Respiratory compensation in projection imaging using a magnification and displacement model

Respiratory motion during the collection of computed tomography (CT) projections generates structured artifacts and a loss of resolution that can render the scans unusable. This motion is problematic in scans of those patients who cannot suspend respiration, such as the very young or intubated patients. Here, the authors present an algorithm that can be used to reduce motion artifacts in CT scans caused by respiration. An approximate model for the effect of respiration is that the object cross section under interrogation experiences time-varying magnification and displacement along two axes. Using this model an exact filtered backprojection algorithm is derived for the case of parallel projections. The result is extended to generate an approximate reconstruction formula for fan-beam projections. Computer simulations and scans of phantoms on a commercial CT scanner validate the new reconstruction algorithms for parallel and fan-beam projections. Significant reduction in respiratory artifacts is demonstrated clinically when the motion model is satisfied. The method can be applied to projection data used in CT, single photon emission computed tomography (SPECT), positron emission tomography (PET), and magnetic resonance imaging (MRI).     

Feldkamp-type cone-beam tomography in the wavelet framework

X-ray computed tomography (CT) is in transition from fan-beam to cone-beam geometry. For cone-beam volumetric imaging, reduction of radiation exposure remains an important issue. Because the wavelet approach was shown to be effective and flexible for two-dimensional (2-D) local region reconstruction, we are motivated to perform wavelet local CT in cone-beam geometry. In this paper, we formulate the Feldkamp cone-beam reconstruction from the wavelet perspective, derive both full-scan and half-scan Feldkamp-type formulas for either global or local reconstruction, and demonstrate the feasibility and utility in synthetic and real data. It is found that using the wavelet Feldkamp approach, a three-dimensional (3-D) region of interest (ROI) can be reconstructed with neither severe image artifacts nor any significant constant bias in our simulation and experiments.     

Direct fourier reconstruction in fan-beam tomography

We consider the problem of reconstructing tomographic imagery from fan-beam projections using the direct Fourier method (DFM). Previous DFM reconstructions from parallel-beam projections produced images of quality comparable to that of filtered convolution back-projection. Moreover, the number of operations using DFM in the parallel-beam case is proportional to N2 log N versus N3 for back projection [3]. The fan-beam case is more complicated because additional interpolation of the nonuniformly spaced rebinned data is required. We derive bounds on the detector spacing in fan-beam CT that enable direct Fourier reconstruction and describe the full algorithm necessary for processing the fan-beam data. The feasibility of the method is demonstrated with an example. A key result of this paper is that high-quality imagery can be reconstructed from fan-beam data using the DFM in 0 (N2 log N) operations.     

光CT的扇束投影重排方法及投影几何分析

在工业过程监控中,由于被测物理过程的发生时间短,因此光CT装置将不可能象医学CT那样有充足的时间进行"静态"成像,而是必须进行实时性较高的"动态"成像(或称为流动成像).其制约是光线扫描的投影视角和投影数量都不可能太多.根据这一情况,在医学CT中常用的一些图像重建算法如反投影法、滤波反投影法和投影重排方法都必须加以改进才能引用.为此,本文研究扇束投影重排方法在光学流动成像中的应用可行性,分析其计算方法和步骤,并确定光线扇束结构中的光源个数、扇形张角和探测器个数之间的约束关系,同时也分析了内插精度对图像质量的影响.在数值模拟实验中,将投影重排方法与反投影法的重建图象进行了比较,进一步评判本文方法的图象质量和成像实时性等方面的性能.     

A fast sinc function gridding algorithm for fourier inversion in computer tomography

The Fourier inversion method for reconstruction of images in computerized tomography has not been widely used owing to the perceived difficulty of interpolating from polar or other measurement grids to the Cartesian grid required for fast numerical Fourier inversion. Although the Fourier inversion method is recognized as being computationally faster than the back-projection method for parallel ray projection data, the artifacts resulting from inaccurate interpolation have generally limited application of the method. This paper presents a computationally efficient gridding algorithm which can be used with direct Fourier transformation to achieve arbitrarily small artifact levels. The method has potential for application to other measurement geometries such as fan-beam projections and diffraction tomography and NMR imaging.     

