Extended families of 2D arrays with near optimal auto and low cross-correlation

I. D. Svalbe, A. Z. Tirkel

Research output: Contribution to journalArticleResearchpeer-review

3 Citations (Scopus)

Abstract

Families of 2D arrays can be constructed where each array has perfect autocorrelation, and the cross-correlation between any pair of family members is optimally low. We exploit equivalent Hadamard matrices to construct many families of p p × p arrays, where p is any 4k-1 prime. From these families, we assemble extended families of arrays with members that exhibit perfect autocorrelation and next-to-optimally low cross-correlation. Pseudo-Hadamard matrices are used to construct extended families using p = 4k + 1 primes. An optimal family of 31 31 × 31 perfect arrays can provide copyright protection to uniquely stamp a robust, low-visibility watermark within every frame of each second of high-definition, 30 fps video. The extended families permit the embedding of many more perfect watermarks that have next-to-minimal cross-correlations.

Original languageEnglish
Article number18
Number of pages19
JournalEURASIP Journal on Advances in Signal Processing
Volume2017
Issue number1
DOIs
Publication statusPublished - 1 Dec 2017

Keywords

  • Correlation
  • Digital watermarks
  • Discrete projection
  • Finite Radon transform
  • Pseudo-noise arrays

Cite this

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Extended families of 2D arrays with near optimal auto and low cross-correlation. / Svalbe, I. D.; Tirkel, A. Z.

In: EURASIP Journal on Advances in Signal Processing, Vol. 2017, No. 1, 18, 01.12.2017.

Research output: Contribution to journalArticleResearchpeer-review

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T1 - Extended families of 2D arrays with near optimal auto and low cross-correlation

AU - Svalbe, I. D.

AU - Tirkel, A. Z.

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N2 - Families of 2D arrays can be constructed where each array has perfect autocorrelation, and the cross-correlation between any pair of family members is optimally low. We exploit equivalent Hadamard matrices to construct many families of p p × p arrays, where p is any 4k-1 prime. From these families, we assemble extended families of arrays with members that exhibit perfect autocorrelation and next-to-optimally low cross-correlation. Pseudo-Hadamard matrices are used to construct extended families using p = 4k + 1 primes. An optimal family of 31 31 × 31 perfect arrays can provide copyright protection to uniquely stamp a robust, low-visibility watermark within every frame of each second of high-definition, 30 fps video. The extended families permit the embedding of many more perfect watermarks that have next-to-minimal cross-correlations.

AB - Families of 2D arrays can be constructed where each array has perfect autocorrelation, and the cross-correlation between any pair of family members is optimally low. We exploit equivalent Hadamard matrices to construct many families of p p × p arrays, where p is any 4k-1 prime. From these families, we assemble extended families of arrays with members that exhibit perfect autocorrelation and next-to-optimally low cross-correlation. Pseudo-Hadamard matrices are used to construct extended families using p = 4k + 1 primes. An optimal family of 31 31 × 31 perfect arrays can provide copyright protection to uniquely stamp a robust, low-visibility watermark within every frame of each second of high-definition, 30 fps video. The extended families permit the embedding of many more perfect watermarks that have next-to-minimal cross-correlations.

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KW - Digital watermarks

KW - Discrete projection

KW - Finite Radon transform

KW - Pseudo-noise arrays

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