Title :
Lagrangian empirical design of variable-rate vector quantizers: consistency and convergence rates
Author_Institution :
Dept. of Math. & Stat., Queen´´s Univ., Kingston, Ont., Canada
fDate :
11/1/2002 12:00:00 AM
Abstract :
The Lagrangian formulation of variable-rate vector quantization is known to yield useful necessary conditions for quantizer optimality and generalized Lloyd algorithms for quantizer design. The Lagrangian formulation is demonstrated to provide a convenient framework for analyzing the empirical design of variable-rate vector quantizers. In particular, the consistency of empirical design based on minimizing the Lagrangian performance over a stationary and ergodic training sequence is shown for sources with finite second moment. The finite sample performance is also studied for independent training data and sources with bounded support
Keywords :
convergence of numerical methods; entropy; sequences; signal sampling; vector quantisation; Lagrangian empirical design; Lagrangian formulation; Lagrangian performance minimization; bounded support; convergence rates; empirical design; entropy-constrained quantization; ergodic training sequence; finite sample performance; finite second moment; generalized Lloyd algorithms; independent training data; independent training sources; quantizer optimality; stationary training sequence; variable-rate vector quantizers; Algorithm design and analysis; Convergence; Councils; Lagrangian functions; Length measurement; Loss measurement; Minimax techniques; Process design; Training data; Vector quantization;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2002.804114
