Laurent Desbat

Comparison of Analytic and Algebraic Methods for Motion-Compensated Cone-Beam CT Reconstruction of the Thorax

Respiratory motion is a major concern in cone-beam (CB) computed tomography (CT) of the thorax. It causes artifacts such as blur, streaks, and bands, in particular when using slow-rotating scanners mounted on the gantry of linear accelerators. In this paper, we compare two approaches for motion-compensated CBCT reconstruction of the thorax. The first one is analytic; it is heuristically adapted from the method of Feldkamp, Davis, and Kress (FDK). The second one is algebraic: the system of linear equations is generated using a new algorithm for the projection of deformable volumes and solved using the simultaneous algebraic reconstruction technique (SART). For both methods, we propose to estimate the motion on patient data using a previously acquired 4-D CT image. The methods were tested on two digital and one mechanical motion-controlled phantoms and on a patient dataset. Our results indicate that the two methods correct most motion artifacts. However, the analytic method does not fully correct streaks and bands even if the motion is perfectly estimated due to the underlying approximation. In contrast, the algebraic method allows us full correction of respiratory-induced artifacts.

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.

Conformal external radiotherapy of prostatic carcinoma: requirements and experimental results

The aim of conformal radiotherapy is to deliver, with high precision, a specific dose (which may be a high dose) to a planning target volume, concurrently with irradiating as little as possible healthy tissue and organs at risk. Radiation therapy may suffer from a number of problems that result in both over- or under-sizing the irradiation fields, making over-rough simplifications of the irradiation ballistics and delivering an insufficient tumoral dose (to spare critical organs and reduce toxicity). One of these problems lies in the accurate positioning of the planning target volume with respect to the irradiation system, thence in the correct execution of the ballistics. In this paper, we describe a system aiming at achieving a higher overall accuracy in the delivery of prostatic boost for carcinoma of the prostate. The system is based on the use of ultrasonic images for measuring the actual position of the prostate just before irradiation. Since these images are registered with pre-operative (CT or MR) images, the position and orientation of the planning target volume is computed with respect to the irradiation system, and can be corrected accordingly. First experiments have been performed on dummies, and the results are discussed.

Compensation of Some Time Dependent Deformations in Tomography

This work concerns 2D+t dynamic tomography. We show that a much larger class of deformations than the affine transforms can be compensated analytically within filtered back projection algorithms in 2D parallel beam and fan beam dynamic tomography. We present numerical experiments on the Shepp and Logan phantom showing that nonaffine deformations can be compensated. A generalization to 3D cone beam tomography is proposed

Attenuation correction in SPECT using consistency conditions for the exponential ray transform

Using data consistency conditions for the exponential ray transform, a method is derived to correct SPECT data for attenuation effects. No transmission measurements are required, and no operator-defined contours are needed. Furthermore, any 3D parallel-ray geometry can be considered for SPECT data acquisition, even unconventional geometries which do not lead to a set of 2D parallel-beam sinograms. The method is presented for both the 2D parallel-beam geometry and a particular 3D case, called the rotating slant hole geometry. Full details of the algorithms are given. Implementation has been carried out and results are presented in 2D and in 3D using simulated data.

Development and Validation of an X‐ray Tomograph for Two‐Phase Flow

Abstract: This paper describes the development and validation of a high spatial resolution X‐ray tomograph designed for the investigation of air‐water two‐phase flow. The device hardware mainly comprises a 60 keV X‐ray source, a detector, and an accurate mechanical bench. Our study concentrated on accurate quantification with emphasis on the reconstruction procedure. As is well known, absorption gradients induce reconstruction artifacts when using standard algorithms based on uniform regularization. In the particular case of two‐phase flow in a pipe, this leads to poor measurement accuracy in the vicinity of the walls. To overcome such effects, improved algorithms were developed during this study that involve spatially adaptive regularization methods. Preliminary calibration performed on static phantoms clearly exhibited the benefits of the advanced reconstruction algorithms. A validation procedure was carried out on an air‐water bubble column, equipped with an optical probe, which could be translated in order to explore the 80 mm × 80 mm square cross section. Comparisons of local void fraction measurements were performed pixel by pixel. They demonstrate the accuracy improvement induced by the advanced reconstruction algorithms.

Statistical model registration for a C-arm CT system

We discuss 3D bone surface reconstruction from a set of few digital X-ray projections acquired with a mobile C-arm system. We first show the C-arm calibration and the modeling of its mechanical deformation. Then a 3D shape reconstruction method based on elastic registration of a statistical model with a set of few projections (2 to 5) is discussed and applied to a lumbar vertebra.

Direct algebraic reconstruction and optimal sampling in vector field tomography

Vector field tomography has been proven to be a very powerful technique for the noninvasive determination of vector field distribution such as in the case of a fluid velocity field. We show that classical tomographic sampling conditions ran essentially be applied to vector field tomography. Thus, essentially the same sampling schemes are obtained, and the interlaced scheme is also shown to be the most efficient scheme in vector field tomography. We then propose a direct algebraic approach for vector field tomography, with an efficient and robust algorithm for interlaced schemes. Numerical experiments showing the superiority of interlaced schemes are provided. >

Data consistency conditions for truncated fanbeam and parallel projections

PURPOSE In image reconstruction from projections, data consistency conditions (DCCs) are mathematical relationships that express the overlap of information between ideal projections. DCCs have been incorporated in image reconstruction procedures for positron emission tomography, single photon emission computed tomography, and x-ray computed tomography (CT). Building on published fanbeam DCCs for nontruncated projections along a line, the authors recently announced new DCCs that can be applied to truncated parallel projections in classical (two-dimensional) image reconstruction. These DCCs take the form of polynomial expressions for a weighted backprojection of the projections. The purpose of this work was to present the new DCCs for truncated parallel projections, to extend these conditions to truncated fanbeam projections on a circular trajectory, to verify the conditions with numerical examples, and to present a model of how DCCs could be applied with a toy problem in patient motion estimation with truncated projections. METHODS A mathematical derivation of the new parallel DCCs was performed by substituting the underlying imaging equation into the mathematical expression for the weighted backprojection and demonstrating the resulting polynomial form. This DCC result was extended to fanbeam projections by a substitution of parallel to fanbeam variables. Ideal fanbeam projections of a simple mathematical phantom were simulated and the DCCs for these projections were evaluated by fitting polynomials to the weighted backprojection. For the motion estimation problem, a parametrized motion was simulated using a dynamic version of the mathematical phantom, and both noiseless and noisy fanbeam projections were simulated for a full circular trajectory. The fanbeam DCCs were applied to extract the motion parameters, which allowed the motion contamination to be removed from the projections. A reconstruction was performed from the corrected projections. RESULTS The mathematical derivation revealed the anticipated polynomial behavior. The conversion to fanbeam variables led to a straight-forward weighted fanbeam backprojection which yielded the same function and therefore the same polynomial behavior as occurred in the parallel case. Plots of the numerically calculated DCCs showed polynomial behavior visually indistinguishable from the fitted polynomials. For the motion estimation problem, the motion parameters were satisfactorily recovered and ten times more accurately for the noise-free case. The reconstructed images showed that only a faint trace of the motion blur was still visible after correction from the noisy motion-contaminated projections. CONCLUSIONS New DCCs have been established for fanbeam and parallel projections, and these conditions have been validated using numerical experiments with truncated projections. It has been shown how these DCCs could be applied to extract parameters of unwanted physical effects in tomographic imaging, even with truncated projections.

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.