A multi-resolution image reconstruction method in X-ray computed tomography

International audienceWe propose a multiresolution X-ray imaging method designed for non-destructive testing/ evaluation (NDT/NDE) applications which can also be used for small animal imaging studies. Two sets of projections taken at different magnifications are combined and a multiresolution image is reconstructed. A geometrical relation is introduced in order to combine properly the two sets of data and the processing using wavelet transforms is described. The accuracy of the reconstruction procedure is verified through a comparison to the standard filtered backprojection (FBP) algorithm on simulated data

Mathematics and Algorithms in Tomography

This was the ninth Oberwolfach conference on the mathematics of tomography. Modalities represented at the workshop included X-ray tomography, radar, seismic imaging, ultrasound, electron microscopy, impedance imaging, photoacoustic tomography, elastography, emission tomography, X-ray CT, and vector tomography along with a wide range of mathematical analysis

Tokamak plasma boundary reconstruction using toroidal harmonics and an optimal control method

This paper proposes a new fast and stable algorithm for the reconstruction of the plasma boundary from discrete magnetic measurements taken at several locations surrounding the vacuum vessel. The resolution of this inverse problem takes two steps. In the first one we transform the set of measurements into Cauchy conditions on a fixed contour $\Gamma\_O$ close to the measurement points. This is done by least square fitting a truncated series of toroidal harmonic functions to the measurements. The second step consists in solving a Cauchy problem for the elliptic equation satisfied by the flux in the vacuum and for the overdetermined boundary conditions on $\Gamma\_O$ previously obtained with the help of toroidal harmonics. It is reformulated as an optimal control problem on a fixed annular domain of external boundary $\Gamma\_O$ and fictitious inner boundary $\Gamma\_I$. A regularized Kohn-Vogelius cost function depending on the value of the flux on $\Gamma\_I$ and measuring the discrepency between the solution to the equation satisfied by the flux obtained using Dirichlet conditions on $\Gamma\_O$ and the one obtained using Neumann conditions is minimized. The method presented here has led to the development of a software, called VacTH-KV, which enables plasma boundary reconstruction in any Tokamak.Comment: Fusion Science and Technology, 201

Doctor of Philosophy

dissertationSingle Photon Emission Computed Tomography (SPECT) myocardial perfusion imaging (MPI), a noninvasive and effective method for diagnosing coronary artery disease (CAD), is the most commonly performed SPECT procedure. Hence, it is not surprising that there is a tremendous market need for dedicated cardiac SPECT scanners. In this dissertation, a novel dedicated stationary cardiac SPECT system that using a segmented-parallel-hole collimator is investigated in detail. This stationary SPECT system can acquire true dynamic SPECT images and is inexpensive to build. A segmented-parallel-hole collimator was designed to fit the existing general-purpose SPECT cameras without any mechanical modifications of the scanner while providing higher detection sensitivity. With a segmented-parallel-hole collimator, each detector was segmented to seven sub-detector regions, providing seven projections simultaneously. Fourteen view-angles over 180 degree were obtained in total with two detectors positioned at 90 degree apart. The whole system was able to provide an approximate 34-fold gain in sensitivity over the conventional single-head SPECT system. The potential drawbacks of the stationary cardiac SPECT system are data truncation from small field of view (FOV) and limited number of view angles. A tailored maximum-likelihood expectation-maximization (ML-EM) algorithm was derived for reconstruction of truncated projections with few view angles. The artifacts caused by truncation and insufficient number of views were suppressed by reducing the image updating step sizes of the pixels outside the FOV. The performance of the tailored ML-EM algorithm was verified by computer simulations and phantom experiments. Compared with the conventional ML-EM algorithm, the tailored ML-EM algorithm successfully suppresses the streak artifacts outside the FOV and reduces the distortion inside the FOV. At 10 views, the tailored ML-EM algorithm has a much lower mean squared error (MSE) and higher relative contrast. In addition, special attention was given to handle the zero-valued projections in the image reconstruction. There are two categories of zero values in the projection data: one is outside the boundary of the object and the other is inside the object region, which is caused by count starvation. A positive weighting factor c was introduced to the ML-EM algorithm. By setting c>1 for zero values outside the projection, the boundary in the image is well preserved even at extremely low iterations. The black lines, caused by the zero values inside the object region, are completely removed by setting 0< c<1. Finally, the segmented-parallel-hole collimator was fabricated and calibrated using a point source. Closed-form explicit expressions for the slant angles and rotation radius were derived from the proposed system geometry. The geometric parameters were estimated independently or jointly. Monte Carlo simulations and real emission data were used to evaluate the proposed calibration method and the stationary cardiac system. The simulation results show that the difference between the estimated and the actual value is less than 0.1 degree for the slant angles and the 5 mm for the rotation radius, which is well below the detector's intrinsic resolution

Novel Inverse-Scattering Methods in Banach Spaces

The scientific community is presently strongly interested in the research of new microwave imaging methods, in order to develop reliable, safe, portable, and cost-effective tools for the non-invasive/non-destructive diagnostic in many fields (such as medicine, civil and industrial engineering, \u2026). In this framework, microwave imaging techniques addressing the full three-dimensional nature of the inspected bodies are still very challenging, since they need to cope with significant computational complexity. Moreover, non-linearity and ill-posedness issues, which usually affects the related inverse scattering problems, need to be faced, too. Another promising topic is the development of phaseless methods, in which only the amplitude of the electric field is assumed to be measurable. This leads to a significant complexity reduction and lower cost for the experimental apparatuses, but the missing information on the phase of the electric field samples exacerbates the ill-posedness problems. In the present Thesis, a novel inexact-Newton inversion algorithm is proposed, in which the iteratively linearized problems are solved in a regularized sense by using a truncated Landweber or a conjugate gradient method developed in the framework of the l^p Banach spaces. This is an improvement that allows to generalize the classic framework of the l^2 Hilbert spaces in which the inexact-Newton approaches are usually defined. The applicability of the proposed imaging method in both the 3D full-vector and 2D phaseless scenarios at microwave frequencies is assessed in this Thesis, and an extensive validation of the proposed imaging method against both synthetic and experimental data is presented, highlighting the advantages over the inexact-Newton scheme developed in the classic framework of the l^2 Hilbert spaces