Reconstruction From Uniformly Attenuated SPECT Projection Data Using the DBH Method

An algorithm was developed for the 2-D reconstruction of truncated and nontruncated uniformly attenuated data acquired from single photon emission computed tomography (SPECT). The algorithm is able to reconstruct data from half-scan (180$^{circ}$ ) and short-scan (180$^{circ}$ +fan angle) acquisitions for parallel- and fan-beam geometries, respectively, as well as data from full-scan (360 $^{circ}$) acquisitions. The algorithm is a derivative, backprojection, and Hilbert transform (DBH) method, which involves the backprojection of differentiated projection data followed by an inversion of the finite weighted Hilbert transform. The kernel of the inverse weighted Hilbert transform is solved numerically using matrix inversion. Numerical simulations confirm that the DBH method provides accurate reconstructions from half-scan and short-scan data, even when there is truncation. However, as the attenuation increases, finer data sampling is required.      

Reordering Schemes for Multiple-Rotation Fan-Beam CT Scanner

The number of detectors in a fan-beam CT scanner can be substantially decreased if a multiple-rotation data collection mode is used to provide appropriate spatial resolution. The efficiency of multiple-rotation schemes using a detector offset combined with angular shift of the detectors in each cycle for projection space filling is examined. It is shown that in reordering into parallel projections, angular interpolation can be avoided if an appropriate angular offset of the source with respect to the axis of a fan can be made in each cycle. To achieve even spacing of rays at the ends of the reordered parallel projections, the shifted positions of each detector must be symmetrical with respect to the position of the detector in the original symmetric fan. Results of the computer simulation are presented.     

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.     

Adaptive model-based motion estimation

A general discrete-time, adaptive, multidimensional framework is introduced for estimating the motion of one or several object features from their successive nonlinear projections on an image plane. The motion model consists of a set of linear difference equations with parameters estimated recursively from a nonlinear observation equation. The model dimensionality corresponds to that of the original, nonprojected motion space, thus allowing to compensate for variable projection characteristics such as paning and zooming of the camera. Extended recursive least-squares and linear-quadratic tracking algorithms are used to adaptively adjust the model parameters and minimize the errors of either smoothing, filtering or prediction of the object trajectories in the projection plane. Both algorithms are derived using a second order approximation of the projection nonlinearities. All the results presented here use a generalized vectorial notation suitable for motion estimation of any finite number of object features and various approximations of the nonlinear projection. The application of the model-based motion estimator for temporal decimation/interpolation in digital video sequence compression systems is presented.     

A Method for Stop-Action Imaging of the Heart Using Gated Computed Tomography

A new method for the reconstruction of limited angle projection data in rotary fan-beam X-ray computed tomography (CT) is presented. Missing views resulting from ECG-gated cardiac CT are estimated, and the standard fan-beam reconstruction algorithm is used to convolve and backproject both measured and estimated views. The estimation of the missing views takes place in three stages: first, the projection data is augmented by incorporating into each missing view the line integrals that do not pass through the heart, and which otherwise would be considered missing due to ECG-gating; second, line integrals corresponding to source positions in the range 180°±fan angle away from missing view angles are reflected; third, those line integrals that remain missing are estimated by interpolation. This method has been applied to ECG-gated cardiac imaging in dogs without requiring extensive interpolation; end-systolic and end-diastolic images were generated with short-interval gating (?cycle) and total scan time (breath holding period) of 12 s. An important advantage of this method over other proposed limited angle reconstruction techniques is that it uses the existing fan-beam convolution-backprojection algorithm for image reconstruction.     

基于Mean Shift和插值图像修复算法的CT图像金属伪影消除方法

近年来CT成像技术在临床医学中广泛应用,但当病人体内含有金属移植物时,由于射线硬化等原因很可能在金属物体周围产生亮暗伪影,降低图像质量,影响诊断的准确性.为了消除CT图像中的金属伪影,本文提出基于Mean Shift和插值图像修复的算法,基本流程为用自适应Mean Shift算法预处理CT图像,平滑噪声和轻度伪影,用简化的Mean Shift算法快速精确分割金属物体,由修复组织信息的插值图像生成先验图像,用先验图像的投影数据替换原投影数据得到校正后的CT图像.经过对比实验,文中算法在去除金属伪影的同时,能够保护原有CT图像的组织结构,取得了更好的处理效果.     

