Noise characteristics for cone beam collimators: a comparison with parallel hole collimator

In order to evaluate the properties of a cone beam (CB) collimator and three-dimensional filtered backprojection algorithm, the noise characteristics of this collimator configuration were determined and comparisons with a parallel hole (PH) collimator were made. Noise characteristics were evaluated using two approaches: the first consisted of assessing the magnitude of local random fluctuations in the reconstructed images, and the second consisted of assessing the noise texture in these images in the frequency domain by evaluating the noise power spectrum. Data used for these measurements were simulated using Monte Carlo models of SPECT systems equipped with cone beam and parallel hole collimators. Finally, to compare experimentally a specially designed high resolution CB collimator with a high resolution (HRES) PH collimator, measurements of a physical phantom were performed. Results of our studies show better noise magnitude for CB collimators; however, for CB collimators with short focal lengths (40-60 cm) the shape of %RMS noise distributions differs from slice to slice.     

X-ray scatter correction algorithm for cone beam CT imaging

Developing and optimizing an x-ray scatter control and reduction technique is one of the major challenges for cone beam computed tomography (CBCT) because CBCT will be much less immune to scatter than fan-beam CT. X-ray scatter reduces image contrast, increases image noise and introduces reconstruction error into CBCT. To reduce scatter interference, a practical algorithm that is based upon the beam stop array technique and image sequence processing has been developed on a flat panel detector-based CBCT prototype scanner. This paper presents a beam stop array-based scatter correction algorithm and the evaluation results through phantom studies. The results indicate that the beam stop array-based scatter correction algorithm is practical and effective to reduce and correct x-ray scatter for a CBCT imaging task.     

Spatial resolution properties in cone beam CT: a simulation study

This work is intended to investigate the spatial resolution properties in cone beam CT by estimating the point spread functions (PSFs) in the reconstructed 3D images through simulation. The point objects were modeled as 3D delta functions. Their projections onto the detector plane were analytically derived and blurred with 2D PSFs estimated and used to represent the detector and focal spot blurring effects. The 2D PSF for detector blurring was computed from the line spread function measured for a typical a-Si/CsI flat panel detector used for general radiography. The focal spot blurring effect was simulated for an x-ray source with a nominal focal spot size of 0.6 mm and 1.33 x magnification at the rotating center. Projection images were computed and sampled with an interval significantly smaller than the detector pixel size to avoid aliasing. Images were reconstructed using the Feldkamp algorithm with the five different filter functions. Reconstructed PSFs were plotted and analyzed to investigate the effects of detector blurring alone, focal spot blurring alone, or a combination of the two on the PSFs and their variations with the radial distance and z-level. Effects of binning and reconstruction filters were also studied. Our results show that the PSFs due to detector blurring are largely symmetric and vary little with the locations of the point objects. With focal spot blurring only or added to detector blurring, the PSFs along the rotation axis were largely symmetric but became increasingly asymmetric as the point objects were moved away from the rotation axis. The PSFs were found to become wider in the axial (anode to cathode) direction as the objects were moved toward the cathode side. The 3D PSFs may be approximated by an ellipsoid with three different axial lengths. They were found to point upright along the rotating axis but tilt toward the rotating axis as the point object was moved away from the axis.     

