Construction of perfect auto-correlation arrays and zero cross-correlation arrays from discrete projections

Benjamin Cavy; Imants Svalbe

doi:10.1007/978-3-319-26145-4_17

Construction of perfect auto-correlation arrays and zero cross-correlation arrays from discrete projections

Benjamin Cavy, Imants Svalbe

School of Physics and Astronomy

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

1 Citation (Scopus)

Abstract

This paper presents a new method by which sets of discrete 1D projections can be used to construct large families of 2D discrete arrays. These compact arrays have targeted, specific periodic correlation values that span the full range between perfect auto-correlation to zero cross-correlation. The array size is variable and the array elements can be binary or contain grey integer values. Arrays with these properties are useful for digital signal synchronisation, communications and watermarking. We show that multiple copies of zero cross-correlation arrays can be co-located without interference and that the presence of individual arrays is able to be determined independently. The arrays with perfect periodic auto-correlation also have high aperiodic auto-correlation and optimally low cross-correlation, making them well-suited for use as digital watermarks.

Original language	English
Title of host publication	Combinatorial Image Analysis: 17th International Workshop, IWCIA 2015 Kolkata, India, November 24-27 2015 Proceedings
Editors	Reneta P Barneva, Bhargab B Bhattacharya, Valentin E Brimkov
Place of Publication	Cham Switzerland
Publisher	Springer
Pages	232-243
Number of pages	12
Volume	9448
ISBN (Print)	9783319261447
DOIs	https://doi.org/10.1007/978-3-319-26145-4_17
Publication status	Published - 2015
Event	International Workshop on Combinatorial Image Analysis: Theory and Applications 2015 - Kolkata, India Duration: 24 Nov 2015 → 27 Nov 2015 Conference number: 17th

Conference

Conference	International Workshop on Combinatorial Image Analysis: Theory and Applications 2015
Abbreviated title	IWCIA 2015
Country/Territory	India
City	Kolkata
Period	24/11/15 → 27/11/15

Keywords

Discrete radon projection
Perfect auto-correlation
Zero-cross-correlation
Ghost images

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10.1007/978-3-319-26145-4_17

Cite this

Cavy, B., & Svalbe, I. (2015). Construction of perfect auto-correlation arrays and zero cross-correlation arrays from discrete projections. In R. P. Barneva, B. B. Bhattacharya, & V. E. Brimkov (Eds.), Combinatorial Image Analysis: 17th International Workshop, IWCIA 2015 Kolkata, India, November 24-27 2015 Proceedings (Vol. 9448, pp. 232-243). Springer. https://doi.org/10.1007/978-3-319-26145-4_17

Cavy, Benjamin ; Svalbe, Imants. / Construction of perfect auto-correlation arrays and zero cross-correlation arrays from discrete projections. Combinatorial Image Analysis: 17th International Workshop, IWCIA 2015 Kolkata, India, November 24-27 2015 Proceedings. editor / Reneta P Barneva ; Bhargab B Bhattacharya ; Valentin E Brimkov. Vol. 9448 Cham Switzerland : Springer, 2015. pp. 232-243

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title = "Construction of perfect auto-correlation arrays and zero cross-correlation arrays from discrete projections",

abstract = "This paper presents a new method by which sets of discrete 1D projections can be used to construct large families of 2D discrete arrays. These compact arrays have targeted, specific periodic correlation values that span the full range between perfect auto-correlation to zero cross-correlation. The array size is variable and the array elements can be binary or contain grey integer values. Arrays with these properties are useful for digital signal synchronisation, communications and watermarking. We show that multiple copies of zero cross-correlation arrays can be co-located without interference and that the presence of individual arrays is able to be determined independently. The arrays with perfect periodic auto-correlation also have high aperiodic auto-correlation and optimally low cross-correlation, making them well-suited for use as digital watermarks. ",

keywords = "Discrete radon projection, Perfect auto-correlation, Zero-cross-correlation, Ghost images",

author = "Benjamin Cavy and Imants Svalbe",

year = "2015",

doi = "10.1007/978-3-319-26145-4_17",

language = "English",

isbn = "9783319261447",

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booktitle = "Combinatorial Image Analysis: 17th International Workshop, IWCIA 2015 Kolkata, India, November 24-27 2015 Proceedings",

publisher = "Springer",

note = "International Workshop on Combinatorial Image Analysis: Theory and Applications 2015, IWCIA 2015 ; Conference date: 24-11-2015 Through 27-11-2015",

