problem regarding applications such as storage on low memory devices or streaming data on the internet. The state of the art in image compression is to use 2-D wavelets. ...
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ISBN:
(纸本)0819450804
Very low bit rate image coding is an important problem regarding applications such as storage on low memory devices or streaming data on the internet. The state of the art in image compression is to use 2-D wavelets. The advantages of wavelet bases lie in their multiscale nature and in their ability to sparsely represent functions that are piecewise smooth. Their main problem on the other hand, is that in 2-D wavelets are not able to deal with the natural geometry of images, i.e they cannot sparsely represent objects that are smooth away from-regular submanifolds. In this paper we propose an approach based on building a sparse representation of images in a redundant geometrically inspired library of functions, followed by suitable coding techniques. Best N-term nonlinear approximations in general dictionaries is, in most cases, a NP-hard problem and sub-optimal approaches have to be followed. In this work we use a greedy strategy, also known as Matching Pursuit to compute the expansion. Finally the last step in our algorithm is an-enhancement layer that encodes the residual image: in our simulation we have used a genuine embedded wavelet codec.
A class of adaptive wavelet transforms that map integers to integers based on the adaptive update lifting scheme is presented. The main feature in the adaptive update lifting scheme is that the update lifting step, wh...
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ISBN:
(纸本)0819450804
A class of adaptive wavelet transforms that map integers to integers based on the adaptive update lifting scheme is presented. The main feature in the adaptive update lifting scheme is that the update lifting step, which is considered as an averaging operator and is performed prior to the prediction step, is adapted to the underlying signal content and the adaptivity decisions can be recovered at the synthesis transform without bookkeeping of the adaptivity decisions. The perfect reconstruction criterion for the integer realisation of such transforms are presented in this paper. These adaptive integer-to-integer wavelet transforms can be used in scalable lossless image coding applications. The lossless image coding and spatially scalable decoding performances are demonstrated.
Overcomplete wavelet representations have become increasingly popular for their ability to provide highly sparse and robust descriptions of natural signals. We describe a method for incorporating an overcomplete wavel...
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ISBN:
(纸本)0819450804
Overcomplete wavelet representations have become increasingly popular for their ability to provide highly sparse and robust descriptions of natural signals. We describe a method for incorporating an overcomplete wavelet representation as part of a statistical model of images which includes a sparse prior distribution over the wavelet coefficients. The wavelet basis functions are parameterized by a small set of 2-D functions. These functions are adapted to maximize the average log-likelihood of the model for a large database of natural images. When adapted to natural images, these functions become selective to different spatial orientations, and they achieve a superior degree of sparsity on natural images as compared with traditional wavelet bases. The learned basis is similar to the Steerable Pyramid basis, and yields slightly higher SNR for the same number of active coefficients. Inference with the learned model is demonstrated for applications such as denoising, with results that compare favorably with other methods.
The more a;priori knowledge we encode into a signalprocessing algorithm, the better performance we can expect. In this paper, we overview several approaches to capturing the structure of singularities ledges, ridges,...
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ISBN:
(纸本)0819432997
The more a;priori knowledge we encode into a signalprocessing algorithm, the better performance we can expect. In this paper, we overview several approaches to capturing the structure of singularities ledges, ridges, etc.) in wavelet-based signalprocessing schemes. Leveraging results from-approximation theory, we discuss nonlinear approximations on trees and point out that an optimal tree approximant exists and is easily computed. The optimal tree approximation inspires a new hierarchical interpretation of the wavelet decomposition and a tree-based wavelet denoising algorithm that suppresses spurious noise bumps.
In this paper we present a non-separable multiresolution structure based on frames which is defined by radial scaling functions of the form of the Shannon scaling function. We also construct the resulting frame multiw...
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ISBN:
(纸本)0819450804
In this paper we present a non-separable multiresolution structure based on frames which is defined by radial scaling functions of the form of the Shannon scaling function. We also construct the resulting frame multiwavelets, which can be isotropic as well. Our construction can be carried out in any number of dimensions and for a great variety of dilation matrices.
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.
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