A benchmark set for the reconstruction of hv-convex discrete sets

AbstractIn this paper we summarize the most important generation methods developed for the subclasses of hv-convex discrete sets. We also present some new generation techniques to complement the former ones thus making it possible to design a complete benchmark set for testing the performance of reconstruction algorithms on the class of hv-convex discrete sets and its subclasses. By using this benchmark set the paper also collects several statistics on hv-convex discrete sets, which are of great importance in the analysis of algorithms for reconstructing such kinds of discrete sets

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

Haplotype Assembly: An Information Theoretic View

This paper studies the haplotype assembly problem from an information theoretic perspective. A haplotype is a sequence of nucleotide bases on a chromosome, often conveniently represented by a binary string, that differ from the bases in the corresponding positions on the other chromosome in a homologous pair. Information about the order of bases in a genome is readily inferred using short reads provided by high-throughput DNA sequencing technologies. In this paper, the recovery of the target pair of haplotype sequences using short reads is rephrased as a joint source-channel coding problem. Two messages, representing haplotypes and chromosome memberships of reads, are encoded and transmitted over a channel with erasures and errors, where the channel model reflects salient features of high-throughput sequencing. The focus of this paper is on the required number of reads for reliable haplotype reconstruction, and both the necessary and sufficient conditions are presented with order-wise optimal bounds.Comment: 30 pages, 5 figures, 1 tabel, journa

A framework for generating some discrete sets with disjoint components by using uniform distributions

AbstractDiscrete tomography deals with the reconstruction of discrete sets from few projections. Assuming that the set to be reconstructed belongs to a certain class of discrete sets with some geometrical properties is a commonly used technique to reduce the number of possibly many different solutions of the same reconstruction problem. The average performance of reconstruction algorithms are often tested on such classes by choosing elements of a given class from uniform random distributions. This paper presents a general framework for generating discrete sets with disjoint connected components using uniform distributions. Especially, the uniform random generation of hv-convex discrete sets and Q-convex discrete sets according to the size of the minimal bounding rectangle are discussed