Electronic noise modeling in statistical iterative reconstruction

Comparison of iterative reconstruction implementations for multislice helical CT

The most mature image reconstruction algorithms in multislice helical computed tomography are based on analytical and iterative methods. Over the past decades, several methods have been developed for iterative reconstructions that improve image quality by reducing noise and artifacts. In the regularization step of iterative reconstruction, noise can be significantly reduced, thereby making low-dose CT. The quality of the reconstructed image can be further improved by using model-based reconstructions. In these reconstructions, the main focus is on modeling the data acquisition process, including the behavior of the photon beams, the geometry of the system, etc. In this article, we propose two model-based reconstruction algorithms using a virtual detector for multislice helical CT. The aim of this study is to compare the effect of using a virtual detector on image quality for the two proposed algorithms with a model-based iterative reconstruction using the original detector model. Since the algorithms are implemented using multiple GPUs, the merging of separately reconstructed volumes can significantly affect image quality. This issue is often referred to as the "long object" problem, for which we also present a solution that plays an important role in the proposed reconstruction processes. The algorithms were evaluated using mathematical and physical phantoms, as well as patient cases. The SSIM, MS-SSIM and L1 metrics were utilized to evaluate the image quality of the mathematical phantom case. To demonstrate the effectiveness of the algorithms, we used the CatPhan 600 phantom. Additionally, anonymized patient scans were used to showcase the improvements in image quality on real scan data.

Deep Filtered Back Projection for CT Reconstruction

Filtered back projection (FBP) is a classic analytical algorithm for computed tomography (CT) reconstruction, with high computational efficiency. However, images reconstructed by FBP often suffer from excessive noise and artifacts. The original FBP algorithm uses a window function to smooth signals and a linear interpolation to estimate projection values at un-sampled locations. In this study, we propose a novel framework named DeepFBP in which an optimized filter and an optimized nonlinear interpolation operator are learned with neural networks. Specifically, the learned filter can be considered as the product of an optimized window function and the ramp filter, and the learned interpolation can be considered as an optimized way to utilize projection information of nearby locations through nonlinear combination. The proposed method remains the high computational efficiency of the original FBP and achieves much better reconstruction quality at different noise levels. It also outperforms the TV-based statistical iterative algorithm, with computational time being reduced in an order of two, and state-of-the-art post-processing deep learning methods that have deeper and more complicated network structures.

A simulation study to evaluate the effect of 2D antiscatter grid primary transmission on flat panel detector based CBCT image quality

Purpose. Two-dimensional antiscatter grids' (2D-ASGs) septal shadows and their impact on primary transmission play a critical role in cone-beam computed tomography (CBCT) image noise and artifact characteristics. Therefore, a numerical simulation platform was developed to evaluate the effect of 2D-ASG's primary transmission on image quality, as a function of grid geometry and CBCT system properties.Methods. To study the effect of 2D-ASG's septal shadows on primary transmission and CBCT image quality, two new methods were introduced; one to simulate projection signal gradients in septal shadows, and the other to simulate septal shadow variations due to gantry flex. Signal gradients in septal shadows were simulated by generating a system point spread function that was directly extracted from projection images of 2D-ASG prototypes in experiments. Variations in septal shadows due to gantry flex were simulated by generating oversampled shadow profiles extracted from experiments. Subsequently, the effect of 2D-ASG's septal shadows on primary transmission and image quality was evaluated.Results.For an apparent septal thickness of 0.15 mm, the primary transmission of 2D-ASG varied between 72%-90% for grid pitches 1-3 mm. In low-contrast phantoms, the effect of 2D-ASG's radiopaque footprint on information loss was subtle. At high spatial frequencies, information loss manifested itself as undersampling artifacts, however, its impact on image quality is subtle when compared to quantum noise. Effects of additive electronic noise and gantry flex induced ring artifacts on image quality varied as a function of grid pitch and septal thickness. Such artifacts were substantially less in lower resolution images.Conclusion. The proposed simulation platform allowed successful evaluation of CBCT image quality variations as a function of 2D-ASG primary transmission properties and CBCT system characteristics. This platform can be potentially used for optimizing 2D-ASG design properties based on the imaging task and properties of the CBCT system.

