Abstract: Cone beam geometry imaging uses an area or two-dimensional array detector and a cone beam x-ray source. Image reconstruction by inverse Radon transformation is used following the calculation of planar integrals. Specifically, the integral is calculated by first changing it to a form wherein fast Fourier transforms can be used to minimize the number of operations in the calculations of the integral.

Abstract: An improved method and apparatus is disclosed for retaining only necessary cone beam projection data acquired along a three dimensional scanning trajectory in order to ensure more computationally efficient processing of Radon data for computerized tomographic image reconstruction consistent with the overall shape of an object irradiated by a cone beam source. If the scanning trajectory is such that an otherwise complete see of Radon data is acquired the image so reconstructed will also be exact. The invention is directed to restricting image reconstruction processing to only that region of support in Radon space actually occupied by the object itself; therefore, computational approximations consistent with the overall shape of the object can be applied to improve image reconstruction efficiency.

Abstract: Relatively large objects are viewed using relatively small area detectors by changing the configurations corresponding to the relative positioning of a source of cone beam imaging energy, the object which is to be viewed, and the area detector. A relatively large area detector is simulated by use of a high quality, high resolution, relatively small area detector. The simulated area detector allows imaging of objects which are too wide and/or too high for an actual area detector. The different configurations may be realized by moving the actual area detector relative to the source or by repositioning the object relative to the area detector. Movement for reconfiguration may be in a plane parallel to a plane in which a scan path is disposed if the object is too wide. If the object is too high, the reconfiguration movement would be perpendicular to a plane in which a scan path, usually circular, is located.

Abstract: A method and apparatus are disclosed for reconstructing a 3D CT image of an object from incomplete x-ray cone beam projection data, additionally employing object boundary information from a separate optical scan. A 3D image of the object is reconstructed slice-by-slice by employing, for each slice, a 2D reconstruction procedure for example, filtered backprojection, on the values of the 2D projection images in the plane of the slice to calculate a 2D image of the object for each of the slices.

Abstract: Method and apparatus for converting x-ray cone beam data (line integrals through an object) to Radon data (planar integrals) for 3D CT image reconstruction by inverse Radon transformation. The radial derivative of each planar integral is determined by integrating to determine weighted line integrals along each of a pair of lines on a normalized detector plane, which lines are defined as intersections with the normalized detector plane of a corresponding pair of integration planes sharing a rotation axis and rotated with respect to each other by a rotation angle .delta..beta., and then dividing the difference between the weighted line integrals by the rotation angle .delta..beta.. The procedure can be employed to convert the cone beam data to values representing planar integrals on any arbitrary set of planes in Radon space, such as a set of coaxial vertical planes.

Abstract: A configuration for three-dimensional cone beam computerized tomography imaging which minimizes the incompleteness of the data set and, at the same time, avoids corrupted data and resulting artifacts when only a portion of an object is imaged, the object being of greater axial extent compared to a cylindrical field of view. At least two circular source scanning trajectories are defined centered on a rotation axis and lying respectively in two endplanes defining the axial extent of the field of view. At least one cone beam x-ray source and at least one corresponding two-dimensional array detector are employed to scan the object along the source scanning trajectories, while acquiring cone beam projection data only from rays passing through the field of view. Preferably, at least one additional circular source scanning trajectory is defined, centered on the rotation axis and lying in a plane intermediate the two endplanes.

Abstract: To achieve a large reduction in the amount of computer time in limited-angle computerized tomography, the reconstructed image is decomposed into two partial images reconstructed from available scan data and missing scan data. Because the former is unchanged during the interative image reconstruction procedure, it is reconstructed from the measured projections only once at the beginning of the iterations and used repeatedly. The composite image formed by summing the two partial images is corrected by the a priori information about the object. The improved partial image due to missing projections is calculated and again summed with the partial image due to measured projections and corrected. These steps are iteratively repeated until a test for convergence yields a final image. A limited-angle x-ray CT system utilizes the projection space version of the iterative transform algorithm.

Abstract: Rapid x-ray inspection of objects larger than an x-ray detector array is based on a translate rotate scanning motion of the object relative to the fan beam source and detector. The scan for computerized tomography imaging is accomplished by rotating the object through 360 degrees at two or more positions relative to the source and detector array; in moving to another position the object is rotated and the object or source and detector are translated. A partial set of x-ray data is acquired at every position which are combined to obtain a full data set for complete image reconstruction. X-ray data for digital radiography imaging is acquired by scanning the object vertically at a first position at one view angle, rotating and translating the object relative to the source and detector to a second position, scanning vertically, and so on to cover the object field of view, and combining the partial data sets.

Abstract: Flaw uniform density location and size for flaws smaller than the beam diameter of an ultrasound beam are determined by measurement of return echos of ultrasound. The return echos are transformed to Fourier space and are normalized to take away any dependence upon factors other than the flaw in the object under test. The Fourier space representation of the return echo after normalization is dependent on a flaw characteristic function. The flaw characteristic function is repeatedly transformed between object space and Fourier space in order to eliminate or minimize errors in the flaw characteristic function. In frequency or Fourier space, the flaw characteristic function is reset to take into account the known Fourier components derived from the return echo waveforms, whereas the object space flaw characteristic function is corrected to take into account the fact that the flaw characteristic function has only two values, 0 and 1.

Abstract: A method is developed to construct the convex hull of an object in limited-angle x-ray computerized tomography. The convex hull is the smallest convex region containing the object, and therefore it can serve as a prior information on the object exterior boundary in reconstructing the object by an iterative limited-angle reconstruction procedure. The convex hull is the same as the exterior boundary of many convex objects and is a good approximation if the shape is not too concave. Greater accuracy is achieved by doing curve fitting near the edges of the x-ray projection data to determine the end points, and performing a low energy x-ray exposure at every scan angle in addition to the usual CT energy one. Over-attenuated x-ray data has utility in constructing the convex hull.

Abstract: This ultrasound imspection method using the Born approximation simplifies the problem of characterizing 3-dimensional flaws of general shape by reducing it to a series of 2-dimensional tomographic image reconstructions. The reconstructed 2-dimensional images represent the 2-dimensional projections or shadows of the 3-dimensional flaw characteristic function which specifies the shape of the flaw. Each projection image is reconstructed independently using well developed computerized tomography techniques. If the shape of the flow is not too irregular or fine details are not of interest, only a few of these projection images are needed. The 3-dimensional flaw shape is reconstructed from the 2-dimensional projection images through a 3-D reconstruction process.

Abstract: The fidelity of limited-angle x-ray computerized tomography imaging is improved by taking multiple scans using x-ray beams at different energies. The projection data of the composite object is decomposed into the projections of the individual component substances. Reconstruction of a single substance is done more accurately than reconstructing the composite object because more a priori information about the object, such as upper and lower bounds of the densities of the substances, is available. The reconstructed images of the components are superimposed to form an image of the composite object. The method is applicable to other imaging modalities.