Partition Reduction for Lossy Data Compression Problem

TL;DR

This paper introduces an algorithm that reduces the number of partitions needed for lossy data compression, ensuring the entropy is attained on a finite cover, thus improving computational efficiency.

Contribution

It presents a novel algorithm for partition reduction in lossy data compression, guaranteeing entropy attainment on finite covers and enhancing computational methods.

Findings

The entropy is attained on some partition for finite covers.

The proposed algorithm reduces the number of partitions needed.

Partition reduction improves computational efficiency in lossy compression.

Abstract

We consider the computational aspects of lossy data compression problem, where the compression error is determined by a cover of the data space. We propose an algorithm which reduces the number of partitions needed to find the entropy with respect to the compression error. In particular, we show that, in the case of finite cover, the entropy is attained on some partition. We give an algorithmic construction of such partition.