Convolutional neural network-based model observer for signal known statistically task in breast tomosynthesis images

BACKGROUND

Since human observer studies are resource-intensive, mathematical model observers are frequently used to assess task-based image quality. The most common implementation of these model observers assume that the signal information is exactly known. However, these tasks cannot thoroughly represent situations where the signal information is not exactly known in terms of size and shape.

PURPOSE

Considering the limitations of the tasks for which signal information is exactly known, we proposed a convolutional neural network (CNN)-based model observer for signal known statistically (SKS) and background known statistically (BKS) detection tasks in breast tomosynthesis images.

METHODS

A wide parameter search was conducted from six different acquisition angles (i.e., 10°, 20°, 30°, 40°, 50°, and 60°) within the same dose level (i.e., 2.3 mGy) under two separate acquisition schemes: (1) constant total number of projections, and (2) constant angular separation between projections. Two different types of signals: spherical (i.e., SKE tasks) and spiculated (i.e., SKS tasks) were used. The detection performance of the CNN-based model observer was compared with that of the Hotelling observer (HO) instead of the IO. Pixel-wise gradient-weighted class activation mapping (pGrad-CAM) map was extracted from each reconstructed tomosynthesis image to provide an intuitive understanding of the trained CNN-based model observer.

RESULTS

The CNN-based model observer achieved a higher detection performance compared to that of the HO for all tasks. Moreover, the improvement in its detection performance was greater for SKS tasks compared to that for SKE tasks. These results demonstrated that the addition of nonlinearity improved the detection performance owing to the variation of the background and signal. Interestingly, the pGrad-CAM results effectively localized the class-specific discriminative region, further supporting the quantitative evaluation results of the CNN-based model observer. In addition, we verified that the CNN-based model observer required fewer images to achieve the detection performance of the HO.

CONCLUSIONS

In this work, we proposed a CNN-based model observer for SKS and BKS detection tasks in breast tomosynthesis images. Throughout the study, we demonstrated that the detection performance of the proposed CNN-based model observer was superior to that of the HO.

STEDNet: Swin transformer-based encoder-decoder network for noise reduction in low-dose CT

BACKGROUND

Low-dose computed tomography (LDCT) can reduce the dose of X-ray radiation, making it increasingly significant for routine clinical diagnosis and treatment planning. However, the noise introduced by low-dose X-ray exposure degrades the quality of CT images, affecting the accuracy of clinical diagnosis. Purpose The noises, artifacts, and high-frequency components are similarly distributed in LDCT images. Transformer can capture global context information in an attentional manner to create distant dependencies on targets and extract more powerful features. In this paper, we reduce the impact of image errors on the ability to retain detailed information and improve the noise suppression performance by fully mining the distribution characteristics of image information.

METHODS

This paper proposed an LDCT noise and artifact suppressing network based on Swin Transformer. The network includes a noise extraction sub-network and a noise removal sub-network. The noise extraction and removal capability are improved using a coarse extraction network of high-frequency features based on full convolution. The noise removal sub-network improves the network's ability to extract relevant image features by using a Swin Transformer with a shift window as an encoder-decoder and skip connections for global feature fusion. Also, the perceptual field is extended by extracting multi-scale features of the images to recover the spatial resolution of the feature maps. The network uses a loss constraint with a combination of L1 and MS-SSIM to improve and ensure the stability and denoising effect of the network.

RESULTS

The denoising ability and clinical applicability of the methods were tested using clinical datasets. Compared with DnCNN, RED-CNN, CBDNet and TSCN, the STEDNet method shows a better denoising effect on RMSE and PSNR. The STEDNet method effectively removes image noise and preserves the image structure to the maximum extent, making the reconstructed image closest to the NDCT image. The subjective and objective analysis of several sets of experiments shows that the method in this paper can effectively maintain the structure, edges, and textures of the denoised images while having good noise suppression performance. In the real data evaluation, the RMSE of this method is reduced by 18.82%, 15.15%, 2.25%, and 1.10% on average compared with DnCNN, RED-CNN, CBDNet, and TSCNN, respectively. The average improvement of PSNR is 9.53%, 7.33%, 2.65%, and 3.69%, respectively.

CONCLUSIONS

This paper proposed a LDCT image denoising algorithm based on end-to-end training. The method in this paper can effectively improve the diagnostic performance of CT images by constraining the details of the images and restoring the LDCT image structure. The problem of increased noise and artifacts in CT images can be solved while maintaining the integrity of CT image tissue structure and pathological information. Compared with other algorithms, this method has better denoising effects both quantitatively and qualitatively.

