Abstract: For filtered back-projection of a projection image data set, the projection image data set is cosine-weighted. The cosine-weighted projection image data set within the image plane of the projection image data set is subjected to a two-dimensional Radon transformation. The Radon transform of the cosine-weighted projection image data set differentiated with respect to the distance from an image origin of an image coordinate system. The derivative of the Radon transform is redundancy-weighted. The redundancy-weighted derivative is subjected to a two-dimensional Radon back-transformation. The Radon back-transform is differentiated and back-projected with respect to an image column coordinate. A differentiation step width entering into the differentiation is varied depending on depth.

Abstract: A technique for 3D tomographic image reconstruction in the circular geometry (e.g., cone-based circular geometry) is disclosed. The technique may include data filtering using an initial 2D Laplace operation and a subsequent, non-local 2D filtering operation. The first filtering step thus only acts locally on the data so that it can be carried out accurately even in presence of (transaxial) data truncation. This feature may provide increased flexibility with respect to truncated projections as compared with certain standard FBP methods. Simulation studies show that the technique yields, for heavily transaxially-truncated data, an image quality that is similar to that obtained with the Feldkamp method applied with an explicit extrapolation scheme.

Abstract: An alternative analytical method for tomographic reconstruction in the 2D parallel-beam geometry is presented. This method may follow a filtering and backprojection scheme and may involve a global filtering in the projection domain and a local filtering in the image domain. For example, the method may include applying Hilbert filtering to the received projection data, computing an antiderivative of the filtered data, backprojecting the antiderivative into the image domain, and computing the 2D Laplacian of the backprojection image.

Abstract: A method for acquiring a 3D image dataset is proposed. A 3D X-ray image dataset of an image object is acquired during scanning of a partial circle by X-ray radiation source and X-ray radiation detector. A first and a second 3D image datasets are calculated from the acquired image dataset. Redundancies are eliminated by averaging the first and second 3D image datasets. A filtering that is antisymmetric in respect of a center of symmetry is performed in respect of the 2D image datasets in calculating the second 3D image dataset. Said filtering has a row-by-row Hilbert transform. Suitable weights can be specified based on an axis defined in space.

Abstract: A method for generation of a scan path for an x-ray source and/or an x-ray detector of an x-ray system is provided. CT-type imaging on the x-ray system is enabled by traversing the scan path upon simultaneous acquisition of a series of x-ray images. An original scan path of the x-ray source and/or of the x-ray detector is provided, where the scan path is defined by a series of original acquisition points. A viewing axis from the x-ray source to the object and/or the detector is identified for at least one acquisition point on the scan path. A modified scan path is generated by displacement of the at least one acquisition point at least partially along the viewing axis so that the scanning movement upon traversing the modified scan path can be reproduced as in the original scan path.

Abstract: A method for obtaining a 3D image dataset of an object of interest is proposed. A plurality of 2D X-ray images are captured and a 3D reconstruction is carried out using filtered back projection. The projection parameters have been measured with the aid of a calibrating phantom, possibly using an interpolation or extrapolation of such measurements. A model of effect strings of the components in an X-ray imaging device is obtained, and the model parameters are identified based on imaging of a calibrating phantom. A projection matrix can then be calculated for any positions on any desired trajectories, without having to use imaging of a calibrating phantom at precisely that position and desired trajectory.

Abstract: A method for producing a 3D image dataset of an object with an imaging system having an x-ray source and an x-ray detector is provided. A series of two-dimensional arrays of cone beam data from the detector is acquired while the source moves along a substantially planar trajectory around the object. The trajectory is described by a series of source points serially numbered by a counter parameter. The cone beam data is differentiated with respect to the counter parameter at a fixed ray direction to produce a derivative of the cone beam data. The derivative is filtered with a Hilbert-like filter to produce filtered cone beam data. The acquired or the filtered cone beam data is multiplied with a redundancy weighting function. The cone beam data is back-projected to reconstruct a 3D image dataset.

Abstract: A method for determining attenuation coefficients for an object using a movable x-ray source and a detector for recording projections is provided. The method includes defining a trajectory for the movable x-ray source, defining filtering lines for the filtering of projection data, and defining positions on the filtering lines, at which the projection derivative is to be formed using a mathematical algorithm for a back-projection. The method also includes defining sampling positions on the trajectory, traversing, by the x-ray source, the trajectory and recording a projection for each sampling position. Projection derivatives with respect to the trajectory path are calculated numerically for each of the positions directly on the filtering lines, and using a mathematical algorithm, attenuation coefficients are determined for the object from the calculated projection derivatives, for the reconstruction.

Abstract: 3D reconstructions can be calculated from grayscale X-ray images taken at different angular positions of an X-ray source and detector rotatable about a common axis. In the present case, X-ray radiation is applied to the object to be imaged such that one half of the X-ray detector receives radiation which differs in one characteristic from the radiation received by the second half of the detector via the object. A kind of dual-energy imaging can then be carried out in a single pass through the angular positions, enabling two 3D reconstructions to be generated simultaneously and then merged.

