In this paper we consider a new method for image data compression. It is based on three-directional spline functions of low degree, viz. piecewise constant functions, and piecewise cubic C-1-functions. In the first ca...
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ISBN:
(纸本)0819437646
In this paper we consider a new method for image data compression. It is based on three-directional spline functions of low degree, viz. piecewise constant functions, and piecewise cubic C-1-functions. In the first case a Haar wavelet type decomposition can be derived, and combined with standard thresholding techniques. In the second case, due to the fact that a spline basis is given by convolution products, the wavelet decomposition and thresholding can be computed on one factor of the convolution product only. Performance of the proposed method is discussed in section 3 where the reconstructed pictures are compared with the ones produced by the analogous decomposition methods provided by the MATLAB wavelet toolbox.
We propose a new, time-frequency formulation of the Gerchberg-Papoulis algorithm for extrapolation of bandlimited signals. The new formulation is obtained by translating the constituent operations of the Gerchberg-Pap...
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ISBN:
(纸本)0819437646
We propose a new, time-frequency formulation of the Gerchberg-Papoulis algorithm for extrapolation of bandlimited signals. The new formulation is obtained by translating the constituent operations of the Gerchberg-Papoulis procedure, the truncation and the Fourier transform, into the language of the finite Zak transform, a time-frequency tool intimately related to the Fourier transform. We will show that the use of the Zak transform results in a significant reduction of the computational complexity of the Gerchberg-Papoulis procedure and in an increased flexibility of the algorithm.
We perform adaptive joint space and frequency tilings including all levels in the Haar-Walsh wavelet packet tree for two-dimensional signals. The method gives surprisingly good results in terms of nonlinear approximat...
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ISBN:
(纸本)0819437646
We perform adaptive joint space and frequency tilings including all levels in the Haar-Walsh wavelet packet tree for two-dimensional signals. The method gives surprisingly good results in terms of nonlinear approximation. The visual quality of the compressed images with this method is the same as the quality using twice the number of coefficients for wavelets and standard wavelet packets when Haar filters are used. When all levels are allowed the cost for description of the location of the winning coefficients is not negligible. A tiling information vector is introduced for description of the chosen basis and the original image can be easily and quickly reconstructed using this information. For image compression this tiling information vector is compressed to only those nodes which correspond to kept coefficients, and this makes the adaptive scheme competitive.
We introduce a new algorithm for progressive or multiresolution image compression. The algorithm improves on the Set Partitioning in Hierarchical Trees (SPIHT) algorithm by replacing the SPIHT encoder. The new encoder...
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ISBN:
(纸本)0819437646
We introduce a new algorithm for progressive or multiresolution image compression. The algorithm improves on the Set Partitioning in Hierarchical Trees (SPIHT) algorithm by replacing the SPIHT encoder. The new encoder optimizes the multiresolution code performance relative to a user-defined probability distribution (or priority function) over the code's rates or resolutions. The new algorithm's decoder is identical to the SPIHT decoder. The resulting code achieves the optimal expected performance across resolutions subject to the constraints imposed by the use of the SPIHT decoder and the distribution (or priorities) over resolutions set by the user. The encoder optimization yields performance improvements at the rates or resolutions of greatest importance (according to the encoder's priority function) at the expense of performance degradation at low priority rates or resolutions. The algorithm is fully compatible at the decoder with the original SPIHT algorithm. In particular, the decoder requires no knowledge of the priority function employed at the encoder. Experimental results on an image containing both text and photographic material yield up to 0.86 dB performance improvement over SPIHT at the resolution of highest priority.
We show how a wavelet basis may be adapted to best represent natural images in terms of sparse coefficients. The wavelet basis, which may be either complete or overcomplete, is specified by a small number of spatial f...
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ISBN:
(纸本)0819437646
We show how a wavelet basis may be adapted to best represent natural images in terms of sparse coefficients. The wavelet basis, which may be either complete or overcomplete, is specified by a small number of spatial functions which are repeated across space and combined in a recursive fashion so as to be self-similar across scale. These functions are adapted to minimize the estimated code length under a model that assumes images are composed as a linear superposition of sparse, indepedent components. When adapted to natural images, the wavelet bases become selective to different spatial orientations. and they achieve a superior degree of sparsity on natural images as compared with traditional wavelet bases.
