Direct inversion of Mojette projections

Imants Svalbe; Andrew Kingston; Jeanpierre Guédon; Nicolas Normand; Shekhar Chandra

doi:10.1109/ICIP.2013.6738214

Direct inversion of Mojette projections

Imants Svalbe, Andrew Kingston, Jeanpierre Guédon, Nicolas Normand, Shekhar Chandra

School of Physics and Astronomy

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

3 Citations (Scopus)

Abstract

We present algorithms to reconstruct images from minimal sets of discrete Mojette projections using direct back-projection (DBP) with various forms of correction. This paper extends previous work on discrete projection inversion by Servières et al [1, 2, 3]. The number of Mojette projections needed for exact inversion by DBP (EI-DBP) scales as O(N²). A new form of discrete interpolation is developed to expand the point spread function (PSF) of a minimal (Katz-sufficient) set of discrete projections to encompass new directions and thus augment the size of the reconstruction region to which EI-DBP applies. Additionally, we propose a Fourier domain filter for Mojette back-projection that is built from the discrete PSF of the given Mojette angle set and the autocorrelation function of the image domain. These discrete reconstruction methods are targeted for use with noisy sets of real projection data.

Original language	English
Title of host publication	2013 IEEE International Conference on Image Processing, ICIP 2013 - Proceedings
Subtitle of host publication	Melbourne, VIC; Australia; 15 September 2013 through 18 September 2013; Category number CFP13CIP-ART; Code 103050
Editors	David Taubman, Min Wu
Place of Publication	Piscataway NJ USA
Publisher	IEEE, Institute of Electrical and Electronics Engineers
Pages	1036-1040
Number of pages	5
ISBN (Print)	9781479923410
DOIs	https://doi.org/10.1109/ICIP.2013.6738214
Publication status	Published - 2013
Event	IEEE International Conference on Image Processing 2013 - Melbourne Convention and Exhibition Centre (MCEC), Melbourne, Australia Duration: 15 Sep 2013 → 18 Sep 2013 Conference number: 20th http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6726158 (IEEE Conference Proceedings)

Publication series

Name
ISSN (Print)	1522-4880
ISSN (Electronic)	2381-8549

Conference

Conference	IEEE International Conference on Image Processing 2013
Abbreviated title	ICIP 2013
Country	Australia
City	Melbourne
Period	15/09/13 → 18/09/13
Internet address	http://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=6726158 (IEEE Conference Proceedings)

Keywords

back-projection
discrete Radon transforms
discrete tomography
Mojette transforms
projection
reconstruction

Access to Document

10.1109/ICIP.2013.6738214

Link to publication in Scopus

Cite this

Svalbe, I., Kingston, A., Guédon, J., Normand, N., & Chandra, S. (2013). Direct inversion of Mojette projections. In D. Taubman, & M. Wu (Eds.), 2013 IEEE International Conference on Image Processing, ICIP 2013 - Proceedings: Melbourne, VIC; Australia; 15 September 2013 through 18 September 2013; Category number CFP13CIP-ART; Code 103050 (pp. 1036-1040). [6738214] IEEE, Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/ICIP.2013.6738214

Svalbe, Imants ; Kingston, Andrew ; Guédon, Jeanpierre ; Normand, Nicolas ; Chandra, Shekhar. / Direct inversion of Mojette projections. 2013 IEEE International Conference on Image Processing, ICIP 2013 - Proceedings: Melbourne, VIC; Australia; 15 September 2013 through 18 September 2013; Category number CFP13CIP-ART; Code 103050. editor / David Taubman ; Min Wu. Piscataway NJ USA : IEEE, Institute of Electrical and Electronics Engineers, 2013. pp. 1036-1040

