Vector entropy imaging theory with application to computerized tomography

Medical imaging theory for x-ray CT and PET is based on image reconstruction from projections. In this paper a novel vector entropy imaging theory under the framework of multiple criteria decision making is presented. We also study the most frequently used image reconstruction methods, namely, least square, maximum entropy, and filtered back-projection methods under the framework, of the single performance criterion optimization. Finally, we introduce some of the results obtained by various reconstruction algorithms using computer-generated noisy projection data from the Hoffman phantom and real CT scanner data. Comparison of the reconstructed images indicates that the vector entropy method gives the best in error (difference between the original phantom data and reconstruction), smoothness (suppression of noise), grey value resolution and is free of ghost images.     

Image filtering for improved dose resolution in CT polymer gel dosimetry

X-ray computed tomography (CT) has been established as a feasible method of performing dosimetry using polyacrylamide gels (PAGs). A small density change occurs in PAG upon irradiation that provides contrast in PAG CT images. However, low dose resolution limits the clinical usefulness of the technique. This work investigates the potential of using image filtering techniques on PAG CT images in order to reduce image noise and improve dose resolution. CT image noise for the scanner and protocol used for the gel images is analyzed and found to be Gaussian distributed and independent of the contrast level in the images. As a result, several filters for reducing spatially invariant noise are investigated: mean, median, midpoint, adaptive mean, alpha-trimmed mean, sigma mean, and a relatively new filter called SUSAN (smallest univalue segment assimilating nucleus). All filters are applied, using 3x3, 5x5, and 7x7 pixel masks, to a CT image of a PAG irradiated with a stereotactic radiosurgery dose distribution. The dose resolution within 95% confidence (D(delta)95%) is calculated and compared for each filtered image, as well the unfiltered image. In addition, the ability of the filters to maintain the spatial integrity of the dose distribution is evaluated and compared. Results clearly indicate that the filters are not equal in their ability to improve D(delta)95% or in their effect on the spatial integrity of the dose distribution. In general, increasing mask size improves D(delta)95% but simultaneously degrades spatial dose information. The mean filter provides the greatest improvement in D(delta)95%, but also the greatest loss of spatial dose information. The SUSAN, mean adaptive, and alpha-trimmed mean filters all provide comparable, but slightly poorer dose resolution. In addition, the SUSAN and adaptive filters both excel at maintaining the spatial distribution of dose and overall are the best performing filters for this application. The midpoint filter, normally useful for Gaussian noise, is poor all-round, dramatically distorting the dose distribution for masks greater than 3x3. The median filter, a common edge preserving noise reduction filter, performs moderately well, but artificially increases high dose gradients. The sigma filter preserves the spatial distribution of dose very well but is least effective at improving dose resolution. In summary, dose resolution can be significantly improved in CT PAG dosimetry through postprocessing of CT images using spatial noise reduction filters. However, such filters are not equal in their ability to improve dose resolution or to maintain the spatial integrity of the dose distribution and an appropriate filter must be chosen depending on clinical demands of the application.     

Image quality of an analog radiation therapy simulator-based tomographic scanner

The spatial resolution and noise level of images produced by a commercial analog tomographic scanner have been measured and compared to those of images reconstructed digitally from projections from the same detector. The full width at half maximum of the line spread function was 3.6 mm for images from the analog scanner and 1.1 mm for the digitally reconstructed images. The standard deviation of the CT numbers over a 10-cm2 circular area at the center of a large water phantom, calculated as a percentage of the linear attenuation coefficient of water, was 3.5% for the analog images, 15.4% for high-resolution digital images, and 3.2% for digital images reconstructed using a convolution filter which reduced the resolution to that of the analog images. The data contributing to each digital image were fewer than those contributing to each analog image by a factor of 10. The noise level did not depend on tube current in either the analog or the digital images. The utility of this analog device in radiation therapy planning will depend upon whether errors in contour localization resulting from transferring data from diagnostic CT scanners exceed the errors due to its poorer image quality.     

