Benefiting from Duplicates of Compressed Data: Shift-Based Holographic Compression of Images

Yehuda Dar, Alfred M. Bruckstein

Research output: Contribution to journalArticlepeer-review

Abstract

Storage systems often rely on multiple copies of the same compressed data, enabling recovery in case of binary data errors, of course, at the expense of a higher storage cost. In this paper, we show that a wiser method of duplication entails great potential benefits for data types tolerating approximate representations, like images and videos. We propose a method to produce a set of distinct compressed representations for a given signal, such that any subset of them allows reconstruction of the signal at a quality depending only on the number of compressed representations utilized. Essentially, we implement the holographic representation idea, where all the representations are equally important in refining the reconstruction. Here, we propose to exploit the shift sensitivity of common compression processes and generate holographic representations via compression of various shifts of the signal. Two implementations for the idea, based on standard compression methods, are presented: the first is a simple, optimization-free design. The second approach originates in a challenging rate-distortion optimization, mitigated by the alternating direction method of multipliers (ADMM), leading to a process of repeatedly applying standard compression techniques. Evaluation of the approach, in conjunction with the JPEG2000 image compression standard, shows the effectiveness of the optimization in providing compressed holographic representations that, by means of an elementary reconstruction process, enable impressive gains of several dBs in PSNR over exact duplications.

Original languageEnglish
Pages (from-to)380-393
Number of pages14
JournalJournal of Mathematical Imaging and Vision
Volume63
Issue number3
DOIs
StatePublished - 1 Mar 2021
Externally publishedYes

Keywords

  • Alternating direction method of multipliers (ADMM)
  • Holographic representations
  • Image compression
  • Rate-distortion optimization
  • Signal compression

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Condensed Matter Physics
  • Computer Vision and Pattern Recognition
  • Geometry and Topology
  • Applied Mathematics

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