Learning low-dose CT degradation from unpaired data with flow-based model

BACKGROUND

There has been growing interest in low-dose computed tomography (LDCT) for reducing the X-ray radiation to patients. However, LDCT always suffers from complex noise in reconstructed images. Although deep learning-based methods have shown their strong performance in LDCT denoising, most of them require a large number of paired training data of normal-dose CT (NDCT) images and LDCT images, which are hard to acquire in the clinic. Lack of paired training data significantly undermines the practicability of supervised deep learning-based methods. To alleviate this problem, unsupervised or weakly supervised deep learning-based methods are required.

PURPOSE

We aimed to propose a method that achieves LDCT denoising without training pairs. Specifically, we first trained a neural network in a weakly supervised manner to simulate LDCT images from NDCT images. Then, simulated training pairs could be used for supervised deep denoising networks.

METHODS

We proposed a weakly supervised method to learn the degradation of LDCT from unpaired LDCT and NDCT images. Concretely, LDCT and normal-dose images were fed into one shared flow-based model and projected to the latent space. Then, the degradation between low-dose and normal-dose images was modeled in the latent space. Finally, the model was trained by minimizing the negative log-likelihood loss with no requirement of paired training data. After training, an NDCT image can be input to the trained flow-based model to generate the corresponding LDCT image. The simulated image pairs of NDCT and LDCT can be further used to train supervised denoising neural networks for test.

RESULTS

Our method achieved much better performance on LDCT image simulation compared with the most widely used image-to-image translation method, CycleGAN, according to the radial noise power spectrum. The simulated image pairs could be used for any supervised LDCT denoising neural networks. We validated the effectiveness of our generated image pairs on a classic convolutional neural network, REDCNN, and a novel transformer-based model, TransCT. Our method achieved mean peak signal-to-noise ratio (PSNR) of 24.43dB, mean structural similarity (SSIM) of 0.785 on an abdomen CT dataset, mean PSNR of 33.88dB, mean SSIM of 0.797 on a chest CT dataset, which outperformed several traditional CT denoising methods, the same network trained by CycleGAN-generated data, and a novel transfer learning method. Besides, our method was on par with the supervised networks in terms of visual effects.

CONCLUSION

We proposed a flow-based method to learn LDCT degradation from only unpaired training data. It achieved impressive performance on LDCT synthesis. Next, we could train neural networks with the generated paired data for LDCT denoising. The denoising results are better than traditional and weakly supervised methods, comparable to supervised deep learning methods.

Ant Colony-Based Hyperparameter Optimisation in Total Variation Reconstruction in X-ray Computed Tomography

In this paper, a computer-aided training method for hyperparameter selection of limited data X-ray computed tomography (XCT) reconstruction was proposed. The proposed method employed the ant colony optimisation (ACO) approach to assist in hyperparameter selection for the adaptive-weighted projection-controlled steepest descent (AwPCSD) algorithm, which is a total-variation (TV) based regularisation algorithm. During the implementation, there was a colony of artificial ants that swarm through the AwPCSD algorithm. Each ant chose a set of hyperparameters required for its iterative CT reconstruction and the correlation coefficient (CC) score was given for reconstructed images compared to the reference image. A colony of ants in one generation left a pheromone through its chosen path representing a choice of hyperparameters. Higher score means stronger pheromones/probabilities to attract more ants in the next generations. At the end of the implementation, the hyperparameter configuration with the highest score was chosen as an optimal set of hyperparameters. In the experimental results section, the reconstruction using hyperparameters from the proposed method was compared with results from three other cases: the conjugate gradient least square (CGLS), the AwPCSD algorithm using the set of arbitrary hyperparameters and the cross-validation method.The experiments showed that the results from the proposed method were superior to those of the CGLS algorithm and the AwPCSD algorithm using the set of arbitrary hyperparameters. Although the results of the ACO algorithm were slightly inferior to those of the cross-validation method as measured by the quantitative metrics, the ACO algorithm was over 10 times faster than cross—Validation. The optimal set of hyperparameters from the proposed method was also robust against an increase of noise in the data and can be applicable to different imaging samples with similar context. The ACO approach in the proposed method was able to identify optimal values of hyperparameters for a dataset and, as a result, produced a good quality reconstructed image from limited number of projection data. The proposed method in this work successfully solves a problem of hyperparameters selection, which is a major challenge in an implementation of TV based reconstruction algorithms.

