Motion estimation is a very important method for improving image quality by compensating the cardiac motion at the best phase reconstructed. We tackle the cardiac motion estimation problem using an image registration approach. We compare the performance of three gradient-based registration methods on clinical data. In addition to simple gradient descent, we test the Nesterov accelerated descent and conjugate gradient algorithms. The results show that accelerated gradient methods provide significant speedup over conventional gradient descent with no loss of image quality.
In this work we apply the circle-and-line acquisition for the 256-detector row medical CT scanner. Reconstruction is based on the exact algorithm of the FBP type suggested recently by one of the co-authors. We derived equations for the cylindrical detector, common for medical CT scanners. To minimize hardware development efforts we use ramp-based reconstruction of the circle data. The line data provides an additional term that corrects the cone beam artifacts that are caused by the incompleteness of the circular trajectory. We illustrate feasibility of our approach using simulated data and real scanned data of the anthropomorphic phantom and evaluate stability of reconstruction to motion and misalignments during the scan. The additional patient dose from the line scan is relatively low compared to the circle scan. The proposed algorithm allows cone beam artifact-free reconstruction with large cone angle.
X-ray 3D rotational angiography based on C-arm systems has become a versatile and established tomographic imaging modality for high contrast objects in interventional environment. Improvements in data acquisition, e.g. by use of flat panel detectors, will enable C-arm systems to resolve even low-contrast details. However, further progress will be limited by the incompleteness of data acquisition on the conventional short-scan circular source trajectories. Cone artifacts, which result from that incompleteness, significantly degrade image quality by severe smearing and shading. To assure data completeness a combination of a partial circle with one or several line segments is investigated. A new and efficient reconstruction algorithm is deduced from a general inversion formula based on 3D Radon theory. The method is theoretically exact, possesses shift-invariant filtered backprojection (FBP) structure, and solves the long object problem. The algorithm is flexible in dealing with various circle and line configurations. The reconstruction method requires nothing more than the theoretically minimum length of scan trajectory. It consists of a conventional short-scan circle and a line segment approximately twice as long as the height of the region-of-interest. Geometrical deviations from the ideal source trajectory are considered in the implementation in order to handle data of real C-arm systems. Reconstruction results show excellent image quality free of cone artifacts. The proposed scan trajectory and reconstruction algorithm assure excellent image quality and allow low-contrast tomographic imaging with C-arm based cone-beam systems. The method can be implemented without any hardware modifications on systems commercially available today.
In multi-slice spiral computed tomography (CT) there is an obvious trend in adding more and more detector rows. The goals are numerous: volume coverage, isotropic spatial resolution, and speed. Consequently, there will be a variety of scan protocols optimizing clinical applications. Flexibility in table feed requires consideration of data redundancies to ensure efficient detector usage. Until recently this was achieved by approximate reconstruction algorithms only. However, due to the increasing cone angles there is a need of exact treatment of the cone beam geometry. A new, exact and efficient 3-PI algorithm for considering three-fold data redundancies was derived from a general, theoretical framework based on 3D Radon inversion using Grangeat's formula. The 3-PI algorithm possesses a simple and efficient structure as the 1-PI method for non-redundant data previously proposed. Filtering is one-dimensional, performed along lines with variable tilt on the detector.
This talk deals with a thorough evaluation of the performance of the 3-PI algorithm in comparison to the 1-PI method. Image quality of the 3-PI algorithm is superior. The prominent spiral artifacts and other discretization artifacts are significantly reduced due to averaging effects when taking into account redundant data. Certainly signal-to-noise ratio is increased. The computational expense is comparable even to that of approximate algorithms. The 3-PI algorithm proves its practicability for applications in medical imaging. Other exact n-PI methods for n-fold data redundancies (n odd) can be deduced from the general, theoretical framework.
Recently one of the authors proposed a reconstruction algorithm, which is theoretically exact and has the truly shift-invariant filtering and backprojection structure. Each voxel is reconstructed using the theoretically minimum section of the spiral, which is located between the endpoints of the PI segment of the voxel. Filtering is one-dimensional, performed along lines with variable tilt on the detector, and consists of five terms. We will present evaluation of the performance of the algorithm. We will also discuss and illustrate empirically the contributions of the five filtering terms to the overall image. A thorough evaluation proved the validity of the algorithm. Excellent image results were achieved even for high pitch values. Overall image quality can be regarded as at least equivalent to the less efficient, exact, Radon-based methods. However, the new algorithm significantly increases efficiency. Thus, the method has the potential to be applied in clinical scanners of the future. The empirical analysis leads to a simple, intuitive understanding of the otherwise obscure terms of the algorithm. Identification and skipping of the practically irrelevant fifth term allows significant speed-up of the algorithm due to uniform distance weighting.