Reconstruction of three-dimensional coronary arterial dynamics from multi-view angiogram sequences

Since actual cardiac and arterial motion is non-rigidand non-uniformbothin space andinti me[1],the quan-tification of dynamic 3-Dcurves with 2-D projections isinaccurate and sensitive to view angles . Ruan[2]andPuentes[3]reconstructed 3-D arterial centerl…     

MRI artifact cancellation due to rigid motion in the imaging plane

A post-processing technique has been developed to suppress the magnetic resonance imaging (MRI) artifact arising from object planar rigid motion. In two-dimensional Fourier transform (2-DFT) MRI, rotational and translational motions of the target during magnetic resonance magnetic resonance (MR) scan respectively impose nonuniform sampling and a phase error an the collected MRI signal. The artifact correction method introduced considers the following three conditions: (1) for planar rigid motion with known parameters, a reconstruction algorithm based on bilinear interpolation and the super-position method is employed to remove the MRI artifact, (2) for planar rigid motion with known rotation angle and unknown translational motion (including an unknown rotation center), first, a super-position bilinear interpolation algorithm is used to eliminate artifact due to rotation about the center of the imaging plane, following which a phase correction algorithm is applied to reduce the remaining phase error of the MRI signal, and (3) to estimate unknown parameters of a rigid motion, a minimum energy method is proposed which utilizes the fact that planar rigid motion increases the measured energy of an ideal MR image outside the boundary of the imaging object; by using this property all unknown parameters of a typical rigid motion are accurately estimated in the presence of noise. To confirm the feasibility of employing the proposed method in a clinical setting, the technique was used to reduce unknown rigid motion artifact arising from the head movements of two volunteers.     

Use of three-dimensional Gaussian interpolation in the projector/backprojector pair of iterative reconstruction for compensation of known rigid-body motion in SPECT

Due to the extended imaging times employed in single photon emission computed tomography (SPECT) and positron emission tomography (PET), patient motion during imaging is a common clinical occurrence. The fast and accurate correction of the three-dimensional (3-D) translational and rotational patient motion in iterative reconstruction is thus necessary to address this important cause of artifacts. We propose a method of incorporating 3-D Gaussian interpolation in the projector/backprojector pair to facilitate compensation for rigid-body motion in addition to attenuation and distance-dependent blurring. The method works as the interpolation step for moving the current emission voxel estimates and attenuation maps in the global coordinate system to the new patient location in the rotating coordinate system when calculating the expected projection. It also is employed for moving back the backprojection of the ratio of the measured projection to the expected projection and backprojection of the unit value (sensitivity factor) to the original location. MCAT simulations with known six-degree-of-freedom (6DOF) motion were employed to evaluate the accuracy of our method of motion compensation. We also tested the method with acquisitions of the data spectrum anthropomorphic phantom where motion during SPECT acquisition was measured using the Polaris IR motion tracking system. No motion artifacts were seen on the reconstructions with the motion compensation.     

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)     

Comparison of Analytic and Algebraic Methods for Motion-Compensated Cone-Beam CT Reconstruction of the Thorax

Respiratory motion is a major concern in cone-beam (CB) computed tomography (CT) of the thorax. It causes artifacts such as blur, streaks, and bands, in particular when using slow-rotating scanners mounted on the gantry of linear accelerators. In this paper, we compare two approaches for motion-compensated CBCT reconstruction of the thorax. The first one is analytic; it is heuristically adapted from the method of Feldkamp, Davis, and Kress (FDK). The second one is algebraic: the system of linear equations is generated using a new algorithm for the projection of deformable volumes and solved using the simultaneous algebraic reconstruction technique (SART). For both methods, we propose to estimate the motion on patient data using a previously acquired 4-D CT image. The methods were tested on two digital and one mechanical motion-controlled phantoms and on a patient dataset. Our results indicate that the two methods correct most motion artifacts. However, the analytic method does not fully correct streaks and bands even if the motion is perfectly estimated due to the underlying approximation. In contrast, the algebraic method allows us full correction of respiratory-induced artifacts.     

