Tsuneo Saito

Derivation and implementation of a cone-beam reconstruction algorithm for nonplanar orbits

B.D. Smith (ibid., vol.MI-4, p.15-25, 1985; Opt. Eng., vol.29, p.524-34, 1990) and P. Grangeat (These de doctorat, 1987; Lecture Notes in Mathematics 1497, p.66-97, 1991) derived a cone-beam inversion formula that can be applied when a nonplanar orbit satisfying the completeness condition is used. Although Grangeats inversion formula is mathematically different from Smiths one, they have similar overall structures to each other. The contribution of the present paper is two-fold. First, based on the derivation of Smith, the authors point out that Grangeats inversion formula and Smiths one can be conveniently described using a single formula (the Smith-Grangeat inversion formula) that is in the form of space-variant filtering followed by cone-beam back projection. Furthermore, the resulting formula is reformulated for data acquisition systems with a planar detector to obtain a new reconstruction algorithm. Second, the authors make two significant modifications to the new algorithm to reduce artifacts and numerical errors encountered in direct implementation of the new algorithm. As for exactness of the new algorithm, the following fact can be stated. The algorithm based on Grangeats intermediate function is exact for any complete orbit, whereas that based on Smiths intermediate function should be considered as an approximate inverse excepting the special case where almost every plane in 3D space meets the orbit. The validity of the new algorithm is demonstrated by simulation studies.

Three-dimensional quantitative coronary angiography

A method for reconstructing the three-dimensional coronary arterial tree structure from biplane two-dimensional angiographic images is presented. This method exploits the geometrical mathematics of X-ray imaging and the tracking of leading edges of injected contrast material into each vessel for identification of corresponding points on two images taken from orthogonal views. The accurate spatial position and dimensions of each vessel in three-dimensional space can be obtained by this reconstruction procedure. The reconstructed arterial configuration is displayed as a shaded surface model, which can be viewed from various angles. Such three-dimensional vascular information provides accurate and reproducible measurements of vascular morphology and function. Flow measurements are obtained by tracking the leading edge of contrast material down the three-dimensional arterial tree. A quantitative analysis of coronary stenosis based on transverse area narrowing and regional blood flow, including the effect of vascoactive drugs, is described. Reconstruction experiments on actual angiographic images of the human coronary artery yield encouraging results toward a realization of computer-assisted three-dimensional quantitative angiography.<<ETX>>

Feasible cone beam scanning methods for exact reconstruction in three-dimensional tomography

Feasible cone beam scanning methods that permit exact reconstruction in three-dimensional tomography are proposed, and their performances are investigated using the theory developed by Kirillov [Sov. Math. Dokl. 2, 268 (1961)], Tuy [SIAM J. Appl. Math. 43, 546 (1983)], and Smith [IEEE Trans. Med. Imaging MI-4, 14 (1985)]. The proposed methods move an apex of a cone on two circles that are perpendicular to each other (orthogonal scan) or on a few twists of a helical curve (helical scan). The obtainable information, the feasibility of reconstruction, and the redundancy of measurement by some typical cone beam scanning methods are analyzed using the relationship between the cone beam projections and the three-dimensional Radon transform. Consequently it is found that the proposed methods can obtain the complete information about the three-dimensional Fourier transform of an object with less redundant measurement. Moreover, based on the analysis, a practically implementable reconstruction algorithm suitable for the proposed methods is derived. Experiments performed with both numerical and real x-ray projections demonstrate the validity of the proposed scanning methods and the reconstruction algorithm. Especially when a large cone angle is used, the proposed methods greatly improve the spatial resolution and the quantitative accuracy of reconstruction as compared with the method of circular apex motion.

