Abstract: The invention relates to a method and a device for reconstructing an image in a spatial volume on the basis of acquired projections, wherein during a reconstruction step each acquired projection or each region of an acquired projection is fed once into a data processing system from a memory for the acquired projections and the intensity of a voxel of the reconstructed spatial volume image is updated during the reconstruction step for each voxel relevant projection or region.

Abstract: A technique is provided for reducing contrast variability in images produced by tomosynthesis. In particular, contrast variability in images produced by a radiation source which has a linear or elongated scan path is reduced. The technique filters the radiographic projections or the reconstructed image slices in a direction transverse to the scan-direction of the radiation source to reduce contrast variations related to the orientation of the structure and the scan geometry.

Abstract: A computed tomography apparatus (10) for performing volumetric helical imaging acquires helical computed tomography imaging data (72) using a tilted gantry geometry. In the tilted gantry geometry, a rotational plane of a rotating radiation source (16) is tilted at an angle (&khgr;) with respect to a direction (Z) of linear motion of a subject. A transform processor (40) transforms (74) the imaging data (72) to a zero tilt geometry. A rebinning processor (50) rebins (110) the transformed imaging data (76) to a non-sheared detector window. A reconstruction processor (54) reconstructs (130) the transformed and rebinned imaging data (112) to generate a three-dimensional image representation (132). Optionally, an image transform processor (56) transforms (134) the reconstructed image representation (132) with an inverse of the zero tilt geometry transformation (74).

Abstract: A method for obtaining wood-cell attributes from cellulose containing samples includes the steps of radiating a cellulose containing sample with a beam of radiation. Radiation attenuation information is collected from radiation which passes through the sample. The source is rotated relative to the sample and the radiation and collecting steps repeated. A projected image of the sample is formed from the collected radiation attenuation information, the projected image including resolvable features of the cellulose containing sample. Cell wall thickness, cell diameter (length) and cell vacoule diameter can be determined. A system for obtaining physical measures from cellulose containing samples includes a radiation source, a radiation detector, and structure for rotating the source relative to said sample. The system forms an image of the sample from the radiation attenuation information, the image including resolvable features of the sample.

Abstract: The present technique provides a method and system for generating tomographic mammography data and processing the data using a computer aided detection and diagnosis (CAD) algorithm. The CAD algorithm may perform various types of analysis, including segmentation, feature extraction, and feature classification. The acquired data may be processed in parallel by the CAD algorithm such that information derived from one processing path may be used to enhance or alter the processing of data in a parallel processing path. The processed data may be used to provide an enhanced mammographic image with features of interest marked for inspection by a radiologist. The features of interest may also be classified to aid the inspection by the radiologist.

Abstract: In order to obtain an image with artifacts suppressed when a helical scan is conducted employing a multi-row detector with a scan plane tilted, preprocessing such as sensitivity correction is applied to data collected by a helical scan employing a multi-row detector with a scan plane tilted (S1), tilt correcting processing is applied for correcting view-to-view variation of the positions of channels in the detector rows relative to an axis of translation due to the tilt of the scan plane (S2), multi-slice/helical interpolation processing is applied for calculating interpolated data from proximate data in an image reconstruction plane (S3), and backprojection processing is applied to the interpolated data to produce an image (S4).

Abstract: A sequence description defining the events for traversing k-space during a medical imaging scan is defined through a k-space graphical view, thereby providing an easy programming interface for MR physicists. From the k-space view, data elements can be generated by object-oriented sequence description components in the form of predefined sequences. The data elements generated by the predefined sequences are stored in a table, the lines in the table defining an ordered list of pulse segments associated with each trajectory in k-space, the table can also hold information on time ordering or sequencing of k-space trajectories, desired triggering for each k-space trajectory and similar data objects. The k-space description/configuration of sequences is then translated to a group of downloadable sequence components.

Abstract: A method and system for generating a plurality of clinically useful images in a short time frame using a single imaging system. The system and method include using a single computer tomography (CT) system for generating a scout image configured to prescribe a tomographic axial/helical or target image and processing the scout projection data of the scout image to generate an enhanced scout image. The enhanced scout image and the target image are displayed, wherein the enhanced scout image and said target image are clinically useful images for diagnostic purposes provided by the single imaging system. More specifically, the single CT generates the enhanced scout image resembling an x-ray radiograph and the target image as a CT scan image.

