This paper introduces a class of wavelet packets based upon a set of biorthogonal basis functions. Using a Kronecker product formulation, we develop a self-similar factorization that obeys a set of perfect reconstruct...
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ISBN:
(纸本)0819450804
This paper introduces a class of wavelet packets based upon a set of biorthogonal basis functions. Using a Kronecker product formulation, we develop a self-similar factorization that obeys a set of perfect reconstruction conditions. This construction is then identified as a wavelet packet decomposition and is applied to the finite field case. Finally, it is demonstrated that the proposed wavelet packets can be applied as a well-known class of error control codes.
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.
We give a physical interpretation for finite tight frames along the lines of Columb's Law in Physics. This allows us to use results from classical mechanics to anticipate results in frame theory. As a consequence,...
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ISBN:
(纸本)0819450804
We give a physical interpretation for finite tight frames along the lines of Columb's Law in Physics. This allows us to use results from classical mechanics to anticipate results in frame theory. As a consequence, we are able to classify those frames for an N-dimensional Hilbert space which are the closest to being tight (in the sense of minimizing potential energy) while having the norms of the frame vectors prescribed in advance. This also yields a fundamental inequality that all finite tight frames must satisfy.
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.
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.
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.
Taking advantage of the new developments in mathematical statistics, a multiscale approach is designed to detect filament or filament-like features in noisy images. The major contribution is to introduce a general fra...
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ISBN:
(纸本)0819450804
Taking advantage of the new developments in mathematical statistics, a multiscale approach is designed to detect filament or filament-like features in noisy images. The major contribution is to introduce a general framework in cases when the data is digital. Our detection method can detect the presence of an underlying curvilinear feature with the lowest possible strength that are still detectible in theory. Simulation results on synthetic data will be reported to illustrate its effectiveness in finite digital situations.
We treat nonparametric estimation of a regression function defined on a 'tensor product irregular grid,' that is, a grid constructed as the Cartesian product of two irregular one-dimensional grids. Our wavelet...
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ISBN:
(纸本)0819450804
We treat nonparametric estimation of a regression function defined on a 'tensor product irregular grid,' that is, a grid constructed as the Cartesian product of two irregular one-dimensional grids. Our wavelet-type estimator is based on a wavelet transform which is the tensor product of two one-dimensional design-adapted wavelet transforms. We propose a denoising scheme and show the performance of the resulting estimator through a simulation study.
This paper describes a new approach for creating compelling virtual acoustic environments by synthesizing and three-dimensionally localizing sounds within the wavelet-domain. A prototype system was developed that comb...
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ISBN:
(纸本)0819450804
This paper describes a new approach for creating compelling virtual acoustic environments by synthesizing and three-dimensionally localizing sounds within the wavelet-domain. A prototype system was developed that combines wavelet-domain convolution for localization with Miner's(1) new method for synthesizing parametrically controlled sounds. Results are presented and discussed, with suggestions as to directions of further interest.
We review the sparse representation principle for processing speech signals. A transformation for encoding the speech signals is learned such that the resulting coefficients are as independent as possible. We use inde...
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ISBN:
(纸本)0819450804
We review the sparse representation principle for processing speech signals. A transformation for encoding the speech signals is learned such that the resulting coefficients are as independent as possible. We use independent component analysis with an exponential prior to learn a statistical representation for speech signals. This representation leads to extremely sparse priors that can be used for encoding speech signals for a variety of purposes. We review applications of this method for speech feature extraction, automatic speech recognition and speaker identification. Furthermore, this method is also suited for tackling the difficult problem of separating two sounds given only a single microphone.
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