High temporal resolution for multislice helical computed tomography

Multislice helical computed tomography (CT) substantially reduces scanning time. However, the temporal resolution of individual images is still insufficient for imaging rapidly moving organs such as the heart and adjacent pulmonary vessels. It may, in some cases, be worse than with current single-slice helical CT. The purpose of this study is to describe a novel image reconstruction algorithm to improve temporal resolution in multislice helical CT, and to evaluate its performance against existing algorithms. The proposed image reconstruction algorithm uses helical interpolation followed by data weighting based on the acquisition time. The temporal resolution, the longitudinal (z-axis) spatial resolution, the image noise, and the in-plane image artifacts created by a moving phantom were compared with those from the basic multislice helical reconstruction (helical filter interpolation, HFI) algorithm and the basic single-slice helical reconstruction algorithm (180 degrees linear interpolation, 180LI) using computer simulations. Computer simulation results were verified with CT examinations of the heart and lung vasculature using a 0.5 second multislice scanner. The temporal resolution of HFI algorithm varies from 0.28 and 0.86 s, depending on helical pitch. The proposed method improves the resolution to a constant value of 0.29 s, independent of pitch, allowing moving objects to be imaged with reduced blurring or motion artifacts. The spatial (z) resolution was slightly worse than with the HFI algorithm; the image noise was worse than with the HFI algorithm but was comparable to axial (step-and-shoot) CT. The proposed method provided sharp images of the moving objects, portraying the anatomy accurately. The proposed algorithm for multislice helical CT allowed us to obtain CT images with high temporal resolution. It may improve the image quality of clinical cardiac, lung, and vascular CT imaging.     

Evaluation of the ordered subset convex algorithm for cone-beam CT

Statistical methods for image reconstruction such as maximum likelihood expectation maximization (ML-EM) are more robust and flexible than analytical inversion methods and allow for accurate modelling of the photon transport and noise. Statistical reconstruction is prohibitively slow when applied to clinical x-ray cone-beam CT due to the large data sets and the high number of iterations required for reconstructing high resolution images. One way to reduce the reconstruction time is to use ordered subsets of projections during the iterations, which has been successfully applied to fan-beam x-ray CT. In this paper, we quantitatively analyse the use of ordered subsets in concert with the convex algorithm for cone-beam x-ray CT reconstruction, for the case of circular acquisition orbits. We focus on the reconstructed image accuracy of a 3D head phantom. Acceleration factors larger than 300 were obtained with errors smaller than 1%, with the preservation of signal-to-noise ratio. Pushing the acceleration factor towards 600 by using an increasing number of subsets increases the reconstruction error up to 5% and significantly increases noise. The results indicate that the use of ordered subsets can be extremely useful for cone-beam x-ray CT.     

Noise and signal decoupling in maximum-likelihood reconstructions and Metz filters for PET brain images

Images reconstructed with the maximum-likelihood-by-expectation-maximization (ML) algorithm have lower noise in some regions, particularly low count areas, compared with images reconstructed with filtered backprojection (FBP). The use of statistically correct noise model coupled with the positivity constraint in the ML algorithm provides this noise improvement, but whether this model confers a general advantage for ML over FBP with no noise model and any reconstruction filter, is unclear. We have studied the quantitative impact of the correct noise model in the ML algorithm applied to simulated and real PET fluoro-deoxyglucose (FDG) brain images, given a simplified but accurate reconstruction model with spatially invariant resolution. For FBP reconstruction, several Metz filters were chosen and images with different resolution were obtained depending on the order (1-400) of the Metz filters. Comparisons were made based on the mean Fourier spectra of the projection amplitudes, the noise-power spectra, and the mean region-of-interest signal and noise behaviour in the images. For images with resolution recovery beyond the intrinsic detector resolution, the noise increased significantly for FBP compared with ML. This indicates that in the process of signal recovery using ML, the noise is decoupled from the signal. Such noise decoupling is not possible for FBP. However, for image resolution equivalent to or less than the intrinsic detector resolution, FBP with Metz filters of various orders can achieve a performance similar to ML. The significance of the noise decoupling advantage in ML is dependent on the reconstructed image resolution required for specific imaging tasks.     