Abstract: A three dimensional mask of the lungs can be automatically created by thresholding, labeling connected components, selecting the dominant object, and alternately employing dilation and erosion operations. With this mask the lungs can be separated from the other anatomic structures on volumetric CT images. Local density maxima in the lungs are then determined by sequentially decreasing thresholds. As the threshold declines, more and more objects (a 3D object is a group of connected voxels with density values larger than the threshold) become apparent. Geometrically overlapped objects at the subsequent threshold levels are either merged into one object or identified as local density maximum (maxima) and plateau. This process terminates if the threshold reaches a predefined density value. Other information about small lung nodules such as compact shape and size are combined into the algorithm to further remove those detected local density maxima that are not likely to be nodules.

Abstract: A method includes scanning an object in a first modality having a first field of view to obtain first modality data including fully sampled field of view data and partially sampled field of view data. The method also includes scanning the object in a second modality having a second field of view larger than the first field of view of obtain second modality data, and reconstructing an image of the object using the second modality data and the first modality partially sampled field of view data.

Abstract: A method is for window-controlled filtering of CT images. A CT raw data record is acquired, for example, with the aid of a CT unit or of a C-arc unit. A primary data record is then reconstructed from the CT raw data record by way of, for example, a sharp convolution core and, for example, a narrow slice sensitivity profile. A transfer function is then provided as functional relationship between window width and image sharpness. The image sharpness of the CT image of a selected slice is then automatically calculated, situated in the primary data record, as a function of a selected window width for the selected slice by way of an image processing procedure on the basis of the transfer function.

Abstract: A method of reconstructing a tomographic image of an object from incomplete projection data using a limited angle tomography technique. The method includes using the protection data to obtain a first reconstruction of the image. Thereafter, regions in the first reconstruction that can be predicted with an acceptable degree of certainty in a final reconstruction, are identified. Prior knowledge in the form of possible density levels and piece-wise smoothness that regions in an image can assume, are applied to those regions of acceptable certainty in the first reconstruction so as to obtain a second reconstruction. The projection data is then applied to projections of the second reconstruction using a constraining method to obtain a third reconstruction. In the same way regions of acceptable certainty are identified and the prior knowledge and the projection data are applied to the third reconstruction and subsequent reconstructions until a final reconstruction is achieved.

Abstract: The invention is based on the knowledge that a representation of an object can be improved via a transmission with regard to a subsequent reconstruction of the object based on the representation, by using simulated data, which correspond to a simulated transmission of the object already prior to a reconstruction as advance information for measuring a transmission of the object and/or for generating the representation from a measured transmission. An inventive method for the representation of an object via a transmission comprises providing simulated data, which correspond to a simulated transmission of the object, for example in a memory, and using the simulated data for measuring a transmission of the object, for example in a computertomograph, to obtain the transmission of the object, by a control and/or using the simulated data for generating the representation from a measured transmission by a data preparation means.

Abstract: A method includes augmenting partially sampled field of view data using fully sampled field of view data.

Abstract: Radiation therapy planning uses a beam commissioning tool and a Monte Carlo dose calculation tool. In the beam commissioning, measured dose data are input into a data processor. The measured dose data are derived from exposing a phantom to radiation from a source; and measuring the radiation dose to obtain a measured dose in the phantom resulting from the exposing step. The dose is measured at a plurality of points within the phantom, at least some of said points being axial points located at positions along a substantially central axis of the radiation source and others of said points being transverse points located at positions along an axis transverse to the central axis. The method further performs a Monte Carlo simulation of the radiation source to determine a simulated dose at the plurality of points; and further models the radiation source using the simulated dose and the measured dose.

Abstract: In order to efficiently obtain projection data having a variety of slice widths (slice patterns) in one scan, an X-ray CT apparatus is provided in which an X-ray tube 40 and an X-ray detector 70 are opposed to each other interposing a subject 100, in which detector a multiplicity of X-ray detector elements are linearly arranged in the channel arrangement direction to form a plurality of rows in the subject body axis direction, for reconstructing a CT tomographic image of the subject based on detected signals from the X-ray detector, wherein the X-ray CT apparatus comprises signal duplicating means 81a for duplicating channel detected signals of the X-ray detector 70 and distributing the duplicated signals to a plurality of groups a, b, etc.; and signal combining means 81b that can combine the distributed duplicated signals in each group in an arbitrary pattern across the detector rows for each channel.

