Reconstruction Algorithm for Fan Beam with a Displaced Center-of-Rotation

A convolutional backprojection algorithm is derived for a fan beam geometry that has its center-of-rotation displaced from the midline of the fan beam. In single photon emission computed tomography (SPECT), where a transaxial converging collimator is used with a rotating gamma camera, it is difficult to precisely align the collimator so that the mechanical center-of-rotation is colinear with the midline of the fan beam. A displacement of the center-of-rotation can also occur in X-ray CT when the X-ray source is mispositioned. Standard reconstruction algorithms which directly filter and backproject the fan beam data without rebinning into parallel beam geometry have been derived for a geometry having its center-of-rotation at the midline of the fan beam. However, in the case of a misalignment of the center-of-rotation, if these conventional reconstruction algorithms are used to reconstruct the fan beam projections, structured artifacts and a loss of resolution will result. We illustrate these artifacts with simulations and demonstrate how the news algorithm corrects for this misalignment. We also show a method to estimate the parameters of the fan beam geometry including the shift in the center-of-rotation.     

Single-slice rebinning reconstruction in spiral cone-beam computed tomography

At the advent of multislice computed tomography ICT) a variety of approximate cone-beam algorithms have been proposed suited for reconstruction of small cone-angle CT data in a spiral mode of operation. The goal of this study is to identify a practical and efficient approximate cone-beam method, extend its potential for medical use, and demonstrate its performance at medium cone-angles required for area detector CT. We will investigate two different approximate single-slice rebinning algorithms for cone-beam CT: the multirow Fourier reconstruction (MFR) and an extension of the advanced single-slice rebinning method (ASSR), which combines the idea of ASSR with a z-filtering approach. Thus, both algorithms, MFR and ASSR, are formulated in the framework of z-filtering using optimized spiral interpolation algorithms. In each view, X-ray samples to be used for reconstruction are identified, which describe an approximation to a virtual reconstruction plane. The performance of approximate reconstruction should improve as the virtual reconstruction plane better fits the spiral focus path. The image quality of the respective reconstruction will be assessed with respect to image artifacts, spatial resolution, contrast resolution, and image noise. It turns out that the ASSR method using tilted reconstruction planes is a practical and efficient algorithm, providing image quality comparable to that of a single-row scanning system even with a 46-row detector at a table feed of 64 mm. Both algorithms tolerate any table feed below the maximum value associated to the detector height. Due to the z-filter approach, all detector data sampled can be used for image reconstruction.     

A cone-beam filtered backprojection reconstruction algorithm for cardiac single photon emission computed tomography

A filtered backprojection reconstruction algorithm was developed for cardiac single photon emission computed tomography with cone-beam geometry. The algorithm reconstructs cone-beam projections collected from ;short scan' acquisitions of a detector traversing a noncircular planar orbit. Since the algorithm does not correct for photon attenuation, it is designed to reconstruct data collected over an angular range of slightly more than 180 degrees with the assumption that the range of angles is oriented so as not to acquire the highly attenuated posterior projections of emissions from cardiac radiopharmaceuticals. This sampling scheme is performed to minimize the attenuation artifacts that result from reconstructing posterior projections. From computer simulations, it is found that reconstruction of attenuated projections has a greater effect upon quantitation and image quality than any potential cone-beam reconstruction artifacts resulting from insufficient sampling of cone-beam projections. With nonattenuated projection data, cone beam reconstruction errors in the heart are shown to be small (errors of at most 2%).     

Artifact analysis and reconstruction improvement in helical cardiac cone beam CT

With the introduction of cone beam (CB) scanners, cardiac volumetric computed tomography (CT) imaging has the potential to become a noninvasive imaging tool in clinical routine for the diagnosis of various heart diseases. Heart rate adaptive reconstruction schemes enable the reconstruction of high-resolution volumetric data sets of the heart. Artifacts, caused by strong heart rate variations, high heart rates and obesity, decrease the image quality and the diagnostic value of the images. The image quality suffers from streak artifacts if suboptimal scan and reconstruction parameters are chosen, demanding improved gating techniques. In this paper, an artifact analysis is carried out which addresses the artifacts due to the gating when using a three-dimensional CB cardiac reconstruction technique. An automatic and patient specific cardiac weighting technique is presented in order to improve the image quality. Based on the properties of the reconstruction algorithm, several assessment techniques are introduced which enable the quantitative determination of the cycle-to-cycle transition smoothness and phase homogeneity of the image reconstruction. Projection data of four patients were acquired using a 16-slice CBCT system in low pitch helical mode with parallel electrocardiogram recording. For each patient, image results are presented and discussed in combination with the assessment criteria.     