Respiratory correlated cone beam CT

A cone beam computed tomography (CBCT) scanner integrated with a linear accelerator is a powerful tool for image guided radiotherapy. Respiratory motion, however, induces artifacts in CBCT, while the respiratory correlated procedures, developed to reduce motion artifacts in axial and helical CT are not suitable for such CBCT scanners. We have developed an alternative respiratory correlated procedure for CBCT and evaluated its performance. This respiratory correlated CBCT procedure consists of retrospective sorting in projection space, yielding subsets of projections that each corresponds to a certain breathing phase. Subsequently, these subsets are reconstructed into a four-dimensional (4D) CBCT dataset. The breathing signal, required for respiratory correlation, was directly extracted from the 2D projection data, removing the need for an additional respiratory monitor system. Due to the reduced number of projections per phase, the contrast-to-noise ratio in a 4D scan reduced by a factor 2.6-3.7 compared to a 3D scan based on all projections. Projection data of a spherical phantom moving with a 3 and 5 s period with and without simulated breathing irregularities were acquired and reconstructed into 3D and 4D CBCT datasets. The positional deviations of the phantoms center of gravity between 4D CBCT and fluoroscopy were small: 0.13 +/- 0.09 mm for the regular motion and 0.39 +/- 0.24 mm for the irregular motion. Motion artifacts, clearly present in the 3D CBCT datasets, were substantially reduced in the 4D datasets, even in the presence of breathing irregularities, such that the shape of the moving structures could be identified more accurately. Moreover, the 4D CBCT dataset provided information on the 3D trajectory of the moving structures, absent in the 3D data. Considerable breathing irregularities, however, substantially reduces the image quality. Data presented for three different lung cancer patients were in line with the results obtained from the phantom study. In conclusion, we have successfully implemented a respiratory correlated CBCT procedure yielding a 4D dataset. With respiratory correlated CBCT on a linear accelerator, the mean position, trajectory, and shape of a moving tumor can be verified just prior to treatment. Such verification reduces respiration induced geometrical uncertainties, enabling safe delivery of 4D radiotherapy such as gated radiotherapy with small margins.     

Helical cardiac cone beam CT reconstruction with large area detectors: a simulation study

Retrospectively gated cardiac volume CT imaging has become feasible with the introduction of heart rate adaptive cardiac CT reconstruction algorithms. The development in detector technology and the rapid introduction of multi-row detectors has demanded reconstruction schemes which account for the cone geometry. With the extended cardiac reconstruction (ECR) framework, the idea of approximate helical cone beam CT has been extended to be used with retrospective gating, enabling heart rate adaptive cardiac cone beam reconstruction. In this contribution, the ECR technique is evaluated for systems with an increased number of detector rows, which leads to larger cone angles. A simulation study has been carried out based on a 4D cardiac phantom consisting of a thorax model and a dynamic heart insert. Images have been reconstructed for different detector set-ups. Reconstruction assessment functions have been calculated for the detector set-ups employing different rotation times, relative pitches and heart rates. With the increased volume coverage of large area detector systems, low-pitch scans become feasible without resulting in extensive scan times, inhibiting single breath hold acquisitions. ECR delivers promising image results when being applied to systems with larger cone angles.     

Helical cone beam CT with an asymmetrical detector

If a multislice or other area detector is shifted to one side to cover a larger field of view, then the data are truncated on one side. We propose a method to restore the missing data in helical cone-beam acquisitions that uses measured data on the longer side of the asymmetric detector array. The method is based on the idea of complementary rays, which is well known in fan beam geometry; in this paper we extend this concept to the cone-beam case. Different cases of complementary data coverage and dependence on the helical pitch are considered. The proposed method is used in our prototype 16-row CT scanner with an asymmetric detector and a 700 mm field of view. For evaluation we used scanned body phantom data and computer-simulated data. To simulate asymmetric truncation, the full, symmetric datasets were truncated by dropping either 22.5% or 45% from one side of the detector. Reconstructed images from the prototype scanner with the asymmetrical detector show excellent image quality in the extended field of view. The proposed method allows flexible helical pitch selection and can be used with overscan, short-scan, and super-short-scan reconstructions.     