Abstract: A method for providing diagnostic information regarding a coronary artery includes performing a Computed Tomography (CT) scan of the coronary artery to obtain structural data regarding the artery, performing a Positron Emission Tomography (PET) scan of the coronary artery to obtain functional data regarding the artery, and combining the structural data with the functional data in a single image.

Abstract: A general computer-implemented method and computer program for an independent MU or dose and fluence calculation of an intensity modulated photon field in intensity modulated radiation therapy (IMRT) is provided. The present invention provides for the verification MU or dose calculation in high dose regions or low dose regions. In general, the dose at an arbitrary spatial point is expressed as a summation of the contributions from all the beamlets in a treatment field, each modulated by a dynamic modulation factor. The verification of a low dose region is based on using the inverted field of the low dose region. The advantage of the present invention that it is an independent method and therefore generally applicable and useful irrespective of the type of leaf sequence algorithm and delivery machines. It provides an automated computer-implemented method or program that generalizes and simplifies dose verification in IMRT.

Abstract: A system, method, and computer-readable medium formats imaging data associated with an object in an n-dimensional file format. Once two-dimensional imaging ray data (projected or reflected data) is acquired, it is saved into an n-dimensional format (500) along with data describing the reference point and focal point of the image. A preferred format (500) comprises a file header (505), a header of the reference point, coordinates of the focal point field, a transformation field, and dimension sub-headers (550, 560). The system comprises a data acquisition module (612), a data storage module (630), a data reading module (640), and a data processing module (610) for formatting the data, reading the formatted data, and fusing the formatted data with other data sets, such as three-dimensional data.

Abstract: In one form, the present invention is a method for rapidly resampling a three-dimensional volume of data to permit efficient interactive viewing and visualization of the data is provided in which a set of parallel line segments defining a surface having a constant slope in at least one direction and intersecting the three-dimensional volume are selected and the data is processed at points on the parallel line segments to generate a reformatted image of the data. A corresponding apparatus embodiment is provided. Processing of data can proceed quickly because it is not necessary to check the parallel line segments during processing of the points on the segments to determine whether the points are within a given data volume.

Abstract: A digital x-ray imaging system employs a pixelated flat panel digital x-ray detector separated by a space from a source of x-rays which is selectively switchable between first and second, different x-ray energy levels, the space accommodating a body to be subjected to x-ray irradiation and imaging. A computer controls the x-ray source to irradiate the body with the first and second energy level x-rays and produce corresponding first and second x-ray images respectively of the first and second energy levels on the detector, the computer processing the respective digital signal outputs of the detector for the first and second digital images respectively of the first and second energy levels for each pixel, in individual succession for all pixels, and selectively produces and displays a soft tissue image or a bone/calcification image.

Abstract: An apparatus and process for determining and displaying a helical artifact index to a system operator are provided. The HAI is determined by acquiring and processing imaging data of a phantom. The HAI is then displayed to the operator on a console so that the operator may, if necessary, reset the scanning parameters or select a new scanning protocol that will result in a reconstructed image of a subject having reduced artifact presence. By providing a likelihood of artifact presence to the system operator, the present invention eliminates the need for the operator to recall those scanning profiles that are susceptible to high artifact presence.

Abstract: A method and an apparatus for processing data enables to display a preview image rapidly in case of processing large volume of data. Index data are generated by rendering the large amount of bit map data and stored in addition to the three-dimensional bit map data. By means that the two-dimensional image resulted from the rendering process is made prepared in advance before accepting the user's command for display and edit, the preview of the content of the data can be displayed rapidly at real-time when the user issues the command interactively.

Abstract: An X-ray tube (X-ray focus) and an X-ray detector opposed to each other across an object synchronously scan the object to acquire radiographic data in each scan position. The radiographic data or data resulting from a filtering process of the radiographic data is projected back to a two-dimensional or three-dimensional reconstruction area virtually set to a region of interest of the object. Reconstruction software is used for causing a computer to perform reconstruction computations for each unit area (block) formed by dividing the reconstruction area. The reconstruction computations are performed successively for one unit area (block) after another in a way optimal to cache size. Data in cache memory are reused at an increased rate, and access to data in memory is reduced to shorten a time consumed by the reconstruction computations.

