Inversion of a new circular-arc Radon transform for Compton scattering tomography

Nguyen, Maï K.; Truong, T.T.

doi:10.1088/0266-5611/26/6/065005

Cited by 54 publications

(73 citation statements)

References 43 publications

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“…With a polar coordinate system centered at O, the equation of a circular arc lying inside a circle of center O and radius p reads (see [42])…”

Section: Internal Scanningmentioning

confidence: 99%

“…has not yet been considered in [42]. Similarly the Radon transform of the electron density on this arc of circle is now expressed by the following Chebyshev integral transform for its angular components…”

Section: External Scanningmentioning

confidence: 99%

“…[2], [4], [11], [18], [5], [22], [29], [1], [23]. The aim of this chapter is to recount the past episodes of research, to give a comprehensive account of what has been accomplished in CST and to describe some new ideas which have arisen recently, see [42,54]. The emphasis of the discussion shall be placed at the theoretical level.…”

Section: Introductionmentioning

confidence: 99%

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Recent Developments on Compton Scatter Tomography: Theory and Numerical Simulations

Truong¹,

Nguyen²

2012

Numerical Simulation - From Theory to Industry

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“…With a polar coordinate system centered at O, the equation of a circular arc lying inside a circle of center O and radius p reads (see [42])…”

Section: Internal Scanningmentioning

confidence: 99%

Section: External Scanningmentioning

confidence: 99%

See 1 more Smart Citation

Recent Developments on Compton Scatter Tomography: Theory and Numerical Simulations

Truong¹,

Nguyen²

2012

Numerical Simulation - From Theory to Industry

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“…In modality 1, the circular arcs C 1 DUH LQVLGH ī p , and the segment SD LV D URWDWLQJ GLDPHWHU RI ī p [4]. Thus the radiation source and the detector move rigidly around the apparatus center O.…”

Section: Compton Scatter Tomographymentioning

confidence: 99%

“…Then (3,4) are rewritten as (8) which has the form of the Chebyshev transform in [6]. Here ı IRU PRGDOLW\ 7KDQNV WR WKH NH\ IRUPXOD > @ (9) the inversion of (8) can be achieved by a clever application of (9).…”

Section: Chebyshev Integral Transformsmentioning

confidence: 99%

The integral equations of Compton Scatter Tomography

Nguyen¹

2012

OJAppS

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-Two new Compton Scatter Tomography modalities, which are aimed at imaging hidden structures in bulk matter for industrial non-destructive control (or testing) and for medical diagnostics are shown to be based on the solutions of a special class of Chebyshev integral transforms. Besides their remarkable analytic properties, they can be inverted by existing methods which lend themselves nicely to numerical treatment and provide convergent, stable and fast computation algorithms. The existence of explicit inversion formulas implies that viable new imaging techniques can be developed, which may take over the current ones in a near future.

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Feasibility analysis on simultaneous electron density and attenuation coefficient reconstruction

2021

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Creating a viable reconstruction method for Compton scatter tomography remains challenging. Accounting for scatter attenuation when the underlying attenuation map is not known is particularly challenging, and current mathematical approaches to this vary widely. This work explores a novel approach to joint scatter and attenuation image reconstruction, which leverages the underlying structural similarity between the two images and incorporates a deep learning model in an alternating iterative reconstruction scheme. Methods: A single-view computed tomography (CT) imaging procedure for recording Compton scatter is first described. A joint reconstruction model, which iterates between algebraically reconstructing scatter images and estimating the attenuation via deep learning, is then proposed. This model is tested on both a generated dataset of 2D phantom images designed to mimic human tissues as well as a realistically simulated dataset based on real CT images. Results: Testing results yield convergence of the model and decent reconstruction quality to distinguish crucial features such as tumors and lesions, demonstrating the potential principled utilities of this configuration and deep learning approach. The model achieved a structural similarity index measure of at least 0.82 for scatter and 0.88 for attenuation reconstructions with the realistically simulated dataset. Conclusion:The iterative, deep learning approach outlined in this work shows potential for future efficient medical imaging procedures, reconstructing images with limited scatter information.

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Inversion of a new circular-arc Radon transform for Compton scattering tomography

Cited by 54 publications

References 43 publications

Recent Developments on Compton Scatter Tomography: Theory and Numerical Simulations

Recent Developments on Compton Scatter Tomography: Theory and Numerical Simulations

The integral equations of Compton Scatter Tomography

Feasibility analysis on simultaneous electron density and attenuation coefficient reconstruction

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