Generalized multi-dimensional adaptive filtering for conventional and spiral single-slice, multi-slice, and cone-beam CT

In modern computed tomography (CT) there is a strong desire to reduce patient dose and/or to improve image quality by increasing spatial resolution and decreasing image noise. These are conflicting demands since increasing resolution at a constant noise level or decreasing noise at a constant resolution level implies a higher demand on x-ray power and an increase of patient dose. X-ray tube power is limited due to technical reasons. We therefore developed a generalized multi-dimensional adaptive filtering approach that applies nonlinear filters in up to three dimensions in the raw data domain. This new method differs from approaches in the literature since our nonlinear filters are applied not only in the detector row direction but also in the view and in the z-direction. This true three-dimensional filtering improves the quantum statistics of a measured projection value proportional to the third power of the filter size. Resolution tradeoffs are shared among these three dimensions and thus are considerably smaller as compared to one-dimensional smoothing approaches. Patient data of spiral and sequential single- and multi-slice CT scans as well as simulated spiral cone-beam data were processed to evaluate these new approaches. Image quality was assessed by evaluation of difference images, by measuring the image noise and the noise reduction, and by calculating the image resolution using point spread functions. The use of generalized adaptive filters helps to reduce image noise or, alternatively, patient dose. Image noise structures, typically along the direction of the highest attenuation, are effectively reduced. Noise reduction values of typically 30%-60% can be achieved in noncylindrical body regions like the shoulder. The loss in image resolution remains below 5% for all cases. In addition, the new method has a great potential to reduce metal artifacts, e.g., in the hip region.     

Development of a Noise Reduction Filter Algorithm for Pediatric Body Images in Multidetector CT

Recently, several types of post-processing image filter which was designed to reduce noise allowing a corresponding dose reduction in CT images have been proposed and these were reported to be useful for noise reduction of CT images of adult patients. However, these have not been reported on adaptation for pediatric patients. Because they are not very effective with small (<20 cm) display fields of view, they could not be used for pediatric (e.g., premature babies and infants) body CT images. In order to solve this restriction, we have developed a new noise reduction filter algorithm which can be applicable for pediatric body CT images. This algorithm is based on a three-dimensional post processing, in which output pixel values are calculated by multi-directional, one-dimensional median filters on original volumetric datasets. The processed directions were selected except in in-plane (axial plane) direction, and consequently the in-plane spatial resolution was not affected by the filter. Also, in other directions, the spatial resolutions including slice thickness were almost maintained due to a characteristic of non-linear filtering of the median filter. From the results of phantom studies, the proposed algorithm could reduce standard deviation values as a noise index by up to 30% without affecting the spatial resolution of all directions, and therefore, contrast-to-noise ratio was improved by up to 30%. This newly developed filter algorithm will be useful for the diagnosis and radiation dose reduction of pediatric body CT images.     

Ordered subset reconstruction for x-ray CT

Statistical methods for image reconstruction such as the maximum likelihood expectation maximization are more robust and flexible than analytical inversion methods and allow for accurate modelling of the counting statistics and photon transport during acquisition of projection data. Statistical reconstruction is prohibitively slow when applied to clinical x-ray CT due to the large data sets and the high number of iterations required for reconstructing high-resolution images. Recently, however, powerful methods for accelerating statistical reconstruction have been proposed which, instead of accessing all projections simultaneously for updating an image estimate, are based on accessing a subset of projections at the time during iterative reconstruction. In this paper we study images generated by the convex algorithm accelerated by the use of ordered subsets (the OS convex algorithm (OSC)) for data sets with sizes, noise levels and spatial resolution representative of x-ray CT imaging. It is only in the case of extremely high acceleration factors (higher than 50, corresponding to fewer than 20 projections per subset), that areas with incorrect grey values appear in the reconstructed images, and that image noise increases compared with the standard convex algorithm. These image degradations can be adequately corrected for by running the final iteration of OSC with a reduced number of subsets. Even by applying such a relatively slow final iteration, OSC produces almost an equal resolution and lesion contrast as the standard convex algorithm, but more than two orders of magnitude faster.     

A method of using noise as a test pattern for determining image enhancement filters

Many digitally based medical imaging systems include both reconstruction algorithms and additional image filters designed to enhance certain image features. However, the manufacturers usually consider these algorithms and filters to be proprietory information. The purpose of this note is to describe a simple procedure for determining the spatial frequency response of these proprietary enhancement filters. The technique uses image noise as a test pattern. The procedure consists of acquiring a small number of noise-only data sets (say 10) of a uniform phantom and reconstructing the images using the different filters with repeated use of the noise data sets. A straightforward analysis then yields the enhancement filter frequency responses.     