Static Fourier transform spectrometers have the ability to combine the principle advantages of the two traditional techniques used for imaging spectrometry: the throughput advantage offered by Fourier transform spectrometers, and the advantage of no moving parts offered by dispersive spectrometers. The imaging versions of these spectrometers obtain both spectral information, and spatial information in one dimension, in a single exposure. The second spatial dimension may be obtained by sweeping a narrow field mask across the object while acquiring successive exposures. When employed as a pushbroom sensor from an aircraft or spacecraft, no moving parts are required, since the platform itself provides this motion. But the use of this narrow field mask to obtain the second spatial dimension prevents the throughput advantage from being realized. We present a technique that allows the use of a field stop that is wide in the along-track direction, while preserving the spatial resolution, and thus enables such an instrument to actually exploit the throughput advantage when used as a pushbroom sensor. The basis of this advance is a deconvolution technique we have developed to recover the spatial resolution in data acquired with a field stop that is wide in the along-track direction. The effectiveness is demonstrated by application of this deconvolution technique to simulated data.
Conventional tomographic imaging techniques are nonlocal: to reconstruct an unknown function f at a point x, one needs to know its radon transform (RT) f((theta) ,p) for all ((theta) ,p). Suppose that one is interested in the recovery of f only for x in some set U. We call U the region of interest (ROI). Define the local data as the integrals of f along the lines that intersect the ROI. We propose algorithms for finding locations and values of jumps (sharp variations) of f from only the local data. In case of transmission tomography, this results in a reduction of the x-ray dose to a patient. The proposed algorithms can also be used in emission tomographies. They allow one: to image jumps of f with better resolution than conventional techniques; to take into account variable attenuation (if it is known); and to obtain meaningful images even if the attenuation is not known. Results of testing the proposed algorithms on the simulated and real data are presented.
Simple and numerically stable approaches to approximate solution of inverse geophysical and potential scattering problems are described. The method we propose consists of two steps. Let v(z) be the inhomogeneity (potential), and let D be its support. First, we find approximations to the zeroth moment (total intensity) v(z)dz and the first moment (center of gravity) zv(z)dz/ v(z)dz of the function v(z). We call this step 'inhomogeneity localization', because in many cases the center of gravity lies inside D or is located close to it. Second, we refine the above moments and find the tensor of the second central moments of v(z). Using this information, we find an ellipsoid D and a real constant v, such that the inhomogeneity (potential) v(z) equals v,z an element of D, and v(z) equals 0,z not an element of D, fits best the scattering data and has the same zeroth, first, and second moments. We call this step 'approximate inversion'. The proposed method does not require any intensive computations, it is very simple to implement and it is relatively stable towards noise in the data.
SC939: Exact Cone Beam Reconstruction: Theory and Practice
This course provides attendees with basic working knowledge of the fundamentals of exact image reconstruction in cone beam CT. The course starts with the general theory, then we discuss various approaches to obtaining inversion formulae, and then we consider specific trajectories, such as helical and circle plus a curve. We include a discussion of implementation techniques, analysis of detector requirements and data usage. We will also discuss image quality of exact Katsevich-type (shift-invariant filtered-backprojection structure) reconstruction.
• Foundations of three-dimensional image reconstruction theory in computed tomography - Radon transform, cone beam transform, Grangeat's formula
• General reconstruction scheme - intersections of the source trajectory with Radon planes, weight function n, inversion of the cone beam transform
• Approaches to obtaining reconstruction formulae, including the Zou-Pan approach - Reconstruction on chords; Gelfand-Graev formula; Pack-Noo approach - Reconstruction on M-lines; and other approaches
• Trajectory-specific choice of the weight function for optimal reconstruction performance, both helical (1-PI, 3-PI, and Fractional-PI) and generalized circle-plus trajectories (open circle + line, and closed circle + curve)
• Implementation details including filtering lines rebinning and detector requirements
• Image quality