Four-dimensional tomographic reconstruction by time domain decomposition

Since the beginnings of tomography, the requirement that the sample does not change during the acquisition of one tomographic rotation is unchanged. We derived and successfully implemented a tomographic reconstruction method which relaxes this decades-old requirement of static samples. In the presented method, dynamic tomographic data sets are decomposed in the temporal domain using basis functions and deploying an L1 regularization technique where the penalty factor is taken for spatial and temporal derivatives. We implemented the iterative algorithm for solving the regularization problem on modern GPU systems to demonstrate its practical use

Joint Reconstruction of Multi-channel, Spectral CT Data via Constrained Total Nuclear Variation Minimization

We explore the use of the recently proposed "total nuclear variation" (TNV) as a regularizer for reconstructing multi-channel, spectral CT images. This convex penalty is a natural extension of the total variation (TV) to vector-valued images and has the advantage of encouraging common edge locations and a shared gradient direction among image channels. We show how it can be incorporated into a general, data-constrained reconstruction framework and derive update equations based on the first-order, primal-dual algorithm of Chambolle and Pock. Early simulation studies based on the numerical XCAT phantom indicate that the inter-channel coupling introduced by the TNV leads to better preservation of image features at high levels of regularization, compared to independent, channel-by-channel TV reconstructions.Comment: Submitted to Physics in Medicine and Biolog

Histogram Tomography

In many tomographic imaging problems the data consist of integrals along lines or curves. Increasingly we encounter "rich tomography" problems where the quantity imaged is higher dimensional than a scalar per voxel, including vectors tensors and functions. The data can also be higher dimensional and in many cases consists of a one or two dimensional spectrum for each ray. In many such cases the data contain not just integrals along rays but the distribution of values along the ray. If this is discretized into bins we can think of this as a histogram. In this paper we introduce the concept of "histogram tomography". For scalar problems with histogram data this holds the possibility of reconstruction with fewer rays. In vector and tensor problems it holds the promise of reconstruction of images that are in the null space of related integral transforms. For scalar histogram tomography problems we show how bins in the histogram correspond to reconstructing level sets of function, while moments of the distribution are the x-ray transform of powers of the unknown function. In the vector case we give a reconstruction procedure for potential components of the field. We demonstrate how the histogram longitudinal ray transform data can be extracted from Bragg edge neutron spectral data and hence, using moments, a non-linear system of partial differential equations derived for the strain tensor. In x-ray diffraction tomography of strain the transverse ray transform can be deduced from the diffraction pattern the full histogram transverse ray transform cannot. We give an explicit example of distributions of strain along a line that produce the same diffraction pattern, and characterize the null space of the relevant transform.Comment: Small corrections from last versio

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

Getting Feasible Variable Estimates From Infeasible Ones: MRF Local Polytope Study

This paper proposes a method for construction of approximate feasible primal solutions from dual ones for large-scale optimization problems possessing certain separability properties. Whereas infeasible primal estimates can typically be produced from (sub-)gradients of the dual function, it is often not easy to project them to the primal feasible set, since the projection itself has a complexity comparable to the complexity of the initial problem. We propose an alternative efficient method to obtain feasibility and show that its properties influencing the convergence to the optimum are similar to the properties of the Euclidean projection. We apply our method to the local polytope relaxation of inference problems for Markov Random Fields and demonstrate its superiority over existing methods.Comment: 20 page, 4 figure

Fast multi-dimensional NMR acquisition and processing using the sparse FFT

Increasing the dimensionality of NMR experiments strongly enhances the spectral resolution and provides invaluable direct information about atomic interactions. However, the price tag is high: long measurement times and heavy requirements on the computation power and data storage. We introduce sparse fast Fourier transform as a new method of NMR signal collection and processing, which is capable of reconstructing high quality spectra of large size and dimensionality with short measurement times, faster computations than the fast Fourier transform, and minimal storage for processing and handling of sparse spectra. The new algorithm is described and demonstrated for a 4D BEST-HNCOCA spectrum.Swedish Research Council (Research Grant 2011-5994)Swedish National Infrastructure for Computing (Grant SNIC 001/12-271