Calculus of Variations and Geometric Measure Theory

T. Guo - N. Karagodin - E. Stepanov

Optimal functional product quantization

created by stepanov on 24 Apr 2023
modified on 14 Sep 2024

[BibTeX]

Preprint

Inserted: 24 apr 2023
Last Updated: 14 sep 2024

Year: 2023

Abstract:

We introduce a mathematically new approach for quantization of vectorial signals. Namely, we are aimed at quantizing vectorial signals on input to a computational device calculating some given function of the input. As opposed to the classical quantization which usually optimizes the quality of just quantizing the signal, without taking into account any further transformation of the latter by means of the computational device, here we optimize the quality of quantization on the output of this device. Moreover, we quantize components of the signal separately. This leads to a quantization problem qualitatively different from the classical one. We study existence of optimal quantizers (which is not at all obvious in this setting) and estimate the optimal cost for several classes of functions.

Keywords: optimal location, quantization


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