Development and validation of a hybrid simulation technique for cone beam CT: application to an oral imaging system

This paper proposes a hybrid technique to simulate the complete chain of an oral cone beam computed tomography (CBCT) system for the study of both radiation dose and image quality. The model was developed around a 3D Accuitomo 170 unit (J Morita, Japan) with a tube potential range of 60-90 kV. The Monte Carlo technique was adopted to simulate the x-ray generation, filtration and collimation. Exact dimensions of the bow-tie filter were estimated iteratively using experimentally acquired flood images. Non-flat radiation fields for different exposure settings were mediated via 'phase spaces'. Primary projection images were obtained by ray tracing at discrete energies and were fused according to the two-dimensional energy modulation templates derived from the phase space. Coarse Monte Carlo simulations were performed for scatter projections and the resulting noisy images were smoothed by Richardson-Lucy fitting. Resolution and noise characteristics of the flat panel detector were included using the measured modulation transfer function (MTF) and the noise power spectrum (NPS), respectively. The Monte Carlo dose calculation was calibrated in terms of kerma free-in-air about the isocenter, using an ionization chamber, and was subsequently validated by comparison against the measured air kerma in water at various positions of a cylindrical water phantom. The resulting dose discrepancies were found <10% for most cases. Intensity profiles of the experimentally acquired and simulated projection images of the water phantom showed comparable fractional increase over the common area as changing from a small to a large field of view, suggesting that the scatter was accurately accounted. Image validation was conducted using two small phantoms and the built-in quality assurance protocol of the system. The reconstructed simulated images showed high resemblance on contrast resolution, noise appearance and artifact pattern in comparison to experimentally acquired images, with <5% difference for voxel values of the aluminum and air insert regions and <3% difference for voxel uniformity across the homogeneous PMMA region. The detector simulation by use of the MTF and NPS data exhibited a big influence on noise and the sharpness of the resulting images. The hybrid simulation technique is flexible and has wide applicability to CBCT systems.     

Three-dimensional SPECT reconstruction of combined cone beam and parallel beam data.

Single photon emission computed tomography (SPECT) using cone beam (CB) collimation exhibits increased sensitivity compared with acquisition geometries using parallel (P) hole collimation. However, CB collimation has a smaller field-of-view which may result in truncated projections and image artifacts. A primary objective of this work is to investigate maximum likelihood-expectation maximization (ML-EM) methods to reconstruct simultaneously acquired parallel and cone beam (P&CB) SPECT data. Simultaneous P&CB acquisition can be performed with commercially available triple camera systems by using two cone-beam collimators and a single parallel-hole collimator. The loss in overall sensitivity (relative to the use of three CB collimators) is about 15 to 20%. We have developed three methods to combine P&CB data using modified ML-EM algorithms. The first method consists of using both data sets to reconstruct a single intermediate image after each iteration using the ML-EM algorithm. The other two iterative algorithms combine intermediate parallel beam (PB) and CB source estimates to enhance image quality. For these methods, a PB estimate and a CB estimate are obtained for the first iteration. The second method consists of summing the PB and CB estimates for each subsequent iteration to obtain new PB and CB estimates. The third method is similar to the second method, with the exception that the new PB estimate simply is set equal to the PB estimate after each iteration. The combined source estimate is used in each subsequent iteration step of the EM algorithm. These algorithms are evaluated using projection data simulated using a Monte Carlo SPECT model. The P&CB SPECT images demonstrate marked improvement as compared with the CB-only reconstruction, particularly when the projections are truncated.     

An iterative approach to the beam hardening correction in cone beam CT

In computed tomography (CT), the beam hardening effect has been known to be one of the major sources of deterministic error that leads to inaccuracy and artifact in the reconstructed images. Because of the polychromatic nature of the x-ray source used in CT and the energy-dependent attenuation of most materials, Beer's law no longer holds. As a result, errors are present in the acquired line integrals or measurements of the attenuation coefficients of the scanned object. In the past, many studies have been conducted to combat image artifacts induced by beam hardening. In this paper, we present an iterative beam hardening correction approach for cone beam CT. An algorithm that utilizes a tilted parallel beam geometry is developed and subsequently employed to estimate the projection error and obtain an error estimation image, which is then subtracted from the initial reconstruction. A theoretical analysis is performed to investigate the accuracy of our methods. Phantom and animal experiments are conducted to demonstrate the effectiveness of our approach.     