A technical solution to avoid partial scan artifacts in cardiac MDCT

Quantitative evaluation of cardiac image data obtained using multidetector row computed tomography (CT) is compromised by partial scan reconstructions, which improve the temporal resolution but significantly increase image-to-image CT number variations for a fixed region of interest compared to full reconstruction images. The feasibility of a new approach to solve this problem is assessed. An anthropomorphic cardiac phantom and an anesthetized pig were scanned on a dual-source CT scanner using both full and partial scan acquisition modes under different conditions. Additional scans were conducted with the electrocardiogram (ECG) signal being in synchrony with the gantry rotation. In the animal study, a simple x-ray detector was used to generate a signal once per gantry rotation. This signal was then used to pace the pig's heart. Phantom studies demonstrated that partial scan artifacts are strongly dependent on the rotational symmetry of angular projections, which is determined by the object shape and composition and its position with respect to the isocenter. The degree of partial scan artifacts also depends on the location of the region of interest with respect to highly attenuating materials (bones, iodine, etc.) within the object. Single-source partial scan images (165 ms temporal resolution) were significantly less affected by partial scan artifacts compared to dual-source partial scan images (82 ms temporal resolution). When the ECG signal was in synchrony with the gantry rotation, the same cardiac phase always corresponded to the same positions of the x-ray tube(s) and, hence, the same scattering and beam hardening geometry. As a result, the range of image-to-image CT number variations for partial scan reconstruction images acquired in synchronized mode was decreased to that achieved using full reconstruction image data. The success of the new approach, which synchronizes the ECG signal with the position of the x-ray tube(s), was demonstrated both in the phantom and animal experiments.     

Low-dose CT reconstruction via edge-preserving total variation regularization

High radiation dose in computed tomography (CT) scans increases the lifetime risk of cancer and has become a major clinical concern. Recently, iterative reconstruction algorithms with total variation (TV) regularization have been developed to reconstruct CT images from highly undersampled data acquired at low mAs levels in order to reduce the imaging dose. Nonetheless, the low-contrast structures tend to be smoothed out by the TV regularization, posing a great challenge for the TV method. To solve this problem, in this work we develop an iterative CT reconstruction algorithm with edge-preserving TV (EPTV) regularization to reconstruct CT images from highly undersampled data obtained at low mAs levels. The CT image is reconstructed by minimizing energy consisting of an EPTV norm and a data fidelity term posed by the x-ray projections. The EPTV term is proposed to preferentially perform smoothing only on the non-edge part of the image in order to better preserve the edges, which is realized by introducing a penalty weight to the original TV norm. During the reconstruction process, the pixels at the edges would be gradually identified and given low penalty weight. Our iterative algorithm is implemented on graphics processing unit to improve its speed. We test our reconstruction algorithm on a digital NURBS-based cardiac-troso phantom, a physical chest phantom and a Catphan phantom. Reconstruction results from a conventional filtered backprojection (FBP) algorithm and a TV regularization method without edge-preserving penalty are also presented for comparison purposes. The experimental results illustrate that both the TV-based algorithm and our EPTV algorithm outperform the conventional FBP algorithm in suppressing the streaking artifacts and image noise under a low-dose context. Our edge-preserving algorithm is superior to the TV-based algorithm in that it can preserve more information of low-contrast structures and therefore maintain acceptable spatial resolution.     

A computer simulation of wavelet noise reduction in computed tomography.

We describe the use of a graphical mathematical spreadsheet programming environment which can be used to simulate the acquisition and reconstruction processes of an x-ray computed tomography (CT) machine. The simulation is used to study the effect of photon counting statistics on the noise in the reconstructed image. Finally we describe and evaluate a novel technique for noise reduction using a nonlinear wavelet filter in which the filter thresholds are calculated individually from the "measured" projection data. This filter is shown to compare favorably to threshold filters based on global estimates of noise variance.     