Weighted backprojection approach to cone beam 3D projection reconstruction for truncated spherical detection geometry

A new analytical three-dimensional cone beam reconstruction algorithm is presented for truncated spherical detection geometry. The basic idea of the proposed algorithm is the formation of spatially invariant 3D blurred back-projected volumetric image by the use of the weighted backprojection of cone beam projection data and subsequent 3D filtering using an acceptance angle dependent rho filter. The backprojection weighting function is calculated on the basis of each given geometrical condition, i.e. detection geometry or degree of truncation, position of cone beam apex, and backprojection point. The proposed algorithm is derived analytically and is computationally efficient. Performance of the algorithm is evaluated by the reconstruction of 3D volumetric images using simulated data from arbitrarily truncated spherical detector geometries.     

A harmonic decomposition reconstruction algorithm for spatially varying focal length collimators

Spatially varying focal length fan-beam collimators can be used in single photon emission computed tomography to improve detection efficiency and to reduce reconstruction artifacts resulting from the truncation of projection data. It has been proven that there exists no convolution backprojection algorithm for this type of collimator, so a complicated interpolation between two nonparallel projection rays is necessary for existing algorithms. The interpolation may generate blurring and artifacts in the reconstructed images. Based on a harmonic decomposition technique and the translation property of Fourier series, a semifrequency resampling technique is proposed to avoid the above mentioned interpolations. By this technique, the harmonic decomposition of projection data for spatially varying focal length fan beam collimators has the same form as that for parallel-beam collimators in the semifrequency domain (Fourier transform with respect to angular variables only). An alternative version of the inverse Cormack transform is then proposed to reconstruct the images. The derived reconstruction algorithm was implemented in a Pentium II/266 PC computer. Numerical simulations demonstrated its efficiency (3 s for 128×128 reconstruction arrays) and its robust performance (compared to the existing algorithms)     

General reconstruction theory for multislice X-ray computed tomography with a gantry tilt

This paper discusses image reconstruction with a tilted gantry in multislice computed tomography (CT) with helical (spiral) data acquisition. The reconstruction problem with gantry tilt is shown to be transformable into the problem of reconstructing a virtual object from multislice CT data with no gantry tilt, for which various algorithms exist in the literature. The virtual object is related to the real object by a simple affine transformation that transforms the tilted helical trajectory of the X-ray source into a nontilted helix, and the real object can be computed from the virtual object using one-dimensional interpolation. However, the interpolation may be skipped since the reconstruction of the virtual object on a Cartesian grid provides directly nondistorted images of the real object on slices parallel to the tilted plane of the gantry. The theory is first presented without any specification of the detector geometry, then applied to the curved detector geometry of third-generation CT scanners with the use of Katsevich's formula for example. Results from computer-simulated data of the FORBILD thorax phantom are given in support of the theory.     

锥束CT去除环形伪影的方法研究

环状伪影是CT技术人员经常遇到的影响重建图像质量的一种伪影,造成环形伪影的因素很多,其中探测器缺陷引起的环形伪影最为常见。环形伪影表现在原始图像结构上是圆环或者是圆弧,理论认证发现探测器响应效率不一致,会使锥束三维CT重建结果产生环形伪影。环形伪影影响了CT图像的分析和后续处理,因此去除环形伪影显得非常具有使用价值。本...     

