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Papers by Nicolas Gindrier

Research paper thumbnail of CB reconstruction for the 3-sin trajectory with transverse truncation

HAL (Le Centre pour la Communication Scientifique Directe), Jul 19, 2021

In cone-beam tomography Differentiated BackProjection method (DBP) is a suitable approach for ima... more In cone-beam tomography Differentiated BackProjection method (DBP) is a suitable approach for image reconstruction from truncated projections. However, the reconstruction of a point with this method is possible only if the point lies on a chord connecting two source positions of the x-ray source trajectory. Using an approach initially proposed for the reverse helix with axial truncation, we present a configuration and its associated (theoretical) reconstruction method to deal with points which do not lie on any chord of the 3-sin trajectory (sine on a cylinder of period 2π/3) and with transversely truncated projections.

Research paper thumbnail of Cone-beam reconstruction from n-sin trajectories with transversely-truncated projections

HAL (Le Centre pour la Communication Scientifique Directe), Aug 3, 2020

In cone-beam tomography, we define the n-sin source trajectory as having n periods of a sinusoid ... more In cone-beam tomography, we define the n-sin source trajectory as having n periods of a sinusoid traced on an imaginary cylinder enclosing the object. A 2-sin is commonly known as a saddle, and it is known that the convex hull of a saddle is the same as the union of all of its chords. The convex hull of a closed trajectory is the Tuy region, where cone-beam reconstruction is possible if there are no truncated projections. However, with truncated projections, the method of differentiated backprojection and Hilbert inversion can be applied along a chord if the chord is visible (not truncated) in the projections. Here, we consider a particular transaxial truncation which prevents chords from always being visible, but we establish that the more powerful method of M-lines can be applied to ensure reconstruction in the reduced field-of-view. The 3-sin, on the other hand, has a Tuy region which is not filled by its chords, and we do not have any cone-beam theory to determine if reconstruction is possible with transverse reconstruction. In our preliminary numerical experiment, the 3-sin seemed to perform equally well as the 2-sin trajectory even though there were no chords passing through the slice we examined. We tentatively suggest that there might be other, yet unknown theory that explains why 3-sin reconstruction is possible with the specified transaxial truncation. We believe that these results on transverse truncation and reconstruction from 2-sin and 3-sin trajectories are new.

Research paper thumbnail of Sufficient Field of View for the M-line Method in Cone-beam CT

This work concerns region-of-interest reconstruction in cone-beam CT with transverse and axial tr... more This work concerns region-of-interest reconstruction in cone-beam CT with transverse and axial truncation. We study two cylindrical fields of view configurations with a saddle X-ray source trajectory. We give sufficient conditions for accurate image reconstruction with the M-line method.

Research paper thumbnail of CB reconstruction for the 3-sin trajectory with transverse truncation

Le Centre pour la Communication Scientifique Directe - HAL - Inria, Jul 19, 2021

In cone-beam tomography Differentiated BackProjection method (DBP) is a suitable approach for ima... more In cone-beam tomography Differentiated BackProjection method (DBP) is a suitable approach for image reconstruction from truncated projections. However, the reconstruction of a point with this method is possible only if the point lies on a chord connecting two source positions of the x-ray source trajectory. Using an approach initially proposed for the reverse helix with axial truncation, we present a configuration and its associated (theoretical) reconstruction method to deal with points which do not lie on any chord of the 3-sin trajectory (sine on a cylinder of period 2π/3) and with transversely truncated projections.

Research paper thumbnail of Cone-beam reconstruction from n-sin trajectorieswith transversely-truncated projections

In cone-beam tomography, we define the n-sin source trajectory as having n periods of a sinusoid ... more In cone-beam tomography, we define the n-sin source trajectory as having n periods of a sinusoid traced on an imaginary cylinder enclosing the object. A 2-sin is commonly known as a saddle, and it is known that the convex hull of a saddle is the same as the union of all of its chords. The convex hull of a closed trajectory is the Tuy region, where cone-beam reconstructionis possible if there are no truncated projections. However, with truncated projections, the method of differentiated backprojection and Hilbert inversion can be applied along a chord if the chordis visible (not truncated) in the projections. Here, we consider a particular transaxial truncation which prevents chords from always being visible, but we establish that the more powerful method of M-lines can be applied to ensure reconstruction in the reduced field-of-view. The 3-sin, on the other hand, has a Tuy region which is not filled by its chords, and we do not have any cone-beam theory to determine if reconstructio...

Research paper thumbnail of Sufficient Field of View for the M-line Method in Cone-beam CT

2020 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC)

This work concerns region-of-interest reconstruction in cone-beam CT with transverse and axial tr... more This work concerns region-of-interest reconstruction in cone-beam CT with transverse and axial truncation. We study two cylindrical fields of view configurations with a saddle X-ray source trajectory. We give sufficient conditions for accurate image reconstruction with the M-line method.