Focused beam-stop array for the measurement of scatter in megavoltage portal and cone beam CT imaging

We describe a focused beam-stop array (BSA) for the measurement of object scatter in imaging systems that utilize x-ray beams in the megavoltage (MV) energy range. The BSA consists of 64 doubly truncated tungsten cone elements of 0.5 cm maximum diameter that are arranged in a regular array on an acrylic slab. The BSA is placed in the accessory tray of a medical linear accelerator at a distance of approximately 50 cm from the focal spot. We derive an expression that allows us to estimate the scatter in an image taken without the array present, given image values in a second image with the array in place. The presence of the array reduces fluence incident on the imaged object. This leads to an object-dependent underestimation bias in the scatter measurements. We apply corrections in order to address this issue. We compare estimates of the flat panel detector response to scatter obtained using the BSA to those derived from Monte Carlo simulations. We find that the two estimates agree to within 10% in terms of RMS error for 30 cm x 30 cm water slabs in the thickness range of 10-30 cm. Larger errors in the scatter estimates are encountered for thinner objects, probably owing to extrafocal radiation sources. However, RMS errors in the estimates of primary images are no more than 5% for water slab thicknesses in the range of 1-30 cm. The BSA scatter estimates are also used to correct cone beam tomographic projections. Maximum deviations of central profiles of uniform water phantoms are reduced from 193 to 19 HU after application of corrections for scatter, beam hardening, and lateral truncation that are based on the BSA-derived scatter estimate. The same corrections remove the typical cupping artifact from both phantom and patient images. The BSA proves to be a useful tool for quantifying and removing image scatter, as well as for validating models of MV imaging systems.     

View-independent reconstruction algorithms for cone beam CT with general saddle trajectory

In Yang et al (2006 Phys. Med. Biol. 51 1157-72), an exact filtered backprojection (FBP) reconstruction algorithm was proposed for cone beam tomography with saddle trajectory based on the seminal works of Pack and Noo (2005a Inverse Problems 21 1105-20; 2005b 8th Int. Meeting on Fully 3D Reconstruction in Radiology and Nuclear Medicine (Salt Lake City) ed F Noo, H Kudo and L G Zeng pp 287-90). However, the artefacts due to discretization and/or sampling errors in the reconstructed images by this method were still visible, especially when the pitch is large. In this paper, two view-independent (VI) algorithms, which are similar to the FDK-type algorithms (Feldkamp et al 1984 J. Opt. Soc. Am. A 1 612-19), are proposed for planar detector geometry. The first VI algorithm involves two filtered projections and a small additional term (two-dimensional (2D) Radon transform term). One of the filtered projections is obtained by ramp filtering (as in the FDK algorithm for circular trajectory) and the other one is obtained by Hilbert transform. The 2D Radon transform term is just like the term which was first derived by Hu (1996 Scanning 18 572-81) for a circular trajectory. The second VI algorithm involves only one filtered projection term, which is obtained by differentiation followed by Hilbert transform and the 2D Radon transform term. Both algorithms involve only one backprojection step with a weighting factor as in the FDK algorithm. The simulation studies show that the pixel values of the reconstructed images by the VI algorithms are more accurate than those by the original view differencing (VD) algorithm, the streak artefacts are also reduced, and their computational times are comparable to that of the original VD algorithm. We also generalize the concept of saddle trajectory and the corresponding reconstruction algorithm. The generalized algorithm is also theoretically exact, has a shift-invariant FBP structure, and does not depend on the concept of pi-line.     