A technique for on-board CT reconstruction using both kilovoltage and megavoltage beam projections for 3D treatment verification

The technologies with kilovoltage (kV) and megavoltage (MV) imaging in the treatment room are now available for image-guided radiation therapy to improve patient setup and target localization accuracy. However, development of strategies to efficiently and effectively implement these technologies for patient treatment remains challenging. This study proposed an aggregated technique for on-board CT reconstruction using combination of kV and MV beam projections to improve the data acquisition efficiency and image quality. These projections were acquired in the treatment room at the patient treatment position with a new kV imaging device installed on the accelerator gantry, orthogonal to the existing MV portal imaging device. The projection images for a head phantom and a contrast phantom were acquired using both the On-Board Imager kV imaging device and the MV portal imager mounted orthogonally on the gantry of a Varian Clinac 21EX linear accelerator. MV projections were converted into kV information prior to the aggregated CT reconstruction. The multilevel scheme algebraic-reconstruction technique was used to reconstruct CT images involving either full, truncated, or a combination of both full and truncated projections. An adaptive reconstruction method was also applied, based on the limited numbers of kV projections and truncated MV projections, to enhance the anatomical information around the treatment volume and to minimize the radiation dose. The effects of the total number of projections, the combination of kV and MV projections, and the beam truncation of MV projections on the details of reconstructed kV/MV CT images were also investigated.     

低剂量迭代重建技术在放疗定位图像中的应用

目的:探讨新型低剂量迭代重建技术应用于放疗定位图像的可行性。方法:基于体模的实验数据,对CT辐射剂量进行分析。对CT值、低对比度分辨率、噪声、均匀性以及几何畸变各项质量评价参数进行定量的分析。对仿真体模进行迭代重建技术扫描重建,并在放射治疗计划系统中对仿真体模进行模拟剂量计算,分析感兴趣体积的绝对剂量和平面内剂量的Gamma通过率。结果:低剂量迭代重建技术能够在保证图像质量的同时减少约60%的CT扫描辐射剂量。当管电压保持不变时,低剂量迭代重建技术对TPS剂量计算的准确性的影响可以忽略不计,感兴趣体积剂量最大差异0.6%,面剂量的Gamma通过率优于99.82%。低剂量迭代重建技术对图像低对比度分辨率有一定影响,需要进一步结合临床影像进行分析。结论:低剂量迭代重建技术可以应用于放疗定位图像中,但是需要注意图像特性和某些图像质量的改变,建议与PET-CT、超声、核磁等检查手段结合综合考虑确定靶区范围。 【关键词】低剂量迭代重建;放射治疗;定位图像     

Analytic system matrix resolution modeling in PET: an application to Rb-82 cardiac imaging

This work explores application of a novel resolution modeling technique based on analytic physical models which individually models the various resolution degrading effects in PET (positron range, photon non-collinearity, inter-crystal scattering and inter-crystal penetration) followed by their combination and incorporation within the image reconstruction task. In addition to phantom studies, the proposed technique was particularly applied to and studied in the task of clinical Rb-82 myocardial perfusion imaging, which presently suffers from poor statistics and resolution properties in the reconstructed images. Overall, the approach is able to produce considerable enhancements in image quality. The reconstructed FWHM for a Discovery RX PET/CT scanner was seen to improve from 5.1 mm to 7.7 mm across the field-of-view (FoV) to approximately 3.5 mm nearly uniformly across the FoV. Furthermore, extended-source phantom studies indicated clearly improved images in terms of contrast versus noise performance. Using Monte Carlo simulations of clinical Rb-82 imaging, the resolution modeling technique was seen to significantly outperform standard reconstructions qualitatively, and also quantitatively in terms of contrast versus noise (contrast between the myocardium and other organs, as well as between myocardial defects and the left ventricle).     

A novel digital tomosynthesis (DTS) reconstruction method using a deformation field map

We developed a novel digital tomosynthesis (DTS) reconstruction method using a deformation field map to optimally estimate volumetric information in DTS images. The deformation field map is solved by using prior information, a deformation model, and new projection data. Patients' previous cone-beam CT (CBCT) or planning CT data are used as the prior information, and the new patient volume to be reconstructed is considered as a deformation of the prior patient volume. The deformation field is solved by minimizing bending energy and maintaining new projection data fidelity using a nonlinear conjugate gradient method. The new patient DTS volume is then obtained by deforming the prior patient CBCT or CT volume according to the solution to the deformation field. This method is novel because it is the first method to combine deformable registration with limited angle image reconstruction. The method was tested in 2D cases using simulated projections of a Shepp-Logan phantom, liver, and head-and-neck patient data. The accuracy of the reconstruction was evaluated by comparing both organ volume and pixel value differences between DTS and CBCT images. In the Shepp-Logan phantom study, the reconstructed pixel signal-to-noise ratio (PSNR) for the 60 degrees DTS image reached 34.3 dB. In the liver patient study, the relative error of the liver volume reconstructed using 60 degrees projections was 3.4%. The reconstructed PSNR for the 60 degrees DTS image reached 23.5 dB. In the head-and-neck patient study, the new method using 60 degrees projections was able to reconstruct the 8.1 degrees rotation of the bony structure with 0.0 degrees error. The reconstructed PSNR for the 60 degrees DTS image reached 24.2 dB. In summary, the new reconstruction method can optimally estimate the volumetric information in DTS images using 60 degrees projections. Preliminary validation of the algorithm showed that it is both technically and clinically feasible for image guidance in radiation therapy.     