Abstract: A method for planning an intensity modulated radiation therapy system comprising outlining a 3D target volume, providing relative radiation intensities of the 3D, a) selecting specific beam directions for the system to use and b) optimizing the system using an arcing paradigm; back-projecting the given intensities to the selected beam entry portals; sub-dividing each entry portal into discrete dose elements; applying thereto a cost function that scores the goodness of the plan by positively rewarding doses in selected regions and negatively rewarding doses in protected regions, and adjusting the weights of each of the dose elements to increase the overall score.

Abstract: In a method and apparatus for computed tomography, a subject is scanned with a conical ray beam emanating from a focus and the attenuated beam is detected with a matrix-like detector array. The focus is moved on a spiral path around a system axis relative to the subject, and the detector array supplies output data corresponding to the received radiation. The output data are supplied during the motion of the focus on a spiral segment and have a length adequate for the reconstruction of a CT image, and are divided into output datasets with respect to sub-segments. Segment images having an inclined image plane relative to the system axis are reconstructed for the sub-segments. The segment images respectively belonging to the sub-segments are combined into a partial image with respect to a target image plane, and the partial images are combined into a resulting CT image with respect to the target image plane.

Abstract: A data processing apparatus comprising a display device for displaying the data; the first recording device for recording the large volume bit map data; the second recording device recording an index data formed as a two-dimensional image obtained by rendering the large volume bit map data; the first data processing device for reading the large volume bit map data from the first recording device and applying the image processing to the large volume bit map data; the second data processing device for reading the large volume bit map data from the first recording device, forming the two-dimensional image data by rendering the large volume bit map data and transferring the image data to the display device; the third data processing device for transmitting the index data to the display device; and the input device for sending the instructions to the first, second and third data processing devices.

Abstract: A method for collecting computed tomography (CT) scan data includes positioning a gantry at a first position, collecting a partial inverted-cone beam projection at a first detector cell at the first gantry position such that the first detector cell defines a focusing position in space, and collecting data from a second detector cell different from the first detector cell as the gantry rotates such that the focusing position remains substantially stationary in space.

Abstract: A correction method is used for reducing artifacts caused by structures of high x-ray absorption in computer tomography images. By such a method, it is possible for interfering objects to be found both automatically and interactively in a computer tomography image. Relatively large interfering objects are preferably split up into a plurality of smaller interfering objects. The computer tomography image for each pixel of a selected image region is filtered as a function of its position relative to the interfering object.

Abstract: An x-ray imaging system according to the present invention comprising a stepped scanning-beam x-ray source and a multi-detector array. The output of the multi-detector array is input to an image reconstruction engine which combines the outputs of the multiple detectors over selected steps of the x-ray beam to generate an x-ray image of the object. A collimating element, preferably in the form of a perforated grid containing an array of apertures, interposed between the x-ray source and an object to be x-rayed. A maneuverable positioner incorporating an x-ray sensitive marker allowing the determination of the precise position coordinates of the maneuverable positioner.

Abstract: In a 3D angio-volume reconstruction method for a three-dimensional subject based on 2D projection exposures, shadowing artifacts are avoided by producing a 3D angio-volume dataset based on 2D mask images and a 3D angio-volume dataset based on 2D fill images, and a vessel tree is isolated in the fill volume dataset by a segmentation and is added to the mask image volume dataset after scaling.

Abstract: A data processing apparatus comprising a display device for displaying the data; the first recording device for recording the large volume bit map data; the second recording device recording an index data formed as a two-dimensional image obtained by rendering the large volume bit map data; the first data processing device for reading the large volume bit map data from the first recording device and applying the image processing to the-large volume bit map data; the second data processing device for reading the large volume bit map data from the first recording device, forming the two-dimensional image data by rendering the large volume bit map data and transferring the image data to the display device; the third data processing device for transmitting the index data to the display device; and the input device for sending the instructions to the first, second and third data processing devices.

Abstract: A driver drives an X-ray tube and a flat panel X-ray detector synchronously to scan sectional planes to be imaged of an object under examination. A back projection unit projects projection data detected in varied scan positions to predetermined lattice points of a three-dimensional lattice virtually set to the region of interest of the object radiographed. An image reconstruction is carried out to generate three-dimensional volume data of the region of interest. The three-dimensional volume data of the region of interest is generated quickly without repeating a radiographic operation.

