PhD defense of Nicolas GINDRIER on 07/20/22

PhD defense of Nicolas GINDRIER from TIMC CAMI team on wednesday, the 20th of July, at 3:30pm or 4pm:

« Cone-beam reconstruction from projections with transverse truncation »

bullet Jury:

  • Emil Sidky, Professeur de l'université de Chicago, reporter
  • Voichita Maxim, Maîtresse de conférence, INSA Lyon, reporter
  • Charles Soussen, Professeur, Centrale-Supélec, examiner
  • Valérie Perrier, Professeure, Grenoble INP, examiner
  • Laurent Desbat, Professeur, Université Grenoble-Alpes, supervisor
  • Rolf Clackdoyle, Directeur de recherche, CNRS, co-supervisor


bullet  Key words:  

truncated data ; region of interest ; tomography ; DBP ; chord ; convex hull

bullet Abstract:

The first medical scanners were created about 50 years ago. They allow to reconstruct the image of a part of the body of a patient from its projections in X-rays. They are part of the field of medical tomography. This thesis deals with the image reconstruction problem from a mathematical and algorithmic point of view. More precisely, we are interested in the problem of truncated data, i.e. when some lines intersecting the object and the X-ray source are not measured. In this case, the known methods for image reconstruction are deficient. We first study in a non-exhaustive way the known 2D (chapter 1) and 3D (chapter 2) analytical reconstruction methods. A reconstruction cannot be stable if the object is outside the Tuy region, often corresponding to the convex hull of the X-ray source trajectory. It appears that the method most suitable for truncation, especially transverse, seems to be the DBP (Differentiated BackProjection) method. It requires the use of chords of the X-ray source trajectory. the X-ray source. This is why we start by studying the link between convex hull and set of chords of a trajectory (chapter 3),  with for one of the objectives the placement of regions of interest  for the purpose of using DBP method. We then study more particularly a precise class of trajectories, which we call the n-sin trajectories. In chapter 4, in a geometrical framework, we study in particular the union of the chords and the convex hull of these trajectories. Then, in chapter 5, we are interested in the use of the DBP for these trajectories. We give conditions for using DBP for an exact reconstruction from these trajectories for various truncation (this thesis deals in part with the little studied case of both axial and transverse truncation). In particular, the 2-sin trajectory is better suited to the DBP method than other n-sin trajectories. It turns out that even with transverse truncation and in chordless regions, reconstructions in the convex hull of the X-ray source trajectory seems sometimes possible, which is not discussed in the literature. We give the beginnings of an explanation. Other tracks (already known in the literature) are also evoked, as with the Katsevich method, effective Katsevich's method, which is efficient to treat the case of axial truncation even in chordless zones.