DaNet: dose-aware network embedded with dose-level estimation for low-dose CT imaging

Many deep learning (DL)-based image restoration methods for low-dose CT (LDCT) problems directly employ the end-to-end networks on low-dose training data without considering dose differences. However, the radiation dose difference has a great impact on the ultimate results, and lower doses increase the difficulty of restoration. Moreover, there is increasing demand to design and estimate acceptable scanning doses for patients in clinical practice, necessitating dose-aware networks embedded with adaptive dose estimation. In this paper, we consider these dose differences of input LDCT images and propose an adaptive dose-aware network. First, considering a large dose distribution range for simulation convenience, we coarsely define five dose levels in advance as lowest, lower, mild, higher and highest radiation dose levels. Instead of directly building the end-to-end mapping function between LDCT images and high-dose CT counterparts, the dose level is primarily estimated in the first stage. In the second stage, the adaptively learned low-dose level is used to guide the image restoration process as the pattern of prior information through the channel feature transform. We conduct experiments on a simulated dataset based on original high dose parts of American Association of Physicists in Medicine challenge datasets from the Mayo Clinic. Ablation studies validate the effectiveness of the dose-level estimation, and the experimental results show that our method is superior to several other DL-based methods. Specifically, our method provides obviously better performance in terms of the peak signal-to-noise ratio and visual quality reflected in subjective scores. Due to the dual-stage process, our method may suffer limitations under more parameters and coarse dose-level definitions, and thus, further improvements in clinical practical applications with different CT equipment vendors are planned in future work.

A dual-domain deep learning-based reconstruction method for fully 3D sparse data helical CT

Helical CT has been widely used in clinical diagnosis. In this work, we focus on a new prototype of helical CT, equipped with sparsely spaced multidetector and multi-slit collimator (MSC) in the axis direction. This type of system can not only lower radiation dose, and suppress scattering by MSC, but also cuts down the manufacturing cost of the detector. The major problem to overcome with such a system, however, is that of insufficient data for reconstruction. Hence, we propose a deep learning-based function optimization method for this ill-posed inverse problem. By incorporating a Radon inverse operator, and disentangling each slice, we significantly simplify the complexity of our network for 3D reconstruction. The network is composed of three subnetworks. Firstly, a convolutional neural network (CNN) in the projection domain is constructed to estimate missing projection data, and to convert helical projection data to 2D fan-beam projection data. This is follwed by the deployment of an analytical linear operator to transfer the data from the projection domain to the image domain. Finally, an additional CNN in the image domain is added for further image refinement. These three steps work collectively, and can be trained end to end. The overall network is trained on a simulated CT dataset based on eight patients from the American Association of Physicists in Medicine (AAPM) Low Dose CT Grand Challenge. We evaluate the trained network on both simulated datasets and clinical datasets. Extensive experimental studies have yielded very encouraging results, based on both visual examination and quantitative evaluation. These results demonstrate the effectiveness of our method and its potential for clinical usage. The proposed method provides us with a new solution for a fully 3D ill-posed problem.

Statistical characterization of the linear attenuation coefficient in polychromatic CT scans

PURPOSE

To provide a unifying statistical model that characterizes the integrated x-ray intensity at the detector after logarithmic transformation and can be extended to the characterization of computed tomography (CT) numbers in the reconstructed image.

METHODS

We study the statistical characteristics of polyenergetic x-ray beams in the detector. Firstly, we consider the characterization of the integrated x-ray intensity at the detector through a probabilistic model (compound Poisson) that describes its statistics. We analyze its properties and derive the probabilistic distribution after the logarithmic transformation analytically. Finally, we propose a more tractable probabilistic distribution with the same features observed in the characterization, the noncentral Gamma (nc-Gamma). This distribution exhibits desirable properties for the statistical characterization across the reconstruction process. We assess the assumptions adopted in the derivation of the statistical models throughout Monte Carlo simulations and validate them with a water phantom and a lung phantom acquired in a Siemens clinical CT scan. We evaluate the statistical similarities between the theoretical distribution and the nc-Gamma using a power analysis with a Kolmogorov-Smirnov test for a 95% confidence level.