CT fan beam reconstruction with a nonstationary axis of rotation

To reconstruct an image using computed tomography (CT), the axis of rotation must pivot at the same point on the reconstruction plane that the X-ray source and the CT detector assembly rotate about around the imaged object. This pivot point is used as a reference point for backprojecting pixel values to their proper coordinates. Reconstructing an image with a nonstationary axis of rotation would backproject pixel values to incorrect coordinate points. A convolution filtered backprojection algorithm has been derived for correcting images that were acquired with a nonstationary axis of rotation using the fan beam geometry with a collinear (flat) detector. The correction method accounts for the vertical displacements of the axis of rotation as the CT scanner rotates around the imaged object, as may be the case when sagging occurs. Software simulations are performed to show how the algorithm corrects for the shift in the axis of rotation     

Free View Reconstruction of Three-Dimensional Integral Imaging Using Tilted Reconstruction Planes With Locally Nonuniform Magnification

In this paper, we present a method for three-dimensional (3D) free view computational volumetric reconstruction of integral imaging (II) on a tilted reconstruction plane with a locally nonuniform magnification ratio. The reconstruction plane of conventional free view II is parallel to the pickup device. Thus only the part of object parallel to the pickup device can be observed. To overcome this problem, the reconstruction plane could be tilted according to the viewing point by the “One Point Perspective Technique.” A reconstructed 3D image, using tilted reconstruction planes, can have more in-focus surfaces of the 3D object compared to using parallel reconstruction planes. To verify the proposed method, we generate the elemental images of the 3D object, reconstruct 3D images on both parallel and tilted reconstruction planes, and compare the results.      

基于小波变换的多分辨率锥束CT图像快速三维重建算法

为了解决FDK重建算法在锥束CT重建中运算量大,耗时较多,以及针对不同的应用环境提供不同分辨率的3维医学图像问题,该文提出一种基于小波变换的多分辨率锥束CT图像快速3维重建算法。首先对采集到的投影图像进行相应尺度的小波变换,得到各尺度小波分解系数,选择相应尺度的小波系数进行FDK重建,可以得到相应低分辨率的3维图像数据,还可根据需要由得到的低分辨率重建数据分别沿着径向取断层图像,进行相应的小波逆变换,进而得到高分辨率的3维图像数据。实验数据表明,该方法不仅能够得到不同分辨率的3维图像数据,而且相较于传统的FDK算法生成分辨率相同、精度相近的高分辨率3维图像数据,重建速度可以提高1倍以上。     

Algorithm for X-ray Scatter, Beam-Hardening, and Beam Profile Correction in Diagnostic (Kilovoltage) and Treatment (Megavoltage) Cone Beam CT

Quantitative reconstruction of cone beam X-ray computed tomography (CT) datasets requires accurate modeling of scatter, beam-hardening, beam profile, and detector response. Typically, commercial imaging systems use fast empirical corrections that are designed to reduce visible artifacts due to incomplete modeling of the image formation process. In contrast, Monte Carlo (MC) methods are much more accurate but are relatively slow. Scatter kernel superposition (SKS) methods offer a balance between accuracy and computational practicality. We show how a single SKS algorithm can be employed to correct both kilovoltage (kV) energy (diagnostic) and megavoltage (MV) energy (treatment) X-ray images. Using MC models of kV and MV imaging systems, we map intensities recorded on an amorphous silicon flat panel detector to water-equivalent thicknesses (WETs). Scattergrams are derived from acquired projection images using scatter kernels indexed by the local WET values and are then iteratively refined using a scatter magnitude bounding scheme that allows the algorithm to accommodate the very high scatter-to-primary ratios encountered in kV imaging. The algorithm recovers radiological thicknesses to within 9% of the true value at both kV and megavolt energies. Nonuniformity in CT reconstructions of homogeneous phantoms is reduced by an average of 76% over a wide range of beam energies and phantom geometries.      

Estimation of the heart respiratory motion with applications for cone beam computed tomography imaging: a simulation study

