N. J. A. Sloane and B. Beferull-Lozano, "Quantizing using lattice intersections, " J. Discr. Comput. Geom., to be published. Home/Search Document Details and Download
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Efficient Quantization for Overcomplete Expansions in R^N - Beferull-Lozano, Ortega (2003) Self-citation (Beferull-lozano) (Correct)
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N. J. A. Sloane and B. Beferull-Lozano, "Quantizing using lattice intersections, " J. Discr. Comput. Geom., to be published.
Efficient Quantization for Overcomplete Expansions in R^N - Beferull-Lozano, Ortega Self-citation (Beferull-lozano) (Correct)
....be extended to higher redundancies and that the problem of finding good quantizers with higher redundancies consists of searching for good lattices and sublattices with certain properties. Extensions to higher dimensions have been analyzed by Sloane and Beferull Lozano recently and can be found in [22]. On the other hand, although we believe that multiple description coding is also a potential application of our framework, we have not explored this application in this paper. This paper is organized as follows. In section II we define the equivalent vector quantizer and the property of ....
....of orthogonal matrices with indeterminate entries. Notice that the matrices HsA actually generate geometrically similar or equivalent sublattices with index K = m v 2, m Z . Explicit constructions in higher dimensions have been provided by Sloane and Beferull Lozano and can be found in [22]. More specifically, constructions are given for dimensions N = 3, 6, 12, 24, 2 k, k 2. For illustration purposes, we present here a simple example for N = 4. Details about the tesselation of the space that is generated are also given in [22] Example 0 2 0 0 1 1 1 1 MA = A, MA2 = 0 0 2 0 ....
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N.J. A. Sloane and B. Beferull-Lozano, "Quantizing using lattice intersections," Journal of Discrete and Computational Geometry, To appear, Accepted in January 2002.
Robust Discretization, with an Application to Graphical.. - Birget, Hong, Memon (2003) (Correct)
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N.J.A. Sloane, B. Beferull-Lozano, \Quantizing Using Lattice Intersections", Discrete Comput. Geometry 25 (2003) 868-881.
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