Research paper thumbnail of CB reconstruction for the 3-sin trajectory with transverse truncation

HAL (Le Centre pour la Communication Scientifique Directe), Jul 19, 2021

In cone-beam tomography Differentiated BackProjection method (DBP) is a suitable approach for ima... more In cone-beam tomography Differentiated BackProjection method (DBP) is a suitable approach for image reconstruction from truncated projections. However, the reconstruction of a point with this method is possible only if the point lies on a chord connecting two source positions of the x-ray source trajectory. Using an approach initially proposed for the reverse helix with axial truncation, we present a configuration and its associated (theoretical) reconstruction method to deal with points which do not lie on any chord of the 3-sin trajectory (sine on a cylinder of period 2π/3) and with transversely truncated projections.

Research paper thumbnail of Cone-beam reconstruction from n-sin trajectories with transversely-truncated projections

HAL (Le Centre pour la Communication Scientifique Directe), Aug 3, 2020

In cone-beam tomography, we define the n-sin source trajectory as having n periods of a sinusoid ... more In cone-beam tomography, we define the n-sin source trajectory as having n periods of a sinusoid traced on an imaginary cylinder enclosing the object. A 2-sin is commonly known as a saddle, and it is known that the convex hull of a saddle is the same as the union of all of its chords. The convex hull of a closed trajectory is the Tuy region, where cone-beam reconstruction is possible if there are no truncated projections. However, with truncated projections, the method of differentiated backprojection and Hilbert inversion can be applied along a chord if the chord is visible (not truncated) in the projections. Here, we consider a particular transaxial truncation which prevents chords from always being visible, but we establish that the more powerful method of M-lines can be applied to ensure reconstruction in the reduced field-of-view. The 3-sin, on the other hand, has a Tuy region which is not filled by its chords, and we do not have any cone-beam theory to determine if reconstruction is possible with transverse reconstruction. In our preliminary numerical experiment, the 3-sin seemed to perform equally well as the 2-sin trajectory even though there were no chords passing through the slice we examined. We tentatively suggest that there might be other, yet unknown theory that explains why 3-sin reconstruction is possible with the specified transaxial truncation. We believe that these results on transverse truncation and reconstruction from 2-sin and 3-sin trajectories are new.

Research paper thumbnail of Sufficient Field of View for the M-line Method in Cone-beam CT

This work concerns region-of-interest reconstruction in cone-beam CT with transverse and axial tr... more This work concerns region-of-interest reconstruction in cone-beam CT with transverse and axial truncation. We study two cylindrical fields of view configurations with a saddle X-ray source trajectory. We give sufficient conditions for accurate image reconstruction with the M-line method.

Research paper thumbnail of CB reconstruction for the 3-sin trajectory with transverse truncation

Le Centre pour la Communication Scientifique Directe - HAL - Inria, Jul 19, 2021

In cone-beam tomography Differentiated BackProjection method (DBP) is a suitable approach for ima... more In cone-beam tomography Differentiated BackProjection method (DBP) is a suitable approach for image reconstruction from truncated projections. However, the reconstruction of a point with this method is possible only if the point lies on a chord connecting two source positions of the x-ray source trajectory. Using an approach initially proposed for the reverse helix with axial truncation, we present a configuration and its associated (theoretical) reconstruction method to deal with points which do not lie on any chord of the 3-sin trajectory (sine on a cylinder of period 2π/3) and with transversely truncated projections.

Research paper thumbnail of Cone-beam reconstruction from n-sin trajectorieswith transversely-truncated projections

In cone-beam tomography, we define the n-sin source trajectory as having n periods of a sinusoid ... more In cone-beam tomography, we define the n-sin source trajectory as having n periods of a sinusoid traced on an imaginary cylinder enclosing the object. A 2-sin is commonly known as a saddle, and it is known that the convex hull of a saddle is the same as the union of all of its chords. The convex hull of a closed trajectory is the Tuy region, where cone-beam reconstructionis possible if there are no truncated projections. However, with truncated projections, the method of differentiated backprojection and Hilbert inversion can be applied along a chord if the chordis visible (not truncated) in the projections. Here, we consider a particular transaxial truncation which prevents chords from always being visible, but we establish that the more powerful method of M-lines can be applied to ensure reconstruction in the reduced field-of-view. The 3-sin, on the other hand, has a Tuy region which is not filled by its chords, and we do not have any cone-beam theory to determine if reconstructio...

Research paper thumbnail of Sufficient Field of View for the M-line Method in Cone-beam CT

2020 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC)

This work concerns region-of-interest reconstruction in cone-beam CT with transverse and axial tr... more This work concerns region-of-interest reconstruction in cone-beam CT with transverse and axial truncation. We study two cylindrical fields of view configurations with a saddle X-ray source trajectory. We give sufficient conditions for accurate image reconstruction with the M-line method.