Biomedical subjects

Pierre Grangeat

Publications and source records attributed to Pierre Grangeat.

4 recordsLinked to original sources

PubMed2004

Exact reconstruction in 2D dynamic CT: compensation of time-dependent affine deformations.

This work is dedicated to the reduction of reconstruction artefacts due to motion occurring during the acquisition of computerized tomographic projections. This problem has to be solved when imaging moving organs such as the lungs or the heart. The proposed method belongs to the class of motion compensation algorithms, where the model of motion is included in the reconstruction formula. We address two fundamental questions. First what conditions on the deformation are required for the reconstruction of the object from projections acquired sequentially during the deformation, and second how do we reconstruct the object from those projections. Here we answer these questions in the particular case of 2D general time-dependent affine deformations, assuming the motion parameters are known. We treat the problem of admissibility conditions on the deformation in the parallel-beam and fan-beam cases. Then we propose exact reconstruction methods based on rebinning or sequential FBP formulae for each of these geometries and present reconstructed images obtained with the fan-beam algorithm on simulated data.

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PubMed2004

Sampling conditions of 3D parallel and fan-beam x-ray CT with application to helical tomography.

We give the sampling conditions of the 3D fan-beam x-ray transform (3DFBXRT). The motivation of this work lies in the fact that helical tomography with a single detector line is simply a sampling of this transform under the helical constraint. We give a precise description of the geometry of the essential support of the 3DFBXRT Fourier transform and show how to derive efficient sampling schemes. We then give efficient sampling schemes in parallel helical tomography. We present numerical experiments showing that efficient sampling on hexagonal interlaced schemes yields better reconstructions than the standard schemes in both parallel helical tomography (using QDO) and 3DFBXRT. We discuss the practical drawbacks and advantages of these efficient schemes and the possible extension to fan-beam helical CT.

Algorithms↗

PubMed2002

Theoretical framework for a dynamic cone-beam reconstruction algorithm based on a dynamic particle model.

Dynamic cone-beam reconstruction algorithms are required to reconstruct three-dimensional (3D) image sequences on dynamic 3D CT combining multi-row two-dimensional (2D) detectors and sub-second scanners. The speed-up of the rotating gantry allows one to improve the temporal resolution of the image sequence, but at the same time, it implies increase in the dose delivered during a given time period to keep constant the signal-to-noise ratio associated with each frame. The alternative solution proposed in this paper is to process data acquisition on several half-turns in order to reduce the dose delivered per rotation with the same signal-to-noise ratio. In order to compensate for time evolution and motion artefacts, we propose to use a dynamic particle model to describe the object evolution during the scan. In this article, we first introduce the dynamic particle model and the dynamic CT acquisition model. Then, we explain the principle of the proposed dynamic cone-beam reconstruction algorithm. Lastly, we present preliminary results on simulated data.

Algorithms↗

PubMed2002

Multichannel algorithm for fast 3D reconstruction.

Some recent medical imaging applications such as functional imaging (PET and SPECT) or interventional imaging (CT fluoroscopy) involve increasing amounts of data. In order to reduce the image reconstruction time, we develop a new fast 3D reconstruction algorithm based on a divide and conquer approach. The proposed multichannel algorithm performs an indirect frequential subband decomposition of the image f to be reconstructed (f = sigma fj) through the filtering of the projections Rf. The subband images fj are reconstructed on a downsampled grid without information suppression. In order to reduce the computation time, we do not backproject the null filtered projections and we downsample the number of projections according to the Shannon conditions associated with the subband image. Our algorithm is based on filtering and backprojection operators. Using the same algorithms for these basic operators, our approach is three and a half times faster than a classical FBP algorithm for a 2D image 512 x 512 and six times faster for a 3D image 32 x 512 x 512.

Algorithms↗