Mathematical framework of cone beam 3D reconstruction via the first derivative of the radon transform

Grangeat, Pierre

doi:10.1007/bfb0084509

Cited by 322 publications

(267 citation statements)

References 19 publications

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“…This data incompleteness can be viewed in terms of Radon space [5] or in terms of the local Fourier transform of a given image voxel. In the case of the SSCB acquisition, image artifacts arise from three major causes: missing frequencies, frequencies mishandled during the reconstruction, and axial truncation.…”

Section: Cone-beam Step-and-shoot Reconstructionmentioning

confidence: 99%

Recent Advances in CT Image Reconstruction

et al. 2013

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Over the past two decades, rapid system and hardware development of x-ray computed tomography (CT) technologies has been accompanied by equally exciting advances in image reconstruction algorithms. The algorithmic development can generally be classified into three major areas: analytical reconstruction, model-based iterative reconstruction, and application-specific reconstruction. Given the limited scope of this chapter, it is nearly impossible to cover every important development in this field; it is equally difficult to provide sufficient breadth and depth on each selected topic. As a compromise, we have decided, for a selected few topics, to provide sufficient high-level technical descriptions and to discuss their advantages and applications.

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Section: Cone-beam Step-and-shoot Reconstructionmentioning

confidence: 99%

Recent Advances in CT Image Reconstruction

et al. 2013

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“…If the acquisition rays were parallel, the sum of line values on the detector plane would coincide with the plane integral, a fundamental hypothesis which is of course violated in case of the cone-beam geometry. This difficulty has been overcome using the Grangeat's relation [14] which allows us to calculate the Radon data derivatives from raw cone-beam data. This approach avoids the whole integral calculation using the best possible estimation of this value, i.e., what is detected in the acquisition plane.…”

Section: Methodsmentioning

confidence: 99%

Multiresolution Reconstruction for Cone-Beam Tomography from Raw Data Projections Using 3D Ridgelets

2011

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This paper presents a novel method which reconstructs any desired 3D image resolution from raw cone-beam CT data. X-ray attenuation through the object is approximated using ridgelet basis functions which allow us to have multiresolution representation levels. Since the Radon data have preferential orientations by nature, a spherical wavelet transform is used to compute the ridgelet coefficients from the Radon shell data. The whole method uses the classical Grangeat's relation for computing derivatives of the Radon data which are then integrated and projected to a spherical wavelet representation and back-reconstructed using a modified version of the well known back-projection algorithm. Unlike previous reconstruction methods, this proposal uses a multiscale representation of the Radon data and therefore allows fast display of low-resolution data level.

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“…Details on the various methods can be found, e.g., in [7], [13], and [17]- [21]. All exact reconstruction methods known to the authors are based on the Radon inversion [22] (10) with (11) A fundamental problem is that the required Radon values cannot be extracted from the measured data directly.…”

Section: Review On Exact Reconstruction Methodsmentioning

confidence: 99%

The n-PI-method for helical cone-beam CT

Proksa

Köhler²,

Graß³

et al. 2000

IEEE Trans. Med. Imaging

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Abstract-A new class of acquisition schemes for helical cone-beam computed tomography (CB-CT) scanning is introduced, and their effect on the reconstruction methods is analyzed. These acquisition schemes are based on a new detector shape that is bounded by the helix. It will be shown that the data acquired with these schemes are compatible with exact reconstruction methods, and the adaptation of exact reconstruction algorithms to the new acquisition geometry is described. At the same time, the so-called PI-sufficiency condition is fulfilled. Moreover, a good fit to the acquisition requirements of the various medical applications of cone-beam CT is achieved. In contrast to other helical cone-beam acquisition and reconstruction methods, the -PI-method introduced in this publication allows for variable pitches of the acquisition helix. This additional feature will introduce a higher flexibility into the acquisition protocols of future medical cone-beam scanners. An approximative -PI-filtered backprojection ( -PI-FBP) reconstruction method is presented and verified. It yields convincing image quality.Index Terms-Exact reconstruction, helical cone-beam computed tomography, PI-method, Radon-inversion.

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Mathematical framework of cone beam 3D reconstruction via the first derivative of the radon transform

Cited by 322 publications

References 19 publications

Recent Advances in CT Image Reconstruction

Recent Advances in CT Image Reconstruction

Multiresolution Reconstruction for Cone-Beam Tomography from Raw Data Projections Using 3D Ridgelets

The n-PI-method for helical cone-beam CT

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