| D. L. Donoho, M. Vetterli, R. A. DeVore, and I. Daubechies, "Data compression and harmonic analysis," IEEE Trans. Inform. Theory, vol. 44, pp. 2435--2476, Oct. 1998. |
....that wavelets offer the best rate of non linear approximation. By this we mean that approximating functions that are locally H older # with discontinuities, by their N biggest wavelet coefficients, one obtains an approximation error in the order of N # and that this is an optimal result (see [5] [6] and references therein) The key to this result is that wavelet bases yield very sparse representations of such signals, mainly because their vanishing moments kill polynomial parts while their multiresolution behaviour allow to localize discontinuities with few non negligible elements. Now, ....
Donoho D.L., Vetterli M., DeVore R. A. and Daubechies I., "Data compression and harmonic analysis," IEEE Transactions on Information Theory, vol. 44, pp. 391--432, 1998.
..... Yet this is still the LSDB. Finally, from Theorems 4.4 and 4.6, we can prove the following corollary: Corollary 4.9. There is no invertible linear transformation providing the statistically independent coordinates for the spike process for 8 . 701 5. THE GENERALIZED SPIKE PROCESS In [14], Donoho et al. analyzed the following generalization of the simple spike process in terms of the KLB and the rate distortion function. This process first picks one coordinate out of coordinates randomly as before, but then the amplitude of this single spike is picked according to the standard ....
D. L. Donoho, M. Vetterli, R. A. DeVore, and I. Daubechies, "Data compression and harmonic analysis, " IEEE Trans. Inform. Theory, vol. 44, no. 6, pp. 2435--2476, 1998, Invited paper. 703
.... asymptotically require less operations than discrete Fourier transforms, oversam pled filter banks provide efficient implementations of frame expansions [29] More importantly, one can expect that these expansions would have advantages over Fourier techniques for many types of practical signals [8]. In particular, wavelet and wavelet like bases have proven very effective in image compression. Given the machinery of the DWT and its implementation through iterated filter banks, a simple way to obtain a frame expansion is to remove all the downsampling. However, such undecimated DWT s have ....
D. L. Donoho, M. Vetterli, R. A. DeVore, and I. Daubechies. Data compression and harmonic analysis. IEEE Trans. Inform. Th., 44(6):2435476, October 1998.
....plausible model. Presently, we work in spline spaces but we consider also using wavelets or multiwavelets which are scalable as well (condition (a) The wavelet deformation model would also have the advantage of simplifying certain regularity criteria thanks to the norm equivalence principle [46]. For example, Sobolev norm kW m p k can be expressed using Triebel sequence norms of Meyer wavelet expansion. Given the regular structure of the basis functions, efficient factorizations of the Hessian matrix might be possible, leading to fast optimization algorithms (condition (b) ....
D. Donoho, M. Vetterli, R. DeVore and I. Daubechies, Data Compression and Harmonic Analysis, IEEE Trans. on Information Theory, vol. 44, no. 6, October 1998. --- 10 ---
....: locally polynomial parts of the signal are filtered out by vanishing moments. Only singularities will give high wavelet coefficients. Now, since wavelet basis have short support, few wavelets will occasionally intersect singular parts of the signal, giving rise to a highly sparse representation [6, 7]. These nice properties are unfortunately not available in two dimensions and this opens the door to new image representations. Indeed, an image can still be modeled as a piecewise smooth 2 D signal with singularities, but the latter are not point like anymore. Higher dimensional singularities may ....
Donoho D.L., Vetterli M., DeVore R.A. and Daubechies I., "Data Compression and Harmonic Analysis," IEEE Transactions on Information Theory, vol. 44, no. 6, pp. 2435--2476, October 1998.
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D.L. Donoho, M. Vetterli, R.A. DeVore, and I. Daubechies. Data compression and harmonic analysis. IEEE Trans. on Information Theory, 44(6):2435--2476, October 1998.
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D. L. Donoho, M. Vetterli, R. A. DeVore, and I. Daubechies, "Data compression and harmonic analysis," IEEE Trans. Inform. Theory, vol. 44, pp. 2435--2476, Oct. 1998.
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D. L. Donoho, M. Vetterli, R. A. DeVore, and I. Daubechies, "Data compression and harmonic analysis," IEEE Trans. Inform. Th., vol. 44, no. 6, pp. 2435--2476, October 1998.
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D. L. Donoho, M. Vetterli, R. A. DeVore, and I. Daubechies, "Data compression and harmonic analysis," IEEE Trans. Informat. Theory, vol. 44, pp. 2435--2476, Oct. 1998.
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D. L. Donoho, M. Vetterli, R. A. DeVore, and I. Daubechies, "Data compression and harmonic analysis," IEEE Trans. Inform. Theory, vol. 44, pp. 2435--2476, Oct. 1998.
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D. Donoho, M. Vetterli, R. DeVore, and I Daubechies, "Data compression and harmonic analysis," IEEE Trans. Inform Theory (Special Issue, Information Theory: 1948-1998 Commemorative Issue), vol. 44, pp. 2435-2476, Oct. 1998.
