Reconstruction of binary matrices from fan-beam projections

The problem of the reconstruction of binary matrices from their fan-beam projections is investigated here. A fan-beam projection model is implemented and afterwards employed in systematic experiments to determine the optimal parameter values for a data acquisition and reconstruction algorithm. The fan-beam model, the reconstruction algorithm which uses the optimization method of Simulated Annealing, the simulation experiments, and the results are then discussed in turn

Parameter Settings for Reconstructing Binary Matrices from Fan-Beam Projections

The problem of reconstruction of binary matrices from their fan-beam projections is studied. A fan-beam projection model is implemented and used in systematic experiments in order to determine the optimal parameter values for data acquisition and reconstruction algorithm. The fan-beam model, the reconstruction algorithm, the simulation experiments, and the results are discussed in the paper

Network Flow Algorithms for Discrete Tomography

Tomography is a powerful technique to obtain images of the interior of an object in a nondestructive way. First, a series of projection images (e.g., X-ray images) is acquired and subsequently a reconstruction of the interior is computed from the available project data. The algorithms that are used to compute such reconstructions are known as tomographic reconstruction algorithms. Discrete tomography is concerned with the tomographic reconstruction of images that are known to contain only a few different gray levels. By using this knowledge in the reconstruction algorithm it is often possible to reduce the number of projections required to compute an accurate reconstruction, compared to algorithms that do not use prior knowledge. This thesis deals with new reconstruction algorithms for discrete tomography. In particular, the first five chapters are about reconstruction algorithms based on network flow methods. These algorithms make use of an elegant correspondence between certain types of tomography problems and network flow problems from the field of Operations Research. Chapter 6 deals with a problem that occurs in the application of discrete tomography to the reconstruction of nanocrystals from projections obtained by electron microscopy.The research for this thesis has been financially supported by the Netherlands Organisation for Scientific Research (NWO), project 613.000.112.UBL - phd migration 201

A diszkrét tomográfia új irányzatai és alkalmazása a neutron radiográfiában = New directions in discrete tomography and its application in neutron radiography

A projekt során alapvetően a diszkrét tomográfia alábbi területein végeztük eredményes kutatásokat: rekonstrukcó legyezőnyaláb-vetületekből; geometriai tulajdonságokon alapuló rekonsrukciós és egyértelműségi eredmények kiterjeszthetőségének vizsgálata; újfajta geometriai jellemzők bevezetése; egzisztenica, unicitás és rekonstrukció vizsgálata abszorpciós vetületek esetén; 2D és 3D rekonstrukciós algoritmusok fejlesztése neutron tomográfiás alkalmazásokhoz; bináris rekonstrukciós algoritmusok tesztelése, benchmark halmazok és kiértékelések; a rekonstruálandó kép geometriai és egyéb strukturális információinak kinyerése közvetlenül a vetületekből. A kidolgozott eljárásaink egy részét az általunk fejlesztett DIRECT elnevezésű diszkrét tomográfiai keretrendszerben implementáltuk, így lehetőség nyílt az ismertetett eljárások tesztelésére és a különböző megközelítések hatékonyságának összevetésére is. Kutatási eredményeinket több, mint 40 nemzetközi tudományos közleményben jelentettük meg, a projekt futamideje alatt két résztvevő kutató is doktori fokozatot szerzett a kutatási témából. A projekt során több olyan kutatási irányvonalat fedtünk fel, ahol elképzeléseink szerint további jelentős elméleti eredményeket lehet elérni, és ezzel egyidőben a gyakorlat számára is új jellegű és hatékonyabb diszkrét képalkotó eljárások tervezhetők és kivitelezhetők. | In the project entitled ""New Directions in Discrete Tomography and Its Applications in Neutron Radiography"" we did successful research mainly on the following topics on Discrete Tomography (DT): reconstruction from fan-beam projections; extension of uniqueness and reconstruction results of DT based on geometrical priors, introduction of new geometrical properties to facilitate the reconstruction; uniqueness and reconstruction in case of absorbed projections; 2D and 3D reconstruction algorithms for applications in neutron tomography; testing binary reconstruction algorithms, developing benchmark sets and evaluations; exploiting structural features of images from their projections. As a part of the project we implemented some of our reconstruction methods in the DIRECT framework (also developed at our department), thus making it possible to test and compare our algorithms. We published more than 40 articles in international conference proceedings and journals. Two of our project members obtained PhD degree during the period of the project (mostly based on their contributions to the work). We also discovered several research areas where further work can yield important theoretical results as well as more effective discrete reconstruction methods for the applications

Dose assessment and reconstruction algorithm optimization in simultaneous breast and lung CT imaging

Cancer is the second leading cause of death in the world, and therefore, there is an undeniable need to ensure early screening and detection systems worldwide. The aim of this project is to study the feasibility of a Cone Beam Computed Tomography (CBCT) scanner for simultaneous breast and lung imaging. Additionally, the development of reconstruction algorithms and the study of their impact to the image quality was considered. Monte Carlo (MC) simulations were performed using the PENELOPE code system. A MC geometry model of a CBCT scanner was implemented for energies of 30 keV and 80 keV for hypothetical scanning protocols. Microcalcifications were inserted into the breast and lung of the computational phantom (ICRP Adult Female Reference), used in the simulations for dose assessment and projection acquisition. Reconstructed images were analyzed in terms of the Contrast-to-Noise Ratio (CNR) and dose calculations were performed for two protocols, one with a normalization factor of 2 mGy in the breast and another with 5 mGy in the lungs. Both, MC geometry model and reconstruction algorithm were validated by means of on-field measurements and data acquisition in a clinical center. Dosimetric and imaging performances were evaluated through Quality Assurance phantoms (Computed Tomography Dose Index and Catphan, respectively). Results indicate that the best implementation of the reconstruction algorithm was achieved with 80 keV, using the Hanning filter and linear interpolation. More specifically, for a spherical lung lesion with a radius of 7 mm a 30% CNR gain was found when the number of projections varied from 12 to 36 (corresponding to a dose increase of a factor of 3). This research suggests the possibility of developing a CBCT modulated beam scanner for simultaneous breast and lung imaging while ensuring dose reduction. However further investigation regarding the number of projections needed for image reconstruction is required

Iterative transmission image reconstruction for the DPET positron emission tomograph

Positron emission tomography (PET) systems use transmission imaging to compensate for attenuation. One commercial example of this approach is the Siemens Inveon Dedicated PET (DPET), a 120mm bore system dedicated to the study of small animals. DPET transmission images are currently reconstructed using single slice rebinning followed by filtered backprojection. Single slice rebinning attributes the attenuation associated with an oblique line integral to the direct midplane intersected thereby. This leads to position-dependent axial blurring, especially for large diameter animals, and objects with abrupt axial changes in diameter. The mathematics underlying filtered backprojection are based on assumptions that are not met by the scanner, including but not limited to data being sampled in a uniform fashion. These limitations can be alleviated by an iterative algorithm if the associated system model is made to match the physical set-up. The downside is typically viewed as a potentially prohibitive increase in the computational cost. In this dissertation, we report on the implementation and use of Simultaneous Iterative Reconstruction Technique (SIRT) (a weighted least-squares solver) for transmission imaging on the DPET. We provide experimental evidence regarding the improvement in transmission image quality. We also show that these new, higher quality images can be computed in less than two minutes on the existing DPET host computer thus making the approach practical. Computational speed is gained both algorithmically through relaxation and use of ordered subsets and implementation-wise through vector based arithmetic and multi-core program execution