EP-4740182-A1 - METHOD FOR RECONSTRUCTING AN OBJECT BY X-RAY TOMOGRAPHY, COMPRISING A CALCULATION OF REGULARIZATION TERMS

Abstract

The invention relates to a method for reconstructing an object by x-ray tomography by means of x-ray sources and detectors. The method comprises the following steps: obtaining (EO) positions of the x-ray sources and detectors; pre-calculating (E1) a set of directions; calculating (E2) a tomographic incompleteness vector map; calculating (E3) a tomographic incompleteness map of the metrics IM(x); calculating (E4) regularization terms from the tomographic incompleteness vector map and from the tomographic incompleteness map of the metrics; and solving (E5), iteratively, a regularized tomographic reconstruction problem by means of the calculated regularization terms.

Inventors

• LAURENDEAU, Matthieu
• JOLIVET, Frédéric
• Gorges, Sébastien
• BERNARD, GUILLAUME
• RIT, Simon
• DESBAT, LAURENT

Assignees

• THALES
• Université Jean Monnet Saint-Étienne
• UNIVERSITE CLAUDE BERNARD - LYON 1
• UNIVERSITE GRENOBLE ALPES
• Institut National Polytechnique de Grenoble
• Centre National de la Recherche Scientifique
• Institut National Des Sciences Appliquées De Lyon
• Institut National de la Santé et de la Recherche Médicale

Dates

Publication Date

20260513

Application Date

20240704

Claims (1)

1. CLAIMS 1. Method for reconstructing an object by X-ray tomography using X-ray sources ^" ; , " 9 , … , " @ ^ and detectors ^A ; , A 9 , … , A @ ^, said object belonging to an imaged space (Ω) defined by a set of voxels, said method comprising the following steps: - obtaining (E0) the positions of the X-ray sources and detectors; - pre-calculating (E1) a set of directions; - calculating (E2) a vector map of tomographic incompleteness comprising for each voxel a vector in a direction ^ ∗ among said set of directions; - calculating (E3) a tomographic incompleteness map of the metrics ^0^^^ defining for each voxel a loss of information in the direction ^ ∗; - calculating (E4) regularization terms from the vector map of incompleteness tomographic and the tomographic incompleteness map of the metrics; and - resolution (E5), iteratively, of a regularized tomographic reconstruction problem using the calculated regularization terms. 2. Reconstruction method according to claim 1, in which the calculation (E2) of the tomographic incompleteness vector map comprises for each voxel of the imaged space ^Ω) the sub-steps of: - selection (E21) from among said sources ^" ; , " 9 , … , " @ ^ of a source for each direction from among said set of directions; and - choice (E22) for each selected source of the direction ^ ∗, the loss of information defined by the tomographic incompleteness map of the metrics ^0^^^ corresponding to the loss of information according to the chosen direction ^ ∗ by said detector associated with said selected source. 3. Reconstruction method according to claim 2, in which the calculation step (E2) of the tomographic incompleteness vector map comprises a preliminary selection sub-step (E20), among said sources ^" ; , " 9 , … , " @ ^, sources projecting the voxel of the object onto their associated detectors, the source being selected among the sources projecting the voxel of the object onto their associated detectors ^A ; , A 9 , … , A @ ^. 4. Reconstruction method according to claim 2 or claim 3, in which the selection (E21) of said source is carried out by calculating a directional local tomographic incompleteness ^^^, ^^ ∈ ℝ ^ according to the expression ∈ ℝ ! , is the projection of a source " ^ onto the plane defined by the point ^ of the voxel and the normal direction ^. 5. A reconstruction method according to claim 4, wherein said chosen direction is chosen as a function of the directional local tomographic incompleteness ^ ^ ^, ^ ^ . 6. A reconstruction method according to claim 4 or claim 5, wherein said chosen direction ^ ∗ is chosen from the calculation of a norm of several directions (v1, …., vn) for which the directional local tomographic incompleteness ^ ^ ^, ^ ^ is calculated. 7. A reconstruction method according to claim 6, wherein said norm is the Lp norm for p ∈ [1 ;+∞], p preferably being equal to +∞. 8. A reconstruction method according to claim 4 or claim 5, wherein said chosen direction ^ ∗ is chosen from the calculation of a weighted average of several directions (v1, …., vn) for which the directional local tomographic incompleteness ^ ^ ^, ^ ^ is calculated. 9. Reconstruction method according to one of claims 1 to 8, in which the regularization terms are calculated for a following regularization function ‖%‖ &é()*+,-*. : where ^u 8 ^ 1,2,3 correspond to the finite differences in different directions, j, k, l corresponding to the indexing for each voxel, and d to the direction of the finite difference. 10. A reconstruction method according to claim 9, in which the regularization function ‖%‖ &é()*+,-*. is of the directional total variation type.