Feature-based rectal contour propagation from planning CT to cone beam CT

The purpose of this work is to develop a novel feature-based registration strategy to automatically map the rectal contours from planning computed tomography (CT) (pCT) to cone beam CT (CBCT). The rectal contours were manually outlined on the pCT. A narrow band with the outlined contour as its interior surface was then constructed, so that we can exclude the volume inside the rectum in the registration process. The corresponding contour in the CBCT was found by using a feature-based registration algorithm, which consists of two steps: (1) automatically searching for control points in the pCT and CBCT based on the features of the surrounding tissue and matching the homologous control points using the scale invariance feature transformation; and (2) using the control points for a thin plate spline transformation to warp the narrow band and mapping the corresponding contours from pCT to CBCT. The proposed contour propagation technique is applied to digital phantoms and clinical cases and, in all cases, the contour mapping results are found to be clinically acceptable. For clinical cases, the method yielded satisfactory results even when there were significant rectal content changes between the pCT and CBCT scans. As a consequence, the accordance between the rectal volumes after deformable registration and the manually segmented rectum was found to be more than 90%. The proposed technique provides a powerful tool for adaptive radiotherapy of prostate, rectal, and gynecological cancers in the future.     

基于Contourlet变换的CT和锥形束CT图像配准算法

目的提出一种基于Contourlet变换,用于放射治疗定位的CT与锥形束CT（cone beam CT,CBCT）图像配准的方法。方法利用Contourlet变换多尺度多方向的分辨特性,将待配准图像进行Contourlet变换分解,分解后的高频方向子带合成梯度图像,采用归一化互信息作为相似性测度,把梯度图像与低频方向子带以加权函数结合,进行临床医学图像的刚性配准,有效弥补了互信息配准中缺少空间信息的不足。结果通过已知空间变换参数图像的配准结果验证了算法的准确性。配准后lO幅图像变换参数的误差极小,且均方根误差接近于0。结论该图像配准算法精确度高,并具有很好的鲁棒性,有助于提高图像引导放射治疗（image guid edradiation therapy,IGRT）中解剖组织结构和靶区的定位精度。     

Image registration algorithm in CT and cone beam CT based on Contourlet transform

目的提出一种基于Contourlet变换,用于放射治疗定位的CT与锥形束CT(cone beam CT,CBCT)图像配准的方法.方法 利用Contourlet变换多尺度多方向的分辨特性,将待配准图像进行Contourlet变换分解,分解后的高频方向子带合成梯度图像,采用归一化互信息作为相似性测度,把梯度图像与低频方向子带以加权函数结合,进行临床医学图像的刚性配准,有效弥补了互信息配准中缺少空间信息的不足.结果 通过已知空间变换参数图像的配准结果验证了算法的准确性.配准后10幅图像变换参数的误差极小,且均方根误差接近于0.结论 该图像配准算法精确度高,并具有很好的鲁棒性,有助于提高图像引导放射治疗(image guided radiation therapy,IGRT)中解剖组织结构和靶区的定位精度.     

A geometric calibration method for cone beam CT systems

Cone beam CT systems are being deployed in large numbers for small animal imaging, dental imaging, and other specialty applications. A new high-precision method for cone beam CT system calibration is presented in this paper. It uses multiple projection images acquired from rotating point-like objects (metal ball bearings) and the angle information generated from the rotating gantry system is also used. It is assumed that the whole system has a mechanically stable rotation center and that the detector does not have severe out-of-plane rotation (<2 degrees). Simple geometrical relationships between the orbital paths of individual BBs and five system parameters were derived. Computer simulations were employed to validate the accuracy of this method in the presence of noise. Equal or higher accuracy was achieved compared with previous methods. This method was implemented for the geometrical calibration of both a micro CT scanner and a breast CT scanner. The reconstructed tomographic images demonstrated that the proposed method is robust and easy to implement with high precision.     