Abstract: A method for increasing the speed of the parabolic marching method by about a factor of 256. This increase in speed can be used to accomplish a number of important objectives. Firstly, the speed can be used to collect data to form true 3-D images or 3-D assembled from 2-D slices. Speed allows larger images to be made. Secondly, the frequency of operation can be increased to 5 MHz to match the operating frequency of reflection tomography. This allow the improved imaging of speed of sound which in turn is used to correct errors in focusing delays in reflection tomography imaging. This allows reflection tomography to reach or closely approach its theoretical spatial resolution of ½ to ¾ wave lengths. A third benefit of increasing the operating frequency of inverse scattering to 5 MHz is the improved out of topographic plane spatial resolution. This improves the ability to detect small lesions.

Abstract: A nuclear medical imaging apparatus receives an associated object (18). A radiation detector (12) is equipped with a slat collimator (14) including a plurality of spaced apart slats (114) separating individual detecting elements of an essentially linear array of detecting elements (116). The slat collimator produces planar collimation and results in projection data which is weighted inversely with distance in the projection direction. An image reconstruction processor (34) converts the projection data obtained by the detector (12) into an image, including correction for the inverse distance weighting. The image reconstruction processor (34) includes a memory, a preconditioning operator P (36), a projection operator S (38), and an iterative loop operator (40) which applies the preconditioning operator P (36) and the projection operator S (38) to the memory contents to calculate updated memory contents.

Abstract: A method for weighting projection data includes selecting a region that includes a plurality of projection data samples, dividing the region into a plurality of equally sized sub-regions, and weighting the equally sized sub-regions using a location dependent z-smoothing weighting function.

Abstract: A method for acquiring and analyzing cardiac data of a patient includes acquiring a first volume of cardiac data from a medical scanner, processing the first volume of cardiac data for image reconstruction and visualization, acquiring a subsequent plurality of volumes of cardiac data from the medical scanner, processing the subsequent plurality of volumes of cardiac data for image reconstruction and visualization, and reconstructing and visualizing the first and subsequent plurality of image sets from the acquired first and the subsequent plurality of volumes of cardiac data, respectively. The method for acquiring and analyzing cardiac data of a patient includes processing the cardiac images for detection and diagnosis of heart diseases.

Abstract: A third generation CT scanner includes a rotating x-ray source (18) and a detector array (16). Each sampling of the detector array generates a source fan data line of data values that are converted (34) to attenuation values in a logarithmic domain and subject to preliminary corrections (36). Attenuation values from a plurality of adjoining source fans are converted (94) back to a non-logarithmic domain as intensity values. A corresponding deconvolution function (88) from a deconvolution function look-up table (90) corresponding to the detector whose intensity value is being corrected is deconvolved with a line (84) of the intensity values which spans a plurality of adjoining source fan data lines to remove the intensity attributable to off-focal radiation (30). The intensity data is converted (102) back into attenuation values in the logarithmic domain and reconstructed (106) into an image representation for display on a monitor (112).

Abstract: Method, system and program product are provided implementing a technique for backprojecting an image from a projection data set. The technique includes splitting the projection data set into a plurality of multi-channel textures, with each multi-channel texture corresponding to a predetermined number of color channels of a multi-color rendering engine. The multi-color rendering engine is employed to simultaneously render the split projection data set and obtain intermediate results for each color channel. The intermediate results of each color channel are then accumulated to generate separate rendered images, wherein multiple images are simultaneously rendered from the projection data set using the separate color channels of the multi-color rendering engine.

Abstract: A methodology and concomitant system for three-dimensional near-field microscopy achieves subwavelength resolution of an object via total internal reflection. The features of this approach include: (i) the evanescent waves used for illumination encode on the scattered field the subwavelength structure of the scattering object—it is thus possible to obtain subwavelength resolved images of the sample as is done in other near-field techniques such as near-field scanning optical microscopy without the technical difficulties encountered with probe-sample interactions; and (ii) the results of the reconstruction are unambiguous in the sense that the relation between the scattered field and the three-dimensional structure of the sample, as described by the spatial dependence of the susceptibility, is made manifest.

