Image reconstruction from truncated fan-beam projections along a circular trajectory using the virtual fan-beam method.

In this paper, we investigate how the virtual fan-beam (VFB) method can be used to perform mathematically correct 2D reconstruction in a region-of-interest (ROI), using truncated fan-beam projections acquired on a circular scan, for truncation that only occurs on one side of the object.We start by choosing a virtual fan-beam trajectory and specifying how to obtain the corresponding virtual projections. Then, three VFB formulas are obtained by applying known super-short-scan (SSS) formulas to this virtual trajectory.

Equal parallel and cone-beam projections: a curious property of D-symmetric object functions.

In tomographic image reconstruction, the object density function is the unknown quantity whose projections are measured by the scanner. In the three-dimensional case, we define the D-reflection of such a density function as the object obtained by a particular weighted reflection about the plane=, and a D-symmetric function as one whose D-reflection is equal to itself. D-symmetric object functions have the curious property that their parallel projection onto the detector plane=is equal to their cone-beam projection onto the same detector with x-ray source location at the origin.

Cone-beam CT sampling incompleteness: analytical and empirical studies of emerging systems and source-detector orbits.

Purpose: Motivated by emerging cone-beam computed tomography (CBCT) systems and scan orbits, we aim to quantitatively assess the completeness of data for 3D image reconstruction-in turn, related to "cone-beam artifacts." Fundamental principles of cone-beam sampling incompleteness are considered with respect to an analytical figure-of-merit [FOM, denoted ] and related to an empirical FOM (denoted ) for measurement of cone-beam artifact magnitude in a test phantom.

Approach: A previously proposed analytical FOM [, defined as the minimum angle between a point in the 3D image reconstruction and the x-ray source over the scan orbit] was analyzed for a variety of CBCT geometries.

A tomographic reconstruction algorithm for cross-sectional imaging of IMRT beams from six projections.

. Patient-specific Quality Assurance (QA) measurements are of key importance in radiotherapy for safe and efficient treatment delivery and allow early detection of clinically relevant errors. Such QA processes remain challenging to implement for complex Intensity Modulated Radiation Therapy (IMRT) radiotherapy fields delivered using a multileaf collimator (MLC) which often feature small open segments and raise QA issues similar to those encountered in small field dosimetry.

Tiny changes in tomographic system matrices can cause large changes in reconstruction quality.

This paper studies the impact of tiny changes in region-of-interest (ROI) tomography system matrices on the variance of the reconstructed ROI. In small-scale and medium-scale examples, the variance in the reconstructed ROI was estimated for different system matrices. The results revealed a striking and counterintuitive phenomenon: a tiny change in the system matrix can dramatically affect the variance of the ROI estimate.

Feasibility of attenuation map alignment in pinhole cardiac SPECT using exponential data consistency conditions.

Purpose: Dedicated cardiac SPECT systems do not typically include an integrated CT scanner and thus attenuation correction requires registration of separately acquired transmission scans. Data consistency conditions are equations that express the redundancy between projections while taking into account the attenuation effects. This study assessed the feasibility of applying exponential data consistency conditions to rebinned pinhole projections for attenuation-map registration in pinhole cardiac SPECT.

Quantification of Tomographic Incompleteness in Cone-Beam Reconstruction.

For situations of cone-beam scanning where the measurements are incomplete, we propose a method to quantify the severity of the missing information at each voxel. This incompleteness metric is geometric; it uses only the relative locations of all cone-beam vertices with respect to the voxel in question, and does not apply global information such as the object extent or the pattern of incompleteness of other voxels. The values are non-negative, with zero indicating "least incompleteness," i.

Filtered-backprojection reconstruction for a cone-beam computed tomography scanner with independent source and detector rotations.

Purpose: A new cone-beam CT scanner for image-guided radiotherapy (IGRT) can independently rotate the source and the detector along circular trajectories. Existing reconstruction algorithms are not suitable for this scanning geometry. The authors propose and evaluate a three-dimensional (3D) filtered-backprojection reconstruction for this situation.

Data consistency conditions for truncated fanbeam and parallel projections.

Purpose: In image reconstruction from projections, data consistency conditions (DCCs) are mathematical relationships that express the overlap of information between ideal projections. DCCs have been incorporated in image reconstruction procedures for positron emission tomography, single photon emission computed tomography, and x-ray computed tomography (CT). Building on published fanbeam DCCs for nontruncated projections along a line, the authors recently announced new DCCs that can be applied to truncated parallel projections in classical (two-dimensional) image reconstruction.

Full data consistency conditions for cone-beam projections with sources on a plane.

Cone-beam consistency conditions (also known as range conditions) are mathematical relationships between different cone-beam projections, and they therefore describe the redundancy or overlap of information between projections. These redundancies have often been exploited for applications in image reconstruction. In this work we describe new consistency conditions for cone-beam projections whose source positions lie on a plane.

Centers and centroids of the cone-beam projection of a ball.

In geometric calibration of cone-beam (CB) scanners, point-like marker objects such as small balls are imaged to obtain positioning information from which the unknown geometric parameters are extracted. The procedure is sensitive to errors in the positioning information, and one source of error is a small bias which can occur in estimating the detector locations of the CB projections of the centers of the balls. We call these detector locations the center projections.

A local shift-variant Fourier model and experimental validation of circular cone-beam computed tomography artifacts.

Large field of view cone-beam computed tomography (CBCT) is being achieved using circular source and detector trajectories. These circular trajectories are known to collect insufficient data for accurate image reconstruction. Although various descriptions of the missing information exist, the manifestation of this lack of data in reconstructed images is generally nonintuitive.