Anisotropic diffusion filtering of PET attenuation data to improve emission images

Attenuation correction in positron emission tomography (PET) is an essential part of clinical and research studies. However, correction using noisy transmission data acquired over short scan durations has been a problem as the noise is introduced into emission images. This study investigates the effect of smoothing the two-dimensional projections of the attenuation maps (mu-map) using the nonlinear anisotropic diffusion filtering method. Experiments are presented on a whole-body study to qualitatively evaluate the efficacy of the method in reducing the random noise and streak artefacts. The results show that image quality is significantly improved with minimal resolution loss. A reduction in statistical noise was quantitatively demonstrated when the same approach was applied to a cylindrical phantom dataset.     

CHO数字观察器在PET图像滤波方法评估中的应用

在临床应用中需要限制扫描时间和药物剂量,这往往会使正电子发射断层扫描(PET)的图像的分辨率变低,噪声变多。为提供可供临床诊断的图像,去噪是一个必须的手段,而在重建后增加一个滤波器是目前最常用的去噪方法。因此对不同滤波器滤波效果的比较是PET图像重建中的重要环节,其中最关键的是滤波参数的选取。目前采用的信噪比(SNR)以及恢复系数(RC)等评估方法可以用来非定量地选取参数,研究者们只能凭经验选取最优参数。而通道化霍特林观察器(CHO)作为一个比较通用的数字观察器,已被用于与PET图像质量相关的各种参数的选择,如重建算法参数、系统设计参数、临床协议参数等,然而其在评估不同滤波方法对图像重建质量的影响中的应用研究还比较少。通过比较CHO计算得到的ROC(receiver operating characteristic)曲线下面积(area under the ROC curve,AUC),选择两种常用的滤波器(即高斯滤波器和非局部均值(Non-Local Mean, NLM)滤波器)的最优参数,并评估它们在PET中的滤波效果。结果表明,对于13 mm球体,σ为1.1~1.4的高斯滤波器和f为0.5~0.9的NLM滤波器可以达到最大的检测能力值,而对于10 mm球体,σ为1.4~2.0的高斯滤波器和f为0.5~0.9的NLM滤波器可以达到最大的检测能力值。虽然两个滤波器所对应的AUC值都能高达0.9,但是NLM滤波器的AUC值高于高斯滤波器。通过IEC图像和病人图像也能发现,NLM滤波后的PET图像中的亮点比高斯滤波的更加清晰,噪声更少。该结论和传统滤波器评估方法得到的结论一致,这说明在PET的病灶检测任务中,CHO能够准确地比较这两种滤波器的性能。     

Noise and resolution in images reconstructed with FBP and OSC algorithms for CT

This paper presents a comparison between an analytical and a statistical iterative reconstruction algorithm for computed transmission tomography concerning their noise and resolution performance. The reconstruction of two-dimensional images from simulated fan-beam transmission data is performed with a filtered back-projection (FBP) type reconstruction and an iterative ordered subsets convex (OSC) maximum-likelihood method. A special software phantom, which allows measuring the resolution and noise in a nonambiguous way, is used to simulate transmission tomography scans with different signal-to-noise ratios (SNR). The noise and modulation transfer function is calculated for FBP and OSC reconstruction at several positions, distributed over the field-of-view (FOV). The reconstruction with OSC using different numbers of subsets shows an inverse linear relation to the number of iterations that are necessary to reach a certain resolution and SNR, i.e., increasing the number of subsets by a factor x reduces the number of required iterations by the same factor. The OSC algorithm is able to achieve a nearly homogeneous high resolution over the whole FOV, which is not achieved with FBP. The OSC method achieves a lower level of noise compared with FBP at the same resolution. The reconstruction with OSC can save a factor of up to nine of x-ray dose compared with FBP in the investigated range of noise levels.