Description

DESCRIPTION Title of the invention: Method for reconstructing an object by X-ray tomography comprising a calculation of regularization terms. [0001] The invention falls within the field of X-ray imaging, and more particularly in the field of X-ray tomographic reconstruction. It relates to a method for reconstructing an object by X-ray tomography comprising a calculation of regularization terms. [0002] The invention finds its application in the field of security, in particular for baggage searches taking place in sensitive sites (airports, train stations, etc.), during events or on any occasion of baggage inspection. It also finds its application in the medical field, for example when using X-ray medical imaging equipment. More generally, the invention finds its application when it is desired to reconstruct an object by tomography. [0003] X-ray tomography provides a two-dimensional or three-dimensional image from a series of tomographic projections via a reconstruction algorithm. The reconstruction algorithms used in tomography have weaknesses when the measured data are highly noisy and/or missing. The reconstruction algorithm then faces the lack of data and can then lead to very inconsistent solutions. [0004] In order to be able to reconstruct an object, the reconstruction algorithm then requires introducing, in addition to input data, a priori on the object to be reconstructed. The a priori on the object are introduced via a regularization thus giving rise to a regularized reconstruction algorithm. [0005] Regularized reconstruction algorithms thus solve an inverse problem from the projection data. This family of algorithms requires adjusting regularization terms. These regularization terms aim to provide a compromise between the data information and the a priori on the object to be reconstructed. Regularization allows to introduce an a priori on the statistical distribution of the imaged object and/or take into account the acquisition geometry. This regularization depends on parameters called here hyper-parameters. The hyper-parameters are calculated before the object reconstruction process, as detailed later. [0006] Most of the time, regularization terms are constructed to limit the number of hyperparameters to be tuned. Indeed, the greater the number of hyperparameters, the more difficult it is to tune them manually. [0007] To automatically tune hyperparameters, some approaches rely on cross-validation methods [Kohavi, 1995], or more recently on machine learning methods [Shen, 2018], [Ding, 2021]. In 2021, work [Zhang, 2021] showed that a Directional Total Variation type regularization is well suited for limited angle reconstruction problems. However, this regularization requires tuning more hyperparameters than a conventional Total Variation [Rudin, 1992]. [0008] The methods currently used to adjust the regularization terms require having reference images, and/or having a large number of diversified data. While it is possible to obtain the reference images by simulations, these methods remain difficult to obtain under experimental conditions. [0009] Furthermore, ideally, the choice of the regularization terms should integrate the geometry of the scanner, i.e. the position of the source(s) and the detector(s). [0010] The 3D theory of computer-assisted tomography has some tools to provide local information of the object to be reconstructed according to the geometry of the scanner. Assuming non-truncated projections, [Tuy, 1983] gives a condition to check whether a continuous trajectory of X-ray sources is sufficient to reconstruct the object. The condition can be written as follows: "each plane that intersects the imaged object must intersect the source trajectory at least once". In practice, all scanners are limited by a finite number of source positions and therefore the Tuy condition is never met. We speak of tomographic incompleteness when the Tuy condition is not met. [0011] Figure 1 shows examples of source-detector trajectories T of a scanner used for the reconstruction of an object. Example a) shows a circular source-detector trajectory. Such a trajectory does not allow an exact reconstruction of the object outside the plane of the trajectory. Indeed, a plane intersecting the object and which is parallel for example to the circle of the trajectory T does not intersect said source-detector trajectory. A helical geometry of the trajectory T, as shown in example b), allows for an exact reconstruction to be obtained. Indeed, whatever the plane taken, it necessarily cuts the helix of the trajectory T. [0012] Several measures have been studied to quantify the impact of tomographic incompleteness. [Metzler, Bowsher, & Jaszczak, 2003], [Lin & Meikle, 2010] and [Liu, et al., 2012] numerically evaluate the percentage of planes that are cut by the source trajectory by sampling the unit sphere. However, this type of measurement is only possible for a continuous source trajectory. However, in practice, acqui