The use of wavelet techniques for the multifractal analysis generalizes the box counting approach, and in addition provides information on eventual deviations of multifractal behavior. By the introduction of a wavelet...
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ISBN:
(纸本)0819437646
The use of wavelet techniques for the multifractal analysis generalizes the box counting approach, and in addition provides information on eventual deviations of multifractal behavior. By the introduction of a wavelet partition function W-q and its corresponding free energy beta (q), the discrepancies between beta (q) and the multifractal free energy tau (q) are shown to be indicative of these deviations. We study with Daubechies wavelets (D-4) some one dimensional examples previously treated with Haar wavelets, and we apply the same ideas to some two dimensional Monte Carlo configurations, that simulate a solution under the action of an attractive potential. In this last case, we study the influence in the multifractal spectra and partition functions of four physical parameters: the intensity of the pairwise potential, the temperature, the range of the model potential, and the concentration of the solution. The wavelet partition function W-q carries more information about the cluster statistics than the multifractal partition function Z(q), and the location of its peaks contributes to the determination of characteristic scales of the measure. In our experiences, the information provided by Daubechies wavelets is slightly more accurate than the one obtained by Haar wavelets.
In this report, we propose combining the Total Variation denoising method with the high loss wavelet compression for high noise level images. Numerical experiments show that TV-denoising can bring more wavelet coeffic...
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ISBN:
(纸本)0819429163
In this report, we propose combining the Total Variation denoising method with the high loss wavelet compression for high noise level images. Numerical experiments show that TV-denoising can bring more wavelet coefficients closer to zero thereby making the compression more efficient while the salient features (edges) of the images can still be retained.
We present a method for accurate estimation of formant frequencies. The method is based on differentiating the phase of the short time Fourier transform. The motivation for the method is its application to the estimat...
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ISBN:
(纸本)0819437646
We present a method for accurate estimation of formant frequencies. The method is based on differentiating the phase of the short time Fourier transform. The motivation for the method is its application to the estimation of the recently introduced "universal warping function" which is aimed at separating the speaker dependence from the phonetic content of a speech utterance. The universal warping function is determined by the nature of the relationship between formants of different speakers for phonetically similar sounds and requires an accurate estimate of formants, The proposed method provides sufficiently accuracy for its estimation.
The problem of recovering an input signal from noisy and linearly distorted data arises in many different areas of scientific investigation;e.g., noisy Radon inversion (tomography) is a problem of special interest and...
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ISBN:
(纸本)0819437646
The problem of recovering an input signal from noisy and linearly distorted data arises in many different areas of scientific investigation;e.g., noisy Radon inversion (tomography) is a problem of special interest and considerable practical relevance in medical imaging. We will argue that traditional methods for solving inverse problems - damping of the singular value decomposition (SVD) or cognate methods - behave poorly when the object to recover has edges. We apply a new system of representation, namely, the curvelets in this setting. Curvelets provide near-optimal representations of otherwise smooth objects with discontinuities along smooth C-2 edges. Inspired by some recent work on nonlinear estimation, we construct a curvelet-based biorthogonal decomposition of the Radon operator and build a reconstruction based on the shrinkage (or thresholding) of the noisy curvelet coefficients. This novel approach is shown to give a new theoretical understanding of the problem of edges in the Radon inversion problem.
The discrete multitone modulation system (DMT) has been demonstrated to be a very useful technique for high speed transmission over frequency selective channels such as the digital subscriber loops. The DR IT system c...
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ISBN:
(纸本)0819437646
The discrete multitone modulation system (DMT) has been demonstrated to be a very useful technique for high speed transmission over frequency selective channels such as the digital subscriber loops. The DR IT system can be realized using a filterbank transceiver, the synthesis bank as the transmitter and the analysis bank as the receiver. With proper time domain equalization, the channel call usually be modeled as an FIR filter with order L. It is known that if a redundancy of length L is introduced, FIR filterbank transceivers with zero ISI (Inter-Symbol Interference) property can be achieved. For example, in DFT based DMT system, redundancy is introduced by adding a cyclic prefix of length L. In this paper, we will derive the minimum length of redundancy required for FIR filterbank transceivers with ISI Free property. For a give channel, we will show that the minimum length is directly related to the Smith form of an appropriately defined channel matrix.
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