Computed tomography (CT) reconstruction methods assume imaging of static objects; object movement during projection data acquisition causes tomogram artifacts. The continuously moving heart, therefore, represents a complicated imaging case. The associated problems due to the heart beating can be overcome either by using very short projection acquisition times, during which the heart may be considered static, or by ECG-gated acquisition. In the latter case, however, the acquisition of a large number of projections may not be completed in a single breath hold, thus heart displacement occurs as an additional problem. This problem has been addressed by applying heart motion models in various respiratory motion compensation algorithms. Our paper focuses on cone beam computed tomography (CBCT), performed in conjunction with isocentric, fluoroscopic equipment, and continuous ECG and respiratory monitoring. Such equipment is used primarily for in-theater three-dimensional (3-D) imaging and benefits particularly from the recent developments in flat panel detector technologies. The objectives of this paper are: (i) to develop a model for the motion of the heart due to respiration during the respiratory cycle; (ii) to apply this model to the tomographic reconstruction algorithm, in order to account for heart movement due to respiration in the reconstruction; and (iii) to initially evaluate this method by means of simulation studies. Based on simulation studies, we were able to demonstrate that heart displacement due to respiration can be estimated from the same projection data, required for a CBCT reconstruction. Our paper includes semiautomatic segmentation of the heart on the X-ray projections and reconstruction of a convex 3-D-heart object that performs the same motion as the heart during respiration, and use of this information into the CBCT reconstruction algorithm. The results reveal significant image quality improvements in cardiac image reconstruction.     

An interior point iterative maximum-likelihood reconstruction algorithm incorporating upper and lower bounds with application to SPECT transmission imaging

The algorithm we consider here is a block-iterative (or ordered subset) version of the interior point algorithm for transmission reconstruction. Our algorithm is an interior point method because each vector of the iterative sequence [x(k)], k = 0, 1, 2, ... satisfies the constraints a(j) < x(j)k < b(j), j = 1, ..., J. Because it is a block-iterative algorithm that reconstructs the transmission attenuation map and places constraints above and below the pixel values of the reconstructed image, we call it the BITAB method. Computer simulations using the three-dimensional mathematical cardiac and torso phantom, reveal that the BITAB algorithm in conjunction with reasonably selected prior upper and lower bounds has the potential to improve the accuracy of the reconstructed attenuation coefficients from truncated fan beam transmission projections. By suitably selecting the bounds, it is possible to restrict the over estimation of coefficients outside the fully sampled region, that results from reconstructing truncated fan beam projections with iterative transmission algorithms such as the maximum-likelihood gradient type algorithm.     

Anti-aliased three-dimensional cone-beam reconstruction oflow-contrast objects with algebraic methods

This paper examines the use of the algebraic reconstruction technique (ART) and related techniques to reconstruct 3-D objects from a relatively sparse set of cone-beam projections. Although ART has been widely used for cone-beam reconstruction of high-contrast objects, e.g., in computed angiography, the work presented here explores the more challenging low-contrast case which represents a little-investigated scenario for ART. Preliminary experiments indicate that for cone angles greater than 20 degrees, traditional ART produces reconstructions with strong aliasing artifacts. These artifacts are in addition to the usual off-midplane inaccuracies of cone-beam tomography with planar orbits. We find that the source of these artifacts is the nonuniform reconstruction grid sampling and correction by the cone-beam rays during the ART projection-backprojection procedure. A new method to compute the weights of the reconstruction matrix is devised, which replaces the usual constant-size interpolation filter by one whose size and amplitude is dependent on the source-voxel distance. This enables the generation of reconstructions free of cone-beam aliasing artifacts, at only little extra cost. An alternative analysis reveals that simultaneous ART (SART) also produces reconstructions without aliasing artifacts, however, at greater computational cost. Finally, we thoroughly investigate the influence of various ART parameters, such as volume initialization, relaxation coefficient lambda, correction scheme, number of iterations, and noise in the projection data on reconstruction quality. We find that ART typically requires only three iterations to render satisfactory reconstruction results.     

Attenuation compensation of cone beam SPECT images using maximum likelihood reconstruction

Attenuation compensation for cone beam single-photon emission computed tomography (SPECT) imaging is performed by cone beam maximum likelihood reconstruction with attenuation included in the transition matrix. Since the transition matrix is too large to be stored in conventional computers, the E-M maximum likelihood estimator is implemented with a ray-tracing algorithm, efficiently recalculating each matrix element as needed. The method was applied and tested in both uniform and nonuniform density phantoms. Test projections sets were obtained from Monte Carlo simulations and experiments using a commercially available cone beam collimator. For representative regions of interest. reconstruction of a uniform sphere is accurate to within 3% throughout, in comparison to a reference image simulated and reconstructed without attenuation. High- and low-activity regions in a uniform density are reconstructed accurately, except that low-activity regions in a more active background have a small error. This error is explainable by the nonnegativity constraints of the E-M estimator and the image statistical noise     

