**Numerical
Modeling and Simulation of Inverse Problems in Medical Imaging**

**Part
of DROITE ANR project
**

**and
ARC6 **"Modélisation
et Simulation Numérique de Problèmes Inverses en Imagerie Médicale"

supported by the labex CAMI, PRIMES, PERSYVAL and the ECCAMI project.

**25/02/2014
and 26/02/2014 **

**Amphithéâtre Emilie du Chatelet **
**bibliothèque Marie Curie, INSA de Lyon**

**Registration
is free but mandatory / Inscription gratuite mais obligatoire **

**Participant
list**

**Program**

**Tuesday
25/02/2014**

**14h00
– 18h00**

14h00- 14h30
*
Data Consistency Conditions: Fanbeam Projections and Circular Trajectory .*

Rolf Clackdoyle, UJM, Saint Etienne

For fanbeam projections, the use of data consistency conditions (DCC) generally requires a full tomographic dataset (such as a 360-degree scan or at least a classical "shortscan") so that the projections can be rebinned either physically or mathematically into parallel projections. Data consistency can be conveniently applied to parallel projections using the well-known Helgason Ludwig conditions. Here we discuss the question of data consistency conditions for a circular trajectory, where we would like to check consistency between small subsets of fanbeam projections. A simple scheme for pairwise DCC of fanbeam projections is possible, which we illustrate with a simulation example. The pairwise DCC has the interesting property that rigid motion in the direction of the line joining the two sources results in _consistent_ data. This property has both disadvantages and advantages for motion detection.

14h45- 15h15
*On
two problems in cone beam computed tomography: Truncation and Motion
in FBP and BPF reconstruction methods.*

Dirk Schaefer, Philips Research, Hamburg, Germany

Cone beam computed tomography (CBCT) with flat detectors is used in C-arm imaging or with off-center geometry in SPECT-CT and radiotherapy systems. The data acquisition of these systems is slow compared to diagnostic CT, and their detectors are typically small such that the projections are truncated. Back-projection filtration (BPF) has only the short range derivative filter on the projections and may therefore better cope with motion corrupted and/or truncated scans compared to filtered back projection (FBP). Advantages and shortcomings of the methods are demonstrated on simulated and clinical data.

15h30 - 16h30
* Stability estimates for the inversion of the truncated Hilbert transform. *

Michel Defrise, VUB, Bruxelles

The Differentiated Back-Projection (or DBP) is a method which allows reducing a 2D or 3D tomographic reconstruction problem with limited data to a set of 1D problems related to the Hilbert transform. For some configurations with limited data, this 1D problem consists in recovering a compactly supported function f from the knowledge of its Hilbert transform on a segment that overlaps the support of f. To characterize the ill-posedness of the inverse problem associated with this operator, it is of interest to know the singular value decomposition of the associated "Truncated Hilbert transform" operator HT. After describing the context in tomography, I will present recent work with A. Al-Aifari and A. Katsevich which establishes the asymptotics of the singular values and singular functions of HT, and show how these results lead to an error bound for a regularized solution.

**16h30 Coffee**

**Wednesday
26/02/2014**

**15h00
- 18h00**

15h00
– 16h30 *
Optimization-based Image Reconstructions from Discrete Data in CT
*

Xiaochuan Pan, Université de Chicago

Algorithm development for image reconstruction remains an active research area in CT and MRI. It is likely that the level of this effort will continue, or be intensified even further, in the foreseeable future. In the presentation, I will discuss some of recent advances in image reconstruction algorithms, with an emphasis on their implication for CT imaging. Using a series of real-data examples that arise in diagnostic and emerging CT imaging, I will illustrate how algorithms may be devised for potentially improving on reconstruction quality in current CT imaging and for reconstructing images of potential utility in emerging CT systems and applications. I will also touch upon a number of seemingly confusing issues concerning, e.g., Nyquist sampling theorem and compressive sensing (CS), and system/algorithm evaluation.

**16h30 Coffee**

*This
DROITE workshops are supported by a grant from << Région
Rhône Alpes>> (ARC
6, T.I.C. et Usages Informatiques Innovants) *

This workshop is supported by the labex CAMI, PRIMES, PERSYVAL, and the ECCAMI project. DROITE is supported by ANR (ANR project ANR-12-BS01-0018).