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
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.
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.
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).