一种改善被动毫米波重建图像质量的方法

凸集投影(POCS)算法是一种广泛使用的超分辨率图像重建方法.针对常规POCS算法收敛速度慢、存在边缘震荡效应的问题,论文结合被动毫米波图像降质模型,提出了一种用于被动毫米波图像超分辨率重建方法.该方法有效利用图像的边缘信息,根据不同的区域选择相应的松弛算子,同时建立边缘约束集来保证边缘图像的尖锐性.实验结果表明.在有效消除边缘震荡效应的同时提高了收敛速度,适用于被动毫米波图像的超分辨率处理.     

Suppression of Metal Artifacts in CT Using a Reconstruction Procedure That Combines MAP and Projection Completion

Metal implants such as hip prostheses and dental fillings produce streak and star artifacts in the reconstructed computed tomography (CT) images. Due to these artifacts, the CT image may not be diagnostically usable. A new reconstruction procedure is proposed that reduces the streak artifacts and that might improve the diagnostic value of the CT images. The procedure starts with a maximum a posteriori (MAP) reconstruction using an iterative reconstruction algorithm and a multimodal prior. This produces an artifact-free constrained image. This constrained image is the basis for an image-based projection completion procedure. The algorithm was validated on simulations, phantom and patient data, and compared with other metal artifact reduction algorithms.      

Fourier rebinning applied to multiplanar circular-orbit cone-beam SPECT

We study the application of Fourier rebinning methods to dual-planar cone-beam SPECT. Dual-planar cone-beam SPECT involves the use of a pair of dissimilar cone-beam collimators on a dual-camera SPECT system. Each collimator has its focus in a different axial plane. While dual-planar data is best reconstructed with fully three-dimensional (3-D) iterative methods, these methods are slow and have prompted a search for faster reconstruction techniques. Fourier rebinning was developed to estimate equivalent parallel projections from 3-D PET data, but it simply expresses a relationship between oblique projections taken in planes not perpendicular to the axis of rotation and direct projections taken in those that are. We find that it is possible to put cone-beam data in this context as well. The rebinned data can then be reconstructed using either filtered backprojection (FBP) or parallel iterative algorithms such as OS-EM. We compare the Feldkamp algorithm and fully 3-D OSEM reconstruction with Fourier-rebinned reconstructions on realistically-simulated Tc-99m HMPAO brain SPECT data. We find that the Fourier-rebinned reconstructions exhibit much less image noise and lower variance in region-of-interest (ROI) estimates than Feldkamp. Also, Fourier-rebinning followed by OSEM with nonuniform attenuation correction exhibits less bias in ROI estimates than Feldkamp with Chang attenuation correction. The Fourier-rebinned ROI estimates exhibit bias and variance comparable to those from fully 3-D OSEM and require considerably less processing time. However, in areas off the axis of rotation, the axial-direction resolution of FORE-reconstructed images is poorer than that of images reconstructed with 3-D OSEM. We conclude that Fourier rebinning is a practical and potentially useful approach to reconstructing data from dual-planar circular-orbit cone-beam systems.     

Sparse‐View CT Image Recovery Using Two‐Step Iterative Shrinkage‐Thresholding Algorithm

We investigate an image recovery method for sparse‐view computed tomography (CT) using an iterative shrinkage algorithm based on a second‐order approach. The two‐step iterative shrinkage‐thresholding (TwIST) algorithm including a total variation regularization technique is elucidated to be more robust than other first‐order methods; it enables a perfect restoration of an original image even if given only a few projection views of a parallel‐beam geometry. We find that the incoherency of a projection system matrix in CT geometry sufficiently satisfies the exact reconstruction principle even when the matrix itself has a large condition number. Image reconstruction from fan‐beam CT can be well carried out, but the retrieval performance is very low when compared to a parallel‐beam geometry. This is considered to be due to the matrix complexity of the projection geometry. We also evaluate the image retrieval performance of the TwIST algorithm using measured projection data.