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Quantizing using lattice intersections, Discrete and Computational Geometry
Sloane, N. J. A.; Beferull-Lozano, B.
(2003). ArticleThe usual quantizer based on an n-dimensional lattice # maps a point x # R n to a closest lattice point. Suppose # is the intersection of lattices # 1 , . . . , # r . Then one may instead combine the information obtained by simultaneously quantizing x with respect to each of the # i . This corresponds to decomposing R n into a honeycomb of cells which are the intersections of the Voronoi cells for the # i , and identifying the cell to which x belongs. This paper shows how to write several standard lattices (the face-centered and body-centered cubic lattices, the root lattices D 4 , E # 6 , E 8 , the Coxeter-Todd, Barnes-Wall and Leech lattices, etc.) in a canonical way as intersections of a...
The usual quantizer based on an n-dimensional lattice # maps a point x # R n to a closest lattice point. Suppose # is the intersection of lattices # 1 , . . . , # r . Then one may instead combine the information obtained by simultaneously quantizing x with respect to each of the # i . This corresponds to decomposing R n into a honeycomb of cells which are the intersections of the Voronoi cells for the # i , and identifying the cell to which x belongs. This paper shows how to write several standard lattices (the face-centered and body-centered cubic lattices, the root lattices D 4 , E # 6 , E 8 , the Coxeter-Todd, Barnes-Wall and Leech lattices, etc.) in a canonical way as intersections of a small number of simpler, decomposable, lattices. The cells of the honeycombs are given explicitly and the mean squared quantizing error calculated in the cases when the intersection lattice is the face-centered or body-centered cubic lattice or the lattice D 4 . 1.
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Robust phoneme discrimination using acoustic waveforms
Cvetkovic, Z.; Beferull-Lozano, B.; Buja, A.
(2002). ArticleWe present a study of separability of acoustic waveforms of speech at phoneme level. The analyzed data consist of 64 ms segments of acoustic waveforms of individual phonemes from TIMIT data base, sampled at 16 kHz. For each phoneme, by means of principal component analysis, we identify subspaces which contain a given proportion of the total energy of the available waveforms in the time-domain, and also in the spectral-magnitude domain. In order to assess the separation between phonemes in the two domains, we perform pairwise classification of phonemes on clean data and on data immersed in white additive Gaussian noise up to 0 dB signal to noise ratio. While the classification based on...
We present a study of separability of acoustic waveforms of speech at phoneme level. The analyzed data consist of 64 ms segments of acoustic waveforms of individual phonemes from TIMIT data base, sampled at 16 kHz. For each phoneme, by means of principal component analysis, we identify subspaces which contain a given proportion of the total energy of the available waveforms in the time-domain, and also in the spectral-magnitude domain. In order to assess the separation between phonemes in the two domains, we perform pairwise classification of phonemes on clean data and on data immersed in white additive Gaussian noise up to 0 dB signal to noise ratio. While the classification based on spectral magnitudes exhibits high sensitivity to additive noise, the time-domain classification proves to be very robust.
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Efficient Quantization for Overcomplete Expansions in
Beferull-Lozano, B.; ortega, A.
(2001). ArticleThe use of quantized redundant expansions is useful in applications where the cost of having oversampling in the representation is much lower than the use of a high-resolution quantization (e.g., oversampled A/D). Most work to date has assumed that simple uniform quantization was used on the redundant expansion and then has dealt with methods to improve the reconstruction. Instead, we consider the design of quantizers for overcomplete expansions. Our goal is to design quantizers such that simple reconstruction algorithms (e.g., linear) provide as good reconstructions as with more complex algorithms. We achieve this goal by designing quantizers with different step sizes for each coefficient...
The use of quantized redundant expansions is useful in applications where the cost of having oversampling in the representation is much lower than the use of a high-resolution quantization (e.g., oversampled A/D). Most work to date has assumed that simple uniform quantization was used on the redundant expansion and then has dealt with methods to improve the reconstruction. Instead, we consider the design of quantizers for overcomplete expansions. Our goal is to design quantizers such that simple reconstruction algorithms (e.g., linear) provide as good reconstructions as with more complex algorithms. We achieve this goal by designing quantizers with different step sizes for each coefficient of the expansion in such a way as to produce a quantizer with periodic structure.
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Construction of Low Complexity Regular Quantizers for Overcomplete Expansions in R^n
Beferull-Lozano, B.; Ortega, A.
(2001). ArticleWe study the construction of structured regular quantizers for overcomplete expansions in RN. Our goal is to design structured quantizers allowing simple reconstruction algorithms with low (memory and computational) complexity and having good performance in terms of accuracy. Most related work to date in quantized redundant expansions has assumed that uniform scalar quantization with the same stepsize was used on the redundant expansion and then has dealt with more complex methods to improve the reconstruction. Instead, we consider the design of scalar quantizers with different stepsizes for each coefficient of an overcomplete expansion in such a way as to produce an equivalent vector...
We study the construction of structured regular quantizers for overcomplete expansions in RN. Our goal is to design structured quantizers allowing simple reconstruction algorithms with low (memory and computational) complexity and having good performance in terms of accuracy. Most related work to date in quantized redundant expansions has assumed that uniform scalar quantization with the same stepsize was used on the redundant expansion and then has dealt with more complex methods to improve the reconstruction. Instead, we consider the design of scalar quantizers with different stepsizes for each coefficient of an overcomplete expansion in such a way as to produce an equivalent vector quantizer with periodic structure. The periodicity makes it possible to achieve good accuracy using simple reconstruction algorithms from the quantized coefficients of the overcomplete expansion.
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Coding Techniques for Oversampled Steerable Transforms
Beferull-Lozano, B.; Ortega, A.
(1999). ArticleIn this paper we study signal representation using oversampled steerable transforms. While in general it may not be efficient to use an oversampled representation for applications like compression, our work investigates efficient techniques for representing the oversampled data, given that after oversampling there exists substantial redundancy. We discuss different strategies which take advantage of this oversampling by establishing some consistency constraints on the representation that reduce uncertainty in the quantization. This results in a coding gain as we increase the oversampling in the steerable transform (number of orientations). Thus, while in general it will not be possible to...
In this paper we study signal representation using oversampled steerable transforms. While in general it may not be efficient to use an oversampled representation for applications like compression, our work investigates efficient techniques for representing the oversampled data, given that after oversampling there exists substantial redundancy. We discuss different strategies which take advantage of this oversampling by establishing some consistency constraints on the representation that reduce uncertainty in the quantization. This results in a coding gain as we increase the oversampling in the steerable transform (number of orientations). Thus, while in general it will not be possible to achieve as good compression performance as with a critically sampled transform, having a compressed steerable representation will be useful for applications where a feature is needed (many significant image features can be extracted from an orientation analysis), and where for performance reasons it is preferable not to have to decompress and analyze each image (as may be necessary if standard non-steerable transforms are used for compression).
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