Quasi-Exact Helical Cone Beam Reconstruction for Micro CT

A cone beam micro-CT system is set up to collect truncated helical cone beam data. This system includes a micro-focal X-ray source, a precision computer-controlled X-Y-Z-theta stage, and an image-intensifier coupled to a large format CCD detector. The helical scanning mode is implemented by rotating and translating the stage while keeping X-ray source and detector stationary. A chunk of bone and a mouse leg are scanned and quasi-exact reconstruction is performed using the approach proposed in J. Hu et al. (2001). This approach introduced the original idea of accessory paths with upper and lower virtual detectors having infinite axial extent. It has a filtered backprojection structure which is desirable in practice and possesses the advantages of being simple to implement and computationally efficient compared to other quasi-exact helical cone beam algorithms for the long object problem

Cardiac Computed Tomography Methods and Systems Using Fast Exact / Quasi Exact Filtered Back Projection Algorithms

The present invention provides systems, methods, and devices for improved computed tomography. More specifically, the present invention includes methods for improved cone-beam computed tomography (CBCT) resolution using improved filtered back projection (FBP) algorithms, which can be used for cardiac tomography and across other tomographic modalities. Embodiments provide methods, systems, and devices for reconstructing an image from projection data provided by a computed tomography scanner using the algorithms disclosed herein to generate an image with improved temporal resolution

Real-time quasi-3D tomographic reconstruction

Developments in acquisition technology and a growing need for time-resolved experiments pose great computational challenges in tomography. In addition, access to reconstructions in real time is a highly demanded feature but has so far been out of reach. We show that by exploiting the mathematical properties of filtered backprojection-type methods, having access to real-time reconstructions of arbitrarily oriented slices becomes feasible. Furthermore, we present RECAST3D, software for visualization and on-demand reconstruction of slices. A user of RECAST3D can interactively shift and rotate slices in a GUI, while the software updates the slice in real time. For certain use cases, the possibility to study arbitrarily oriented slices in real time directly from the measured data provides sufficient visual and quantitative insight. Two such applications are discussed in this article

Cone-Beam Composite-Circling Scan and Exact Image Reconstruction for a Quasi-Short Object

Here we propose a cone-beam composite-circling mode to solve the quasi-short object problem, which is to reconstruct a short portion of a long object from longitudinally truncated cone-beam data involving the short object. In contrast to the saddle curve cone-beam scanning, the proposed scanning mode requires that the X-ray focal spot undergoes a circular motion in a plane facing the short object, while the X-ray source is rotated in the gantry main plane. Because of the symmetry of the proposed mechanical rotations and the compatibility with the physiological conditions, this new mode has significant advantages over the saddle curve from perspectives of both engineering implementation and clinical applications. As a feasibility study, a backprojection filtration (BPF) algorithm is developed to reconstruct images from data collected along a composite-circling trajectory. The initial simulation results demonstrate the correctness of the proposed exact reconstruction method and the merits of the proposed mode

Real-time tomographic reconstruction

With tomography it is possible to reconstruct the interior of an object without destroying. It is an important technique for many applications in, e.g., science, industry, and medicine. The runtime of conventional reconstruction algorithms is typically much longer than the time it takes to perform the tomographic experiment, and this prohibits the real-time reconstruction and visualization of the imaged object. The research in this dissertation introduces various techniques such as new parallelization schemes, data partitioning methods, and a quasi-3D reconstruction framework, that significantly reduce the time it takes to run conventional tomographic reconstruction algorithms without affecting image quality. The resulting methods and software implementations put reconstruction times in the same ballpark as the time it takes to do a tomographic scan, so that we can speak of real-time tomographic reconstruction.NWONumber theory, Algebra and Geometr

Filtered backprojection inversion of the cone beam transform for a general class of curves

We extend a cone beam transform inversion formula, proposed earlier for helices by one of the authors, to a general class of curves. The inversion formula remains efficient, because filtering is shift-invariant and is performed along a one-parametric family of lines. The conditions that describe the class are very natural. Curves C are smooth, without self-intersections, have positive curvature and torsion, do not bend too much, and do not admit lines which are tangent to C at one point and intersect C at another point. The notions of PI lines and PI segments are generalized, and their properties are studied. The domain U is found, where PI lines are guaranteed to be unique. Results of numerical experiments demonstrate very good image quality

Томографічна реконструкція «великих» об’єктів при використанні часткових сканувань

Представлено алгоритми томографічної реконструкції «великих» об’єктів. Розглянуто випадки використання часткових сканувань горизонтальних і вертикальних секцій при розмірах об’єктів, що в декілька разів перевищують кут конусного променя та розміри матриці детекторів. Наведено результати моделювання томографічної реконструкції математичних фантомів.Представлены алгоритмы томографической реконструкции «больших» объектов. Рассмотрены случаи использования частичных сканирований горизонтальных и вертикальных секций при размерах объектов, в несколько раз превышающих угол конусного луча и размеры матрицы детекторов. Приведены результаты моделирования томографической реконструкции математических фантомов.The tomographic reconstruction algorithms for «large» objects are presented. The cases of using partial scans of horizontal and vertical sections if the objects sizes are greater by several fold than the angle of cone-beam and the matrix detector sizes are considered. The results of the tomographic reconstruction modeling using the mathematical phantoms are given

Mathematical Methods in Tomography

This is the seventh Oberwolfach conference on the mathematics of tomography, the first one taking place in 1980. Tomography is the most popular of a series of medical and scientific imaging techniques that have been developed since the mid seventies of the last century