RESULTS

The Kolmogorov-Smirnov goodness-of-fit test obtained for the Monte Carlo simulation shows an extremely high agreement between the empirical distribution of the post-logarithmic-integrated x-ray intensity and the nc-Gamma. The experimental validation performed with both phantoms confirmed the excellent match between the theoretical distribution, the proposed nc-Gamma, and sample distributions in all situations.

CONCLUSION

We derive an analytical model describing the post-log distribution of the linear attenuation coefficient in the sensor for polychromatic CT scans. We also demonstrate that the nc-Gamma distribution approximates well the theoretical distribution. This distribution also approximates well the CT numbers after reconstruction since it naturally extends across linear operations involved in filtered back projection reconstructions. This probabilistic model may provide the analytical foundation to define new likelihood-based reconstruction methodologies for polychromatic scans.

Artifact removal using a hybrid-domain convolutional neural network for limited-angle computed tomography imaging

The suppression of streak artifacts in computed tomography with a limited-angle configuration is challenging. Conventional analytical algorithms, such as filtered backprojection (FBP), are not successful due to incomplete projection data. Moreover, model-based iterative total variation algorithms effectively reduce small streaks but do not work well at eliminating large streaks. In contrast, FBP mapping networks and deep-learning-based postprocessing networks are outstanding at removing large streak artifacts; however, these methods perform processing in separate domains, and the advantages of multiple deep learning algorithms operating in different domains have not been simultaneously explored. In this paper, we present a hybrid-domain convolutional neural network (hdNet) for the reduction of streak artifacts in limited-angle computed tomography. The network consists of three components: the first component is a convolutional neural network operating in the sinogram domain, the second is a domain transformation operation, and the last is a convolutional neural network operating in the CT image domain. After training the network, we can obtain artifact-suppressed CT images directly from the sinogram domain. Verification results based on numerical, experimental and clinical data confirm that the proposed method can significantly reduce serious artifacts.

SPULTRA: Low-Dose CT Image Reconstruction With Joint Statistical and Learned Image Models

Low-dose CT image reconstruction has been a popular research topic in recent years. A typical reconstruction method based on post-log measurements is called penalized weighted-least squares (PWLS). Due to the underlying limitations of the post-log statistical model, the PWLS reconstruction quality is often degraded in low-dose scans. This paper investigates a shifted-Poisson (SP) model based likelihood function that uses the pre-log raw measurements that better represents the measurement statistics, together with a data-driven regularizer exploiting a Union of Learned TRAnsforms (SPULTRA). Both the SP induced data-fidelity term and the regularizer in the proposed framework are nonconvex. The proposed SPULTRA algorithm uses quadratic surrogate functions for the SP induced data-fidelity term. Each iteration involves a quadratic subproblem for updating the image, and a sparse coding and clustering subproblem that has a closed-form solution. The SPULTRA algorithm has a similar computational cost per iteration as its recent counterpart PWLS-ULTRA that uses post-log measurements, and it provides better image reconstruction quality than PWLS-ULTRA, especially in low-dose scans.

Image reconstruction for interrupted-beam x-ray CT on diagnostic clinical scanners

Low-dose x-ray CT is a major research area with high clinical impact. Compressed sensing using view-based sparse sampling and sparsity-promoting regularization has shown promise in simulations, but these methods can be difficult to implement on diagnostic clinical CT scanners since the x-ray beam cannot be switched on and off rapidly enough. An alternative to view-based sparse sampling is interrupted-beam sparse sampling. SparseCT is a recently-proposed interrupted-beam scheme that achieves sparse sampling by blocking a portion of the beam using a multislit collimator (MSC). The use of an MSC necessitates a number of modifications to the standard compressed sensing reconstruction pipeline. In particular, we find that SparseCT reconstruction is feasible within a model-based image reconstruction framework that incorporates data fidelity weighting to consider penumbra effects and source jittering to consider the effect of partial source obstruction. Here, we present these modifications and demonstrate their application in simulations and real-world prototype scans. In simulations compared to conventional low-dose acquisitions, SparseCT is able to achieve smaller normalized root-mean square differences and higher structural similarity measures on two reduction factors. In prototype experiments, we successfully apply our reconstruction modifications and maintain image resolution at quarter-dose reduction level. The SparseCT design requires only small hardware modifications to current diagnostic clinical scanners, opening up new possibilities for CT dose reduction.