Abstract: A method for correcting artifacts in an image dataset reconstructed by filtered back projection is proposed. The artifacts are occurred as a result of temporal changes of attenuation values during rotational recording of X-ray projection images with an angular speed. A linear, analytically-derived, filter-type relationship between the attenuation values of the image dataset at a reference point and the real attenuation values is determined from the sum of a respective application of an angle speed-dependent weighting factor, a point spread function and a temporal derivation, evaluated at the reference time. The linear relationship is inverted and the inverted linear relationship is applied to the attenuation values of the image dataset for the correction.

Abstract: A method for reconstruction of a three-dimensional image data set from projection images of an object captured with an X-ray device from different projection angles is proposed. At least one sub-area of the object is outside the coverage of the X-ray device, or as a result of strong attenuation by a metal so that no projection data is present in the sub-area. Filter lines are determined n the projection images. A first local transformation is performed along the filter lines on the projection images. The missing projection data on the transformed projection data is augmented. A non-local transformation is performed on the transformed projection data for determining of filtered, augmented projection data. The non-local transformation is different from a ramp filter which is created by the first local transformation and the non-local transformation. The three-dimensional image data set is determined by back-projection of the filtered, augmented projection data.

Abstract: A method is provided for quickly and simply generating a three-dimensional tomographic x-ray imaging. Tomosynthetic projection images are recorded from different recording angles along a tomosynthetic scanning path and three-dimensional image data is reconstructed from the tomosynthetic projection images. The tomosynthetic projection images are recorded by a tomosynthetic x-ray device with a plurality of x-ray sources arranged on a holder at a distance from one another. Each projection image is recorded by a different x-ray source being fixed in one place during recording the tomosynthetic projection images.

Abstract: A method for reconstruction of a two-dimensional sectional image corresponding to a sectional plane through a recorded object from two-dimensional projection images recorded along a recording trajectory at different projection angles with an X-ray device is proposed. The sectional plane having at least two intersection points with the imaging trajectory is selected. After selection of the sectional plane, an intermediate function on the sectional plane is determined by backprojection of the projection images processed with a differentiation filter. The object densities forming the sectional image are determined from the intermediate function by a two-dimensional iterative deconvolution method.

Abstract: A method for recording and reconstructing a three-dimensional image dataset is proposed. A plurality of projection images are acquired under different recording geometries in relation to an object to be recorded by an X-ray apparatus, in particular a C-arm X-ray apparatus. At least two projection images are recorded for at least one recording geometry, in particular for every recording geometry. The three-dimensional image dataset is reconstructed from the project images.

Abstract: A method for reconstruction of an actual three-dimensional image dataset of an object during a monitoring process is proposed. Two-dimensional. X-ray projection images which correspond to a recording geometry are continuously recorded from different projection angles. The three-dimensional image dataset are reconstructed from a first number of these projection images, especially by a back projection method. The proportion of the oldest projection image contained in the current three-dimensional image dataset is removed from the three-dimensional image dataset and the proportion of the actual projection image is inserted in the three-dimensional image dataset after each recording of the actual projection image.

Abstract: At least one embodiment of the invention relates to a method for the reconstruction of image data from an examined object, using measuring data, wherein the measuring data were first recorded during a relative movement between a radiation source on a computer tomography system and the examined object. In at least one embodiment, the image reconstruction is based on a back projection of the filtered measuring data. During the back projection, a back projection weight that depends on the respective image point is used and the power with which the back projection weight is used is selectable.

Abstract: A method for producing a 3D image dataset of an object with an imaging system having an x-ray source and an x-ray detector is provided. A series of two-dimensional arrays of cone beam data from the detector is acquired while the source moves along a substantially planar trajectory around the object. The trajectory is described by a series of source points serially numbered by a counter parameter. The cone beam data is differentiated with respect to the counter parameter at a fixed ray direction to produce a derivative of the cone beam data. The derivative is filtered with a Hilbert-like filter to produce filtered cone beam data. The acquired or the filtered cone beam data is multiplied with a redundancy weighting function. The cone beam data is back-projected to reconstruct a 3D image dataset.

Abstract: A method for generation of a scan path for an x-ray source and/or an x-ray detector of an x-ray system is provided. CT-type imaging on the x-ray system is enabled by traversing the scan path upon simultaneous acquisition of a series of x-ray images. An original scan path of the x-ray source and/or of the x-ray detector is provided, where the scan path is defined by a series of original acquisition points. A viewing axis from the x-ray source to the object and/or the detector is identified for at least one acquisition point on the scan path. A modified scan path is generated by displacement of the at least one acquisition point at least partially along the viewing axis so that the scanning movement upon traversing the modified scan path can be reproduced as in the original scan path.

Abstract: A method for recording a projection dataset of a object to be recorded using a plurality of X-ray sources is provided, which X-ray sources are spaced apart from one another on average by an angle ? relative to an isocenter. A plurality of projection images from different recording directions are recorded in succession while activating the corresponding X-ray sources. Two X-ray sources are activated in succession having a spacing of at least 2 ? relative to the isocenter.

Abstract: A method is provided for quickly and simply generating a three-dimensional tomographic x-ray imaging. Tomosynthetic projection images are recorded from different recording angles along a tomosynthetic scanning path and three-dimensional image data is reconstructed from the tomosynthetic projection images. The tomosynthetic projection images are recorded by a tomosynthetic x-ray device with a plurality of x-ray sources arranged on a holder at a distance from one another. Each projection image is recorded by a different x-ray source being fixed in one place during recording the tomosynthetic projection images.