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Cavy, B & Svalbe, I 2015, Construction of perfect auto-correlation arrays and zero cross-correlation arrays from discrete projections. in RP Barneva, BB Bhattacharya & VE Brimkov (eds), Combinatorial Image Analysis: 17th International Workshop, IWCIA 2015 Kolkata, India, November 24-27 2015 Proceedings. vol. 9448, Springer, Cham Switzerland, pp. 232-243, International Workshop on Combinatorial Image Analysis: Theory and Applications 2015, Kolkata, India, 24/11/15. https://doi.org/10.1007/978-3-319-26145-4_17

Construction of perfect auto-correlation arrays and zero cross-correlation arrays from discrete projections. / Cavy, Benjamin; Svalbe, Imants.

Combinatorial Image Analysis: 17th International Workshop, IWCIA 2015 Kolkata, India, November 24-27 2015 Proceedings. ed. / Reneta P Barneva; Bhargab B Bhattacharya; Valentin E Brimkov. Vol. 9448 Cham Switzerland : Springer, 2015. p. 232-243.

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Research › peer-review

TY - GEN

T1 - Construction of perfect auto-correlation arrays and zero cross-correlation arrays from discrete projections

AU - Cavy, Benjamin

AU - Svalbe, Imants

N1 - Conference code: 17th

PY - 2015

Y1 - 2015

N2 - This paper presents a new method by which sets of discrete 1D projections can be used to construct large families of 2D discrete arrays. These compact arrays have targeted, specific periodic correlation values that span the full range between perfect auto-correlation to zero cross-correlation. The array size is variable and the array elements can be binary or contain grey integer values. Arrays with these properties are useful for digital signal synchronisation, communications and watermarking. We show that multiple copies of zero cross-correlation arrays can be co-located without interference and that the presence of individual arrays is able to be determined independently. The arrays with perfect periodic auto-correlation also have high aperiodic auto-correlation and optimally low cross-correlation, making them well-suited for use as digital watermarks.

AB - This paper presents a new method by which sets of discrete 1D projections can be used to construct large families of 2D discrete arrays. These compact arrays have targeted, specific periodic correlation values that span the full range between perfect auto-correlation to zero cross-correlation. The array size is variable and the array elements can be binary or contain grey integer values. Arrays with these properties are useful for digital signal synchronisation, communications and watermarking. We show that multiple copies of zero cross-correlation arrays can be co-located without interference and that the presence of individual arrays is able to be determined independently. The arrays with perfect periodic auto-correlation also have high aperiodic auto-correlation and optimally low cross-correlation, making them well-suited for use as digital watermarks.

KW - Discrete radon projection

KW - Perfect auto-correlation

KW - Zero-cross-correlation

KW - Ghost images

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DO - 10.1007/978-3-319-26145-4_17

M3 - Conference Paper

SN - 9783319261447

VL - 9448

SP - 232

EP - 243

BT - Combinatorial Image Analysis: 17th International Workshop, IWCIA 2015 Kolkata, India, November 24-27 2015 Proceedings

A2 - Barneva, Reneta P

A2 - Bhattacharya, Bhargab B

A2 - Brimkov, Valentin E

PB - Springer

CY - Cham Switzerland

T2 - International Workshop on Combinatorial Image Analysis: Theory and Applications 2015

Y2 - 24 November 2015 through 27 November 2015

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Cavy B, Svalbe I. Construction of perfect auto-correlation arrays and zero cross-correlation arrays from discrete projections. In Barneva RP, Bhattacharya BB, Brimkov VE, editors, Combinatorial Image Analysis: 17th International Workshop, IWCIA 2015 Kolkata, India, November 24-27 2015 Proceedings. Vol. 9448. Cham Switzerland: Springer. 2015. p. 232-243 https://doi.org/10.1007/978-3-319-26145-4_17

Construction of perfect auto-correlation arrays and zero cross-correlation arrays from discrete projections

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