On the V‐Line Radon Transform and Its Imaging Applications

Morvidone, Marcela; Nguyen, Maï K.; Truong, T.T.; Zaidi, Habib

doi:10.1155/2010/208179

Cited by 54 publications

(64 citation statements)

References 12 publications

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“…They rely on individual analytical relations between f (x, y) and its projections g(ξ, ω). Detailed implementations for FBP in the TV case can be found elsewhere [1,7,8]. …”

Section: Analytic Methodsmentioning

confidence: 99%

“…The Conical Radon Transform family is a mathematical model of this new principle for camera gamma imaging [1][2][3][4][5]. Image reconstruction from its projections is guaranteed since the Conical Radon Transforms are analytically invertible [6].…”

Section: Introductionmentioning

confidence: 99%

“…Some aspects of the bi-dimensional Conical Radon Transform (TV) have been already studied and both, analytical [1,7,8] and algebraic [9] inversion have been obtained. In particular, it was shown that the TV can be inverted by a filtered back-projection technique (FBP) completely adapted to the geometry of the problem.…”

Section: Introductionmentioning

confidence: 99%

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SVD inversion for the bi-dimensional Conical Radon Transform

Cebeiro

Morvidone

2013

J. Phys.: Conf. Ser.

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Abstract.In nuclear medicine, the Conical Radon Transforms family includes 2D and 3D models for scatter radiation imaging. The underlying idea is taking advantage of Comptom effect in order to provide image reconstruction without rotating the detector system. Several techniques currently applied for the classical Radon transform may also be useful in this new context. Nevertheless, since the physical model is rather different, it is necessary to assess the performance of each method. In previous works, we have studied inversion by filtered-backprojection and adaptive algebraic reconstruction techniques. In this paper we study the performance of a method based in the factorization of the projection matrix in order to invert the projections. Particularly, we test our algorithms on the bi-dimensional Conical Radon Transform, a simple member of the Conical Radon family. We obtain useful results on the performance of the three methods which should be valuable in the more realistic 3D context.

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“…They rely on individual analytical relations between f (x, y) and its projections g(ξ, ω). Detailed implementations for FBP in the TV case can be found elsewhere [1,7,8]. …”

Section: Analytic Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

SVD inversion for the bi-dimensional Conical Radon Transform

Cebeiro

Morvidone

2013

J. Phys.: Conf. Ser.

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“…Proof: See [22], [23]. An alternative inversion formula is based on the results of the classical Radon transform.…”

Section: Inversionsmentioning

confidence: 99%

Inversion of the V-line transform for breast cancer detection with Compton camera

Gouia‐Zarrad

2017

BIOMATH

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Abstract-In the recent past, Compton camera became an attractive alternative to the Anger camera in scintimammography, known as nuclear medicine breast imaging or molecular breast imaging. This novel imaging modality leads to the use of the V-line transform, which integrates a function along coupled rays with a common vertex. In previous works the attenuation phenomena was mostly neglected. However, in scintimammography ignoring the effect of the attenuation of photon can significantly degrade the quality of the reconstruction image. In this paper, we introduce the attenuated V-line transform and establish a new integral relation between the attenuated V-line transform and the exponential Radon transform. The results are not only interesting as original mathematical discoveries, but also can be useful in challenging applications e.g., in breast imaging for tumor detection close to the chest wall.Keywords-V-line transform; attenuated V-line transform; imaging of breast cancer; breast cancer detection; Compton camera.

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“…The crux of the matter is that one can show that from this data set, a three-dimensional object reconstruction is possible. Moreover, a two-dimensional version of this scattered radiation has been shown to be feasible in the last few years, referred to as V-line emission imaging (VEI) [9], [10]. Thus, it is tempting (and logical) to combine Compton scattering tomography with V-line emission imaging as the first bimodal scatter radiation imaging, which is the topic of this work.…”

Section: Introductionmentioning

confidence: 99%

Combined Modalities of Compton Scattering Tomography

Rigaud

Régnier

Nguyen

et al. 2013

IEEE Trans. Nucl. Sci.

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Abstract-The requirement to scope and analyze hidden parts of the human body and the limitations of current imaging technologies is motivating the development of novel approaches. In clinical PET/CT systems, the attenuation and activity maps of the studied body region are recovered from measurements. However, the modeling of Compton scattering enables to obtain the attenuation map through the electron density directly from transmission data, thus obviating the need of a CT scan. In this context, a bimodality imaging approach (gamma-ray transmission/emission imaging) using scattered radiation referred to as Compton scattering tomography (CST) is presented. This concept is modeled by two generalized Radon transforms and proposes to reconstruct the electron density, the attenuation map, and the activity concentration of the studied body region. Simulation results demonstrate the feasibility and viability of this novel imaging concept. The present approach could be an interesting alternative to current tomographic imaging techniques.

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On the V‐Line Radon Transform and Its Imaging Applications

Cited by 54 publications

References 12 publications

SVD inversion for the bi-dimensional Conical Radon Transform

SVD inversion for the bi-dimensional Conical Radon Transform

Inversion of the V-line transform for breast cancer detection with Compton camera

Combined Modalities of Compton Scattering Tomography

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