Four-dimensional cone beam CT with adaptive gantry rotation and adaptive data sampling

We have developed a new four-dimensional cone beam CT (4D-CBCT) on a Varian image-guided radiation therapy system, which has radiation therapy treatment and cone beam CT imaging capabilities. We adapted the speed of gantry rotation time of the CBCT to the average breath cycle of the patient to maintain the same level of image quality and adjusted the data sampling frequency to keep a similar level of radiation exposure to the patient. Our design utilized the real-time positioning and monitoring system to record the respiratory signal of the patient during the acquisition of the CBCT data. We used the full-fan bowtie filter during data acquisition, acquired the projection data over 200 deg of gantry rotation, and reconstructed the images with a half-scan cone beam reconstruction. The scan time for a 200-deg gantry rotation per patient ranged from 3.3 to 6.6 min for the average breath cycle of 3-6 s. The radiation dose of the 4D-CBCT was about 1-2 times the radiation dose of the 4D-CT on a multislice CT scanner. We evaluated the 4D-CBCT in scanning, data processing and image quality with phantom studies. We demonstrated the clinical applicability of the 4D-CBCT and compared the 4D-CBCT and the 4D-CT scans in four patient studies. The contrast-to-noise ratio of the 4D-CT was 2.8-3.5 times of the contrast-to-noise ratio of the 4D-CBCT in the four patient studies.     

High-quality 3D correction of ring and radiant artifacts in flat panel detector-based cone beam volume CT imaging

The use of an x-ray flat panel detector is increasingly becoming popular in 3D cone beam volume CT machines. Due to the deficient semiconductor array manufacturing process, the cone beam projection data are often corrupted by different types of abnormalities, which cause severe ring and radiant artifacts in a cone beam reconstruction image, and as a result, the diagnostic image quality is degraded. In this paper, a novel technique is presented for the correction of error in the 2D cone beam projections due to abnormalities often observed in 2D x-ray flat panel detectors. Template images are derived from the responses of the detector pixels using their statistical properties and then an effective non-causal derivative-based detection algorithm in 2D space is presented for the detection of defective and mis-calibrated detector elements separately. An image inpainting-based 3D correction scheme is proposed for the estimation of responses of defective detector elements, and the responses of the mis-calibrated detector elements are corrected using the normalization technique. For real-time implementation, a simplification of the proposed off-line method is also suggested. Finally, the proposed algorithms are tested using different real cone beam volume CT images and the experimental results demonstrate that the proposed methods can effectively remove ring and radiant artifacts from cone beam volume CT images compared to other reported techniques in the literature.     

A comprehensive study on the relationship between the image quality and imaging dose in low-dose cone beam CT

While compressed sensing (CS)-based algorithms have been developed for the low-dose cone beam CT (CBCT) reconstruction, a clear understanding of the relationship between the image quality and imaging dose at low-dose levels is needed. In this paper, we qualitatively investigate this subject in a comprehensive manner with extensive experimental and simulation studies. The basic idea is to plot both the image quality and imaging dose together as functions of the number of projections and mAs per projection over the whole clinically relevant range. On this basis, a clear understanding of the tradeoff between the image quality and imaging dose can be achieved and optimal low-dose CBCT scan protocols can be developed to maximize the dose reduction while minimizing the image quality loss for various imaging tasks in image-guided radiation therapy (IGRT). Main findings of this work include (1) under the CS-based reconstruction framework, image quality has little degradation over a large range of dose variation. Image quality degradation becomes evident when the imaging dose (approximated with the x-ray tube load) is decreased below 100 total mAs. An imaging dose lower than 40 total mAs leads to a dramatic image degradation, and thus should be used cautiously. Optimal low-dose CBCT scan protocols likely fall in the dose range of 40-100 total mAs, depending on the specific IGRT applications. (2) Among different scan protocols at a constant low-dose level, the super sparse-view reconstruction with the projection number less than 50 is the most challenging case, even with strong regularization. Better image quality can be acquired with low mAs protocols. (3) The optimal scan protocol is the combination of a medium number of projections and a medium level of mAs/view. This is more evident when the dose is around 72.8 total mAs or below and when the ROI is a low-contrast or high-resolution object. Based on our results, the optimal number of projections is around 90 to 120. (4) The clinically acceptable lowest imaging dose level is task dependent. In our study, 72.8 mAs is a safe dose level for visualizing low-contrast objects, while 12.2 total mAs is sufficient for detecting high-contrast objects of diameter greater than 3 mm.