An extended completeness condition for exact cone-beam reconstruction and its application

The completeness condition is an important concept that specifies the capability of exact image reconstruction from a set of cone-beam projections. Unfortunately, the existing completeness conditions associated with Tuys (1983), Smiths (1985), and Grangeats (1991) inversion formulae are too restrictive in various situations where some projections are partially measured. The authors derive an extended completeness condition that improves the existing results. The new condition is a direct consequence of a reconstruction algorithm that is in the form of space-variant filtering followed by cone-beam backprojection. The new condition is less restrictive compared with the existing ones and provides an effective means to incorporate partially measured projections into image reconstruction.<<ETX>>

A fast convergence frequency domain adaptive filter

This correspondence presents a new fast convergence algorithm for frequency domain adaptive filter and its applicability to acoustic noise cancellation in speech signals.

Characteristics of hot ions with strong radiofrequency heating in the GAMMA 10 tandem mirror

Radiofrequency waves in the ion cyclotron range of frequency (ICRF) are mainly used for plasma production and heating in the central cell of the GAMMA 10 tandem mirror. GAMMA 10 has minimum-B anchor cells with a non-axisymmetric magnetic field configuration. The ICRF heating system in the central cell has been improved to create a more axisymmetric plasma. A high ion temperature is attained with the system, and high energy ions with energies of more than 50 keV are detected both parallel and perpendicular to the magnetic field lines. Strong temperature anisotropy is observed and strong Alfven ion cyclotron (AIC) modes are excited due to the anisotropy. With the AIC modes, the number of high energy ions detected at the end of the mirror increase and the number of high energy ions with a pitch angle in the central cell of nearly 90° decrease.

Three‐dimensional helical‐scan computed tomography using cone‐beam projections

A fast data-acquisition method for 3-D X-ray computed tomography is proposed. The method continuously rotates a cone-beam X-ray source and a 2-D detector constructed by stacking 1-D circular detector arrays for the fan-beam computed tomography. Simultaneously, a patient is translated in the field of view of the X-ray source. This method is called helical-san, because it provides cone-beam projections measured by moving an X-ray source on a helix surrounding the patient. An approximate convolution backprojection image reconstruction algorithm for the helical-scan is developed by extending L.A. Feldkamps (1984) cone-beam reconstruction algorithm, for the circular-scan. How one should choose geometrical parameters of the data-acquisition system is discussed. Furthermore, the performance of the proposed method is analyzed by evaluating the point spread function of the reconstruction algorithm.<<ETX>>

Fast and stable cone-beam filtered backprojection method for non-planar orbits

We propose a new cone-beam shift-variant filtered backprojection (FBP) method for non-planar orbit data acquisitions. The new method is exact, fast and stable to discretization errors. It is based on the hybrid FBP framework whose key feature is to combine the shift-variant filtering with the ramp filtering to produce the filtered projections. We show that an adequate combination of the two filterings allows us to minimize contributions of the time-consuming and numerically unstable shift-variant filtering. We demonstrate the performances of the new method by simulation studies. We also apply the new method to real x-ray data acquired from our experimental system of monochromatic computed tomography.

Development of a fluorescent x‐ray source for medical imaging

A fluorescent x‐ray source for medical imaging, such as K‐edge subtraction angiography and monochromatic x‐ray CT, has been developed. Using a 6.5 GeV accumulation ring in Tsukuba, fluorescent x rays, which range from about 30 to 70 keV are generated by irradiating several target materials. Measurements have been made of output intensities and energy spectra for different target angles and extraction angles. The intensities of fluorescent x rays at a 30 mA beam current are on the order of 1–3×106 photons/mm2/s at 30 cm from the local spot where the incident beam is collimated to 1 mm2. A phantom which contains three different contrast media (iodine, barium, gadolinium) was used for the K‐edge energy subtraction, and element selective CT images were obtained.

Extended cone-beam reconstruction using Radon transform

We extend Grangeats formula (1991) so that partially measured cone-beam projections can be incorporated into image reconstruction in a successful way. The extension is based on a simple fact that multiple partially measured projections may be combined to compute the 3-D Radon data inaccessible from any single orbit point. Furthermore, we show a few examples for which Grangeats formula does not provide a method for exact reconstruction but the extended formula does.