Image quality and dose characteristics for an O-arm intraoperative imaging system with model-based image reconstruction

PURPOSE

To assess the imaging performance and radiation dose characteristics of the O-arm CBCT imaging system (Medtronic Inc., Littleton MA) and demonstrate the potential for improved image quality and reduced dose via model-based image reconstruction (MBIR).

METHODS

Two main studies were performed to investigate previously unreported characteristics of the O-arm system. First is an investigation of dose and 3D image quality achieved with filtered back-projection (FBP) - including enhancements in geometric calibration, handling of lateral truncation and detector saturation, and incorporation of an isotropic apodization filter. Second is implementation of an MBIR algorithm based on Huber-penalized likelihood estimation (PLH) and investigation of image quality improvement at reduced dose. Each study involved measurements in quantitative phantoms as a basis for analysis of contrast-to-noise ratio and spatial resolution as well as imaging of a human cadaver to test the findings under realistic imaging conditions.

RESULTS

View-dependent calibration of system geometry improved the accuracy of reconstruction as quantified by the full-width at half maximum of the point-spread function - from 0.80 to 0.65 mm - and yielded subtle but perceptible improvement in high-contrast detail of bone (e.g., temporal bone). Standard technique protocols for the head and body imparted absorbed dose of 16 and 18 mGy, respectively. For low-to-medium contrast (<100 HU) imaging at fixed spatial resolution (1.3 mm edge-spread function) and fixed dose (6.7 mGy), PLH improved CNR over FBP by +48% in the head and +35% in the body. Evaluation at different dose levels demonstrated 30% increase in CNR at 62% of the dose in the head and 90% increase in CNR at 50% dose in the body.

CONCLUSIONS

A variety of improvements in FBP implementation (geometric calibration, truncation and saturation effects, and isotropic apodization) offer the potential for improved image quality and reduced radiation dose on the O-arm system. Further gains are possible with MBIR, including improved soft-tissue visualization, low-dose imaging protocols, and extension to methods that naturally incorporate prior information of patient anatomy and/or surgical instrumentation.

Ultra-Low-Dose Sparse-View Quantitative CT Liver Perfusion Imaging

Radiation dose of computed tomography liver perfusion imaging can be reduced by collecting fewer x-ray projections in each gantry rotation, but the resulting aliasing artifacts could affect the hepatic perfusion measurement. We investigated the effect of projection undersampling on the assessment of hepatic arterial blood flow (H_ABF) in hepatocellular carcinoma (HCC) when dynamic contrast-enhanced (DCE) liver images were reconstructed with filtered backprojection (FBP) and compressed sensing (CS). DCE liver images of a patient with HCC acquired with a 64-row CT scanner were reconstructed from all the measured projections (984-view) with the standard FBP and from one-third (328-view) and one-fourth (246-view) of all available projections with FBP and CS. Each of the 5 sets of DCE liver images was analyzed with a model-based deconvolution algorithm from which H_ABF maps were generated and compared. Mean H_ABF in the tumor and normal tissue measured by the 328-view CS and FBP protocols was within 5% differences from that assessed by the reference full-view FBP protocol. In addition, the tumor size measured by using the 328-view CS and FBP average images was identical to that determined by using the full-view FBP average image. By contrast, both the 246-view CS and FBP protocols exhibited larger differences (>20%) in anatomical and functional assessments compared with the full-view FBP protocol. The preliminary results suggested that computed tomography perfusion imaging in HCC could be performed with 3 times less projection measurement than the current full-view protocol (67% reduction in radiation dose) when either FBP or CS was used for image reconstruction.

Joint solution for PET image segmentation, denoising, and partial volume correction

Segmentation, denoising, and partial volume correction (PVC) are three major processes in the quantification of uptake regions in post-reconstruction PET images. These problems are conventionally addressed by independent steps. In this study, we hypothesize that these three processes are dependent; therefore, jointly solving them can provide optimal support for quantification of the PET images. To achieve this, we utilize interactions among these processes when designing solutions for each challenge. We also demonstrate that segmentation can help in denoising and PVC by locally constraining the smoothness and correction criteria. For denoising, we adapt generalized Anscombe transformation to Gaussianize the multiplicative noise followed