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abstract = "We present algorithms to reconstruct images from minimal sets of discrete Mojette projections using direct back-projection (DBP) with various forms of correction. This paper extends previous work on discrete projection inversion by Servi{\`e}res et al [1, 2, 3]. The number of Mojette projections needed for exact inversion by DBP (EI-DBP) scales as O(N2). A new form of discrete interpolation is developed to expand the point spread function (PSF) of a minimal (Katz-sufficient) set of discrete projections to encompass new directions and thus augment the size of the reconstruction region to which EI-DBP applies. Additionally, we propose a Fourier domain filter for Mojette back-projection that is built from the discrete PSF of the given Mojette angle set and the autocorrelation function of the image domain. These discrete reconstruction methods are targeted for use with noisy sets of real projection data.",

keywords = "back-projection, discrete Radon transforms, discrete tomography, Mojette transforms, projection, reconstruction",

author = "Imants Svalbe and Andrew Kingston and Jeanpierre Gu{\'e}don and Nicolas Normand and Shekhar Chandra",

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Svalbe, I, Kingston, A, Guédon, J, Normand, N & Chandra, S 2013, Direct inversion of Mojette projections. in D Taubman & M Wu (eds), 2013 IEEE International Conference on Image Processing, ICIP 2013 - Proceedings: Melbourne, VIC; Australia; 15 September 2013 through 18 September 2013; Category number CFP13CIP-ART; Code 103050., 6738214, IEEE, Institute of Electrical and Electronics Engineers, Piscataway NJ USA, pp. 1036-1040, IEEE International Conference on Image Processing 2013, Melbourne, Australia, 15/09/13. https://doi.org/10.1109/ICIP.2013.6738214

Direct inversion of Mojette projections. / Svalbe, Imants; Kingston, Andrew; Guédon, Jeanpierre; Normand, Nicolas; Chandra, Shekhar.

2013 IEEE International Conference on Image Processing, ICIP 2013 - Proceedings: Melbourne, VIC; Australia; 15 September 2013 through 18 September 2013; Category number CFP13CIP-ART; Code 103050. ed. / David Taubman; Min Wu. Piscataway NJ USA : IEEE, Institute of Electrical and Electronics Engineers, 2013. p. 1036-1040 6738214.

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

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N2 - We present algorithms to reconstruct images from minimal sets of discrete Mojette projections using direct back-projection (DBP) with various forms of correction. This paper extends previous work on discrete projection inversion by Servières et al [1, 2, 3]. The number of Mojette projections needed for exact inversion by DBP (EI-DBP) scales as O(N2). A new form of discrete interpolation is developed to expand the point spread function (PSF) of a minimal (Katz-sufficient) set of discrete projections to encompass new directions and thus augment the size of the reconstruction region to which EI-DBP applies. Additionally, we propose a Fourier domain filter for Mojette back-projection that is built from the discrete PSF of the given Mojette angle set and the autocorrelation function of the image domain. These discrete reconstruction methods are targeted for use with noisy sets of real projection data.

AB - We present algorithms to reconstruct images from minimal sets of discrete Mojette projections using direct back-projection (DBP) with various forms of correction. This paper extends previous work on discrete projection inversion by Servières et al [1, 2, 3]. The number of Mojette projections needed for exact inversion by DBP (EI-DBP) scales as O(N2). A new form of discrete interpolation is developed to expand the point spread function (PSF) of a minimal (Katz-sufficient) set of discrete projections to encompass new directions and thus augment the size of the reconstruction region to which EI-DBP applies. Additionally, we propose a Fourier domain filter for Mojette back-projection that is built from the discrete PSF of the given Mojette angle set and the autocorrelation function of the image domain. These discrete reconstruction methods are targeted for use with noisy sets of real projection data.

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KW - discrete Radon transforms

KW - discrete tomography

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BT - 2013 IEEE International Conference on Image Processing, ICIP 2013 - Proceedings

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A2 - Wu, Min

PB - IEEE, Institute of Electrical and Electronics Engineers

CY - Piscataway NJ USA

T2 - IEEE International Conference on Image Processing 2013

Y2 - 15 September 2013 through 18 September 2013

ER -

Svalbe I, Kingston A, Guédon J, Normand N, Chandra S. Direct inversion of Mojette projections. In Taubman D, Wu M, editors, 2013 IEEE International Conference on Image Processing, ICIP 2013 - Proceedings: Melbourne, VIC; Australia; 15 September 2013 through 18 September 2013; Category number CFP13CIP-ART; Code 103050. Piscataway NJ USA: IEEE, Institute of Electrical and Electronics Engineers. 2013. p. 1036-1040. 6738214 https://doi.org/10.1109/ICIP.2013.6738214