Direct determination of geometric alignment parameters for cone-beam scanners.

This paper describes a comprehensive method for determining the geometric alignment parameters for cone-beam scanners (often called calibrating the scanners or performing geometric calibration). The method is applicable to x-ray scanners using area detectors, or to SPECT systems using pinholes or cone-beam converging collimators. Images of an alignment test object (calibration phantom) fixed in the field of view of the scanner are processed to determine the nine geometric parameters for each view.

Planogram rebinning with the frequency-distance relationship.

We present an efficient rebinning algorithm for positron emission tomography (PET) systems with panel detectors. The rebinning algorithm is derived in the planogram coordinate system which is the native data format for PET systems with panel detectors and is the 3-D extension of the 2-D linogram transform developed by Edholm. Theoretical error bounds and numerical results are included.

In vivo prompt gamma neutron activation analysis for the screening of boron-10 distribution in a rabbit knee: a simulation study.

Boron neutron capture synovectomy (BNCS) is under development as a potential treatment modality for rheumatoid arthritis (RA). RA is characterized by the inflammation of the synovium (the membrane lining articular joints), which leads to pain and a restricted range of motion. BNCS is a two-part procedure involving the injection of a boronated compound directly into the diseased joint followed by irradiation with a low-energy neutron beam.

Even more inversion formulas for the 2D Radon Transform of functions of compact and convex support.

In 2004, Clackdoyle and Noo published a class of inversion formulas for the 2D Radon Transform which depends on the known radius of support of the unknown function. In this work, we extend this class of inversion formulas from functions of circular support to functions with any compact and convex support. We point out the potential benefits of these new inversion formulas in the context of reconstruction from truncated projections.

Algebraic and analytic reconstruction methods for dynamic tomography.

In this work, we discuss algebraic and analytic approaches for dynamic tomography. We present a framework of dynamic tomography for both algebraic and analytic approaches. We finally present numerical experiments.

The effect of acquisition interval and spatial resolution on dynamic cardiac imaging with a stationary SPECT camera.

The current SPECT scanning paradigm that acquires images by slow rotation of multiple detectors in body-contoured orbits around the patient is not suited to the rapid collection of tomographically complete data. During rapid image acquisition, mechanical and patient safety constraints limit the detector orbit to circular paths at increased distances from the patient, resulting in decreased spatial resolution. We consider a novel dynamic rotating slant-hole (DyRoSH) SPECT camera that can collect full tomographic data every 2 s, employing three stationary detectors mounted with slant-hole collimators that rotate at 30 rpm.

Cone-beam reconstruction using the backprojection of locally filtered projections.

This paper describes a flexible new methodology for accurate cone beam reconstruction with source positions on a curve (or set of curves). The inversion formulas employed by this methodology are based on first backprojecting a simple derivative in the projection space and then applying a Hilbert transform inversion in the image space. The local nature of the projection space filtering distinguishes this approach from conventional filtered-backprojection methods.

A two-step Hilbert transform method for 2D image reconstruction.

The paper describes a new accurate two-dimensional (2D) image reconstruction method consisting of two steps. In the first step, the backprojected image is formed after taking the derivative of the parallel projection data. In the second step, a Hilbert filtering is applied along certain lines in the differentiated backprojection (DBP) image.

Normalizing projection images: a study of image normalizing procedures for single particle three-dimensional electron microscopy.

In the process of three-dimensional reconstruction of single particle biological macromolecules several hundreds, or thousands, of projection images are taken from tens or hundreds of independently digitized micrographs. These different micrographs show differences in the background grey level and particle contrast and, therefore, have to be normalized by scaling their pixel values before entering the reconstruction process. In this work several normalization procedures are studied using a statistical comparison framework.

Fast fully 3-D image reconstruction in PET using planograms.

We present a method of performing fast and accurate three-dimensional (3-D) backprojection using only Fourier transform operations for line-integral data acquired by planar detector arrays in positron emission tomography. This approach is a 3-D extension of the two-dimensional (2-D) linogram technique of Edholm. By using a special choice of parameters to index a line of response (LOR) for a pair of planar detectors, rather than the conventional parameters used to index a LOR for a circular tomograph, all the LORs passing through a point in the field of view (FOV) lie on a 2-D plane in the four-dimensional (4-D) data space.

Inversion of the 3D exponential x-ray transform for a half equatorial band and other semi-circular geometries.

This work presents new mathematical results on the inversion of the exponential x-ray transform. It is shown that a reconstruction formula can be obtained for any dataset whose projection directions consist of a union of half great circles on the unit sphere. A basic example of such a dataset is the semi-equatorial band.

Exact inversion of the exponential x-ray transform for rotating slant-hole (RSH) SPECT.

The RSH SPECT scanner provides parallel-beam attenuated projections for a fully 3D acquisition geometry. The geometry can be represented by circles on the unit sphere of projection directions, one circle for each position of the detector head. Unlike most other fully 3D geometries this one is particularly challenging because there are no 2D subsets in the data.

Image reconstruction from fan-beam projections on less than a short scan.

This work is concerned with 2D image reconstruction from fan-beam projections. It is shown that exact and stable reconstruction of a given region-of-interest in the object does not require all lines passing through the object to be measured. Complete (non-truncated) fan-beam projections provide sufficient information for reconstruction when 'every line passing through the region-of-interest intersects the vertex path in a non-tangential way'.