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

Non-convex image reconstruction via Expectation Propagation

Tomographic image reconstruction can be mapped to a problem of finding solutions to a large system of linear equations which maximize a function that includes \textit{a priori} knowledge regarding features of typical images such as smoothness or sharpness. This maximization can be performed with standard local optimization tools when the function is concave, but it is generally intractable for realistic priors, which are non-concave. We introduce a new method to reconstruct images obtained from Radon projections by using Expectation Propagation, which allows us to reframe the problem from an Bayesian inference perspective. We show, by means of extensive simulations, that, compared to state-of-the-art algorithms for this task, Expectation Propagation paired with very simple but non log-concave priors, is often able to reconstruct images up to a smaller error while using a lower amount of information per pixel. We provide estimates for the critical rate of information per pixel above which recovery is error-free by means of simulations on ensembles of phantom and real images.Comment: 12 pages, 6 figure

Evaluation of Single-Chip, Real-Time Tomographic Data Processing on FPGA - SoC Devices

A novel approach to tomographic data processing has been developed and evaluated using the Jagiellonian PET (J-PET) scanner as an example. We propose a system in which there is no need for powerful, local to the scanner processing facility, capable to reconstruct images on the fly. Instead we introduce a Field Programmable Gate Array (FPGA) System-on-Chip (SoC) platform connected directly to data streams coming from the scanner, which can perform event building, filtering, coincidence search and Region-Of-Response (ROR) reconstruction by the programmable logic and visualization by the integrated processors. The platform significantly reduces data volume converting raw data to a list-mode representation, while generating visualization on the fly.Comment: IEEE Transactions on Medical Imaging, 17 May 201

Lensfree computational microscopy tools for cell and tissue imaging at the point-of-care and in low-resource settings.

The recent revolution in digital technologies and information processing methods present important opportunities to transform the way optical imaging is performed, particularly toward improving the throughput of microscopes while at the same time reducing their relative cost and complexity. Lensfree computational microscopy is rapidly emerging toward this end, and by discarding lenses and other bulky optical components of conventional imaging systems, and relying on digital computation instead, it can achieve both reflection and transmission mode microscopy over a large field-of-view within compact, cost-effective and mechanically robust architectures. Such high throughput and miniaturized imaging devices can provide a complementary toolset for telemedicine applications and point-of-care diagnostics by facilitating complex and critical tasks such as cytometry and microscopic analysis of e.g., blood smears, Pap tests and tissue samples. In this article, the basics of these lensfree microscopy modalities will be reviewed, and their clinically relevant applications will be discussed