Abstract: In cone-beam volume computed tomography or similar imaging techniques, the effects of x-ray scatter are reduced through using a beam compensation filter (a bow tie filter), air gap technique, and an antiscatter grid and corrected through the use of a beam stop array combined with interpolation or convolution operation. Images are taken with the beam stop array, and a larger number of images are taken without the beam stop array. The images taken with the beam stop array are spatially interpolated to derive scatter information, which is then angularly interpolated to provide as many scatter images as there are images taken without the beam stop array. The interpolations are performed through cubic spline interpolation or any other interpolation techniques or low-pass filtering operation (convolution operation with a selected kernel). Each scatter image is subtracted from a corresponding one of the images taken without the beam stop array to provide a sequence of scatter-corrected images.

Abstract: A method for correcting for beam hardening in an initial CT image, which is composed of pixels arranged in a matrix, correction data are determined from the initial image by re-projection of the pixels from the initial image at a large number of projection angles, the pixels from the initial image being compared with a threshold value for each of the projection angles during the re-projection, and the re-projection being carried out for only those pixels from the initial image which have a pixel value above the threshold value. The correction data are used to determine a corrected image from the initial image.

Abstract: A method for facilitating a reduction of artifacts includes generating a first image of an object with a scanning system in native mode, generating a second image of the object with the scanning system with z-smoothing greater than any z-smoothing performed in native mode, and generating an artifact-candidate image by taking the difference between the first image and the second image.

Abstract: A method for acquiring views of an object includes acquiring a first quantity of views at a first position on a z-axis, acquiring a second quantity of views different from the first quantity at a second position on the z-axis different from the first position, and acquiring a third quantity of views equivalent to the first quantity at a third position on the z-axis different from the first position and the second position. A method is also described for processing these views to reconstruct the object.

Abstract: In one aspect, the present invention is a method for scanning an object with a multi-slice CT imaging system having multiple detector rows each having an isocenter. The method includes steps of helically scanning an object with the multi-slice CT imaging system to obtain data segments including peripheral data segments, combining data from a first peripheral data segment with an opposite, second peripheral segment to form a data set for reconstruction of an image slice; and reconstructing the combined data into image slices.

Abstract: An object detection apparatus includes a data acquisition system configured to acquire diagnostic data of the subject, an image reconstructor configured to reconstruct at least one image of the subject from the diagnostic data, and a data retrieval device configured to retrieve a first set of bookmarks identifying a first set of objects of interest in the at least one image. The object detection apparatus further includes a computer programmed to display the at least one image on a console and detect input from the user corresponding to a second set of bookmarks identifying a second set of objects of interest in the image. The computer is further programmed to selectively allow the user to incorporate each bookmark of the first set of bookmarks into the second set of bookmarks.

Abstract: A method for generating an adaptively interpolated projection of an object with an imaging system includes generating a first projection using a first interpolation kernel, generating a second projection using a second interpolation kernel, different from the first interpolation kernel, and taking a difference between the first projection and the second projection to generate a differential signal.

Abstract: A method is provided to reconstruct the three-dimensional image of an X-ray contrast agent-filled object having at least one plane of symmetry using a single plane two-dimensional X-ray projection. The projection is obtained by irradiating the object with X-rays substantially perpendicular to a selected plane of symmetry of the object. The absorbance value of each pixel in the projection, which is related to the distance travelled by the X-ray within the object, is then divided by 2 to define the z coordinates on each side of the x-y plane of symmetry of the object. The z coordinates together with the x,y coordinates of each pixel define the three-dimensional contour of the object.

Abstract: An X-ray computerized tomographic apparatus includes an X-ray tube device configured to irradiate an object to be examined with a pyramidal X-ray beam, a detector which has a plurality of detecting elements arrayed in a slice direction in which X-rays transmitted through the object are detected, a data extending unit which creates virtual data corresponding to an extension region located outside a region in which the detecting elements are arranged in the slice direction on the basis of real data detected by the detecting element, and a reconstructing unit which reconstructs image data on the basis of the real data and virtual data.

Abstract: One aspect of the present invention is a method for reconstructing computed tomographic (CT) images. The method includes generating a plurality of projection data, calculating a plurality of base weights using the projection data for each series of images to be reconstructed, storing the base weights in an external memory, and applying a z-smoothing module to the base weights to determine a plurality of final weights. The view weighting process then includes applying the final weights to the projection data for each image.