A backprojection filtering algorithm for a spatially varying focal length collimator

Fan-beam collimators are used in single photon emission computed tomography to improve the sensitivity for imaging of small organs. The disadvantage of fan-beam collimation is the truncation of projection data surrounding the organ of interest or, in those cases of imaging large patients, of the organ itself producing reconstruction artifacts. A spatially varying focal length fan-beam collimator has been proposed to eliminate the truncation problem and to maintain good sensitivity for the organ of interest. The collimator is constricted so that the focal lengths of the holes vary across the face of the collimator with the shortest focal lengths at the center and the longer focal lengths at the periphery of the collimator. The variation of the focal length can have various functional forms but in the authors' work it is assumed to increase monotonically toward the edge of the collimator. A backprojection filtering reconstruction algorithm is derived for this type of collimation. The algorithm first backprojects the projections, then performs a two-dimensional filtering. The algorithm is efficient and has been tested via computer simulations.     

Reducing frequency-domain artifacts of binary image due to coarse sampling by repeated interpolation and smoothing of Radon projections

We develop a method to calculate 2D spectrum of a binary image with better quality than that obtained via direct 2D-FFT. With FFT, jagged edges of objects due to coarse sampling introduce artifacts into the frequency domain, especially in the high-frequency area. With the proposed method, Radon projections of the binary image along lines at different viewing angles are calculated. Each projection is extended by interpolation, then smoothed and decimated. The interpolation–smoothing–decimation operation is repeated several times to reduce ruggedness and improve quality of the Radon projections considerably. One-dimensional FFT of each refined Radon projection is calculated, resulting in a set of frequency-domain samples distributed on a polar coordinate system. These samples are interpolated onto a Cartesian grid to give the required 2D spectrum of the sampled binary image. Numerical computations on several objects show that the method can provide significant improvement to the spectrum as compared with direct 2D-FFT.     

Multislice helical CT: image temporal resolution

A multislice helical computed tomography (CT) halfscan (HS) reconstruction algorithm is proposed for cardiac applications. The imaging performances (in terms of the temporal resolution, z-axis resolution, image noise, and image artifacts) of the HS algorithm are compared to the existing algorithms using theoretical models and clinical data. A theoretical model of the temporal resolution performance (in terms of the temporal sensitivity profile) is established for helical CT, in general, i.e., for any number of detector rows and any reconstruction algorithm used. It is concluded that the HS reconstruction results in improved image temporal resolution than the corresponding 180 degrees LI (linear interpolation) reconstruction and is more immune to the inconsistent data problem induced by cardiac motions. The temporal resolution of multislice helical CT with the HS algorithm is comparable to that of single-slice helical CT with the HS algorithm. In practice, the 180 degrees LI and HS-LI algorithms can be used in parallel to generate two image sets from the same scan acquisition, one (180 degrees LI) for improved z-resolution and noises, and the other (HS-LI) for improved image temporal resolution.     

X-ray CT metal artifact reduction using wavelets: an application for imaging total hip prostheses

Traditional computed tomography (CT) reconstructions of total joint prostheses are limited by metal artifacts from corrupted projection data. Published metal artifact reduction methods are based on the assumption that severe attenuation of X-rays by prostheses renders corresponding portions of projection data unavailable, hence the "missing" data are either avoided (in iterative reconstruction) or interpolated (in filtered backprojection with data completion; typically, with filling data "gaps" via linear functions). In this paper, we propose a wavelet-based multiresolution analysis method for metal artifact reduction, in which information is extracted from corrupted projection data. The wavelet method improves image quality by a successive interpolation in the wavelet domain. Theoretical analysis and experimental results demonstrate that the metal artifacts due to both photon starving and beam hardening can be effectively suppressed using our method. As compared to the filtered backprojection after linear interpolation, the wavelet-based reconstruction is significantly more accurate for depiction of anatomical structures, especially in the immediate neighborhood of the prostheses. This superior imaging precision is highly advantageous in geometric modeling for fitting hip prostheses.