A comparison of some methods for direct 2D reconstruction from discrete projected views

Preeti Gopal; Ajit Rajwade; Sharat Chandran; Imants Svalbe

doi:10.1007/978-3-319-32360-2_9

A comparison of some methods for direct 2D reconstruction from discrete projected views

Preeti Gopal, Ajit Rajwade, Sharat Chandran, Imants Svalbe

School of Physics and Astronomy

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

Abstract

Tomographic acquisitions can be described mathematically as discrete projective transforms. Direct reconstruction methods aim to compute an accurate inverse for such transforms. We assemble a limited set of measurements and then apply the inversion to obtain a high-fidelity image of the original object. In this work, we compare the following direct inversion techniques for sets of discrete projections: Radon-i(inverse)Radon, a least squared error method and filtered back-projection for Mojette inversion. We observe that filtered back-projection is the best of these methods, as the reconstruction errors that arise using this method depend least strongly on the image structure. We aim to improve results for the filtered back-projection method by optimizing the design of the regularizing filter and here present work towards eliminating the regularization threshold that is used as part of this method.

Original language	English
Title of host publication	Discrete Geometry for Computer Imagery
Subtitle of host publication	19th IAPR International Conference, DGCI 2016, Nantes, France, April 18–20, 2016, Proceedings
Editors	Nicolas Normand, Jeanpierre Guédon, Florent Autrusseau
Publisher	Springer
Pages	117-128
Number of pages	12
ISBN (Electronic)	9783319323602
ISBN (Print)	9783319323596
DOIs	https://doi.org/10.1007/978-3-319-32360-2_9
Publication status	Published - 1 Jan 2016
Event	International Conference on Discrete Geometry for Computer Imagery 2016 - La Cité Nantes Events Center, Nantes, France Duration: 18 Apr 2016 → 20 Apr 2016 Conference number: 19th https://link.springer.com/book/10.1007/978-3-319-32360-2 (Proceedings)

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	9647
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	International Conference on Discrete Geometry for Computer Imagery 2016
Abbreviated title	DGCI 2016
Country/Territory	France
City	Nantes
Period	18/04/16 → 20/04/16
Other	Discrete Geometry for Computer Imagery 19th IAPR International Conference, DGCI 2016, Nantes, France, April 18-20, 2016. Proceedings
Internet address	https://link.springer.com/book/10.1007/978-3-319-32360-2 (Proceedings)

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10.1007/978-3-319-32360-2_9

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Gopal, P., Rajwade, A., Chandran, S., & Svalbe, I. (2016). A comparison of some methods for direct 2D reconstruction from discrete projected views. In N. Normand, J. Guédon, & F. Autrusseau (Eds.), Discrete Geometry for Computer Imagery: 19th IAPR International Conference, DGCI 2016, Nantes, France, April 18–20, 2016, Proceedings (pp. 117-128). (Lecture Notes in Computer Science; Vol. 9647). Springer. https://doi.org/10.1007/978-3-319-32360-2_9

Gopal, Preeti ; Rajwade, Ajit ; Chandran, Sharat et al. / A comparison of some methods for direct 2D reconstruction from discrete projected views. Discrete Geometry for Computer Imagery: 19th IAPR International Conference, DGCI 2016, Nantes, France, April 18–20, 2016, Proceedings. editor / Nicolas Normand ; Jeanpierre Guédon ; Florent Autrusseau. Springer, 2016. pp. 117-128 (Lecture Notes in Computer Science).

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title = "A comparison of some methods for direct 2D reconstruction from discrete projected views",

abstract = "Tomographic acquisitions can be described mathematically as discrete projective transforms. Direct reconstruction methods aim to compute an accurate inverse for such transforms. We assemble a limited set of measurements and then apply the inversion to obtain a high-fidelity image of the original object. In this work, we compare the following direct inversion techniques for sets of discrete projections: Radon-i(inverse)Radon, a least squared error method and filtered back-projection for Mojette inversion. We observe that filtered back-projection is the best of these methods, as the reconstruction errors that arise using this method depend least strongly on the image structure. We aim to improve results for the filtered back-projection method by optimizing the design of the regularizing filter and here present work towards eliminating the regularization threshold that is used as part of this method.",

author = "Preeti Gopal and Ajit Rajwade and Sharat Chandran and Imants Svalbe",

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booktitle = "Discrete Geometry for Computer Imagery",

note = "International Conference on Discrete Geometry for Computer Imagery 2016, DGCI 2016 ; Conference date: 18-04-2016 Through 20-04-2016",

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Gopal, P, Rajwade, A, Chandran, S & Svalbe, I 2016, A comparison of some methods for direct 2D reconstruction from discrete projected views. in N Normand, J Guédon & F Autrusseau (eds), Discrete Geometry for Computer Imagery: 19th IAPR International Conference, DGCI 2016, Nantes, France, April 18–20, 2016, Proceedings. Lecture Notes in Computer Science, vol. 9647, Springer, pp. 117-128, International Conference on Discrete Geometry for Computer Imagery 2016, Nantes, France, 18/04/16. https://doi.org/10.1007/978-3-319-32360-2_9

A comparison of some methods for direct 2D reconstruction from discrete projected views. / Gopal, Preeti; Rajwade, Ajit; Chandran, Sharat et al.

Discrete Geometry for Computer Imagery: 19th IAPR International Conference, DGCI 2016, Nantes, France, April 18–20, 2016, Proceedings. ed. / Nicolas Normand; Jeanpierre Guédon; Florent Autrusseau. Springer, 2016. p. 117-128 (Lecture Notes in Computer Science; Vol. 9647).

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

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AB - Tomographic acquisitions can be described mathematically as discrete projective transforms. Direct reconstruction methods aim to compute an accurate inverse for such transforms. We assemble a limited set of measurements and then apply the inversion to obtain a high-fidelity image of the original object. In this work, we compare the following direct inversion techniques for sets of discrete projections: Radon-i(inverse)Radon, a least squared error method and filtered back-projection for Mojette inversion. We observe that filtered back-projection is the best of these methods, as the reconstruction errors that arise using this method depend least strongly on the image structure. We aim to improve results for the filtered back-projection method by optimizing the design of the regularizing filter and here present work towards eliminating the regularization threshold that is used as part of this method.

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Gopal P, Rajwade A, Chandran S, Svalbe I. A comparison of some methods for direct 2D reconstruction from discrete projected views. In Normand N, Guédon J, Autrusseau F, editors, Discrete Geometry for Computer Imagery: 19th IAPR International Conference, DGCI 2016, Nantes, France, April 18–20, 2016, Proceedings. Springer. 2016. p. 117-128. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-319-32360-2_9

A comparison of some methods for direct 2D reconstruction from discrete projected views

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