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D.L. Donoho, M. Vetterli, R.A. DeVore, and I. Daubechies. Data compression and harmonic analysis. IEEE Trans. on Information Theory, 44(6):2435--2476, October 1998.
....wavelet methods. 1 INTRODUCTION The design of a complete or overcomplete expansion that allows for compact representation of certain relevant classes of signals is a central problem in signal image processing and its applications. Parsimonious representation of data is important for compression [1], furthermore, achieving a compact representation of a signal also means intimate knowledge of the signal features and this can be useful for many other tasks including denoising, classification and interpolation. The success of the wavelet transform is mainly due to its ability to characterize ....
D.L. Donoho, M. Vetterli, R.A. DeVore, and I. Daubechies, "Data compression and harmonic analysis," IEEE Trans. on Information Theory, vol. 44(6), pp. 2435--2476, October 1998.
....take advantage of sparse representations of image data where most information is packed into a small number of samples. Typically, these representations are achieved via invertible and non redundant transforms. Currently, the most popular choices for this purpose are the wavelet transform [1] [2], 3] and the discrete cosine transform [4] The success of wavelets is mainly due to the good performance for piecewise smooth functions in one dimension. Unfortunately, such is not the case in two dimensions. In essence, wavelets are good at catching zero dimensional or point singularities, but ....
D.L. Donoho, M. Vetterli, R. A. DeVote, and I. Daubechies, "Data compression and harmonic analysis," IEEE Trans. Inform. Th., vol. 44, no. 6, pp. 2435-2476, October 1998.
....a practical compression algorithm based on optimal quadtree decomposition that, in some cases, achieve the oracle performance. 1. INTRODUCTION The interaction of approximation theory and compression is an active area of research, especially in the context of wavelet based signal processing (see [1, 2] for reviews) The set up usually considers classes of signals (piecewise smooth signals, specified by an appropriate norm) and classes of bases (Fourier series, wavelet bases) Then, the intuition is that if a certain expansion has good approximation properties (e.g. its N term linear or ....
D. L. Donoho, M. Vetterli, R. A. DeVore, and I. Daubechies, "Data compression and harmonic analysis," IEEE Trans. Inform. Th., vol. 44, no. 6, pp. 2435--2476, October 1998.
....tasks take advantage of sparse representations of image data where maximum information is packed into a small number of samples. Typically, these representations are achieved via non redundant and invertible transforms. Currently, the most popular choice for this purpose is wavelet transforms [1, 2]. The main power of wavelets comes from the fact that they are well adapted to changes or singularities that are commonly found in real life signals. In multidimensional cases, most often tensor product wavelets or separable schemes are employed. As a generalization from the case, wavelets in ....
D. L. Donoho, M. Vetterli, R. A. DeVore, and I. Daubechies, "Data compression and harmonic analysis," IEEE Trans. Info. Theory, vol. 44, no. 6, pp. 2435--2476, October 1998.
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D. L. Donoho, M. Vetterli, R. A. DeVore, and I. Daubechies, "Data compression and harmonic analysis," IEEE Trans. Inform. Theory, vol. 44, pp. 2435--2476, Oct. 1998.
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D. L. Donoho, M. Vetterli, R. A. DeVore, and I. Daubechies, "Data compression and harmonic analysis," IEEE Trans. Inform. Theory, vol. 44, pp. 2435--2476, Oct. 1998.
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D. L. Donoho, M. Vetterli, R. A. DeVore, and I. Daubechies, "Data compression and harmonic analysis," IEEE Trans. Inform. Theory 44, pp. 2435--2476, Oct. 1998.
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D. L. Donoho, M. Vetterli, R. A. DeVore, and I. Daubechies, "Data compression and harmonic analysis," IEEE Trans. Inform. Theory, vol. 44, pp. 2435--2476, Oct. 1998.
No context found.
D.L. Donoho, M. Vetterli, R.A. DeVore, and I. Daubechies. Data compression and harmonic analysis. IEEE Trans. on Information Theory, 44(6):2435--2476, October 1998.
No context found.
D. L. Donoho, M. Vetterli, R. A. Devore, and I. Daubechies, "Data compression and harmonic analysis," IEEE Trans. Inform. Theory, vol. 44, pp. 2435--2476, 1998.
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D.L. Donoho, M. Vetterli, R.A. DeVore, and I. Daubechie, "Data Compression and Harmonic Analysis," IEEE Trans. Information Theory, vol. 6, pp. 2435-2476, 1998.
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Donoho D.L., Vetterli M., DeVore R.A. and Daubechies I., "Data Compression and Harmonic Analysis," IEEE Transactions on Information Theory, vol. 44, no. 6, pp. 2435--2476, October 1998.
No context found.
D.L. Donoho, M. Vetterli, R.A. DeVore, and I. Daubechies. Data compression and harmonic analysis. IEEE Trans. on Information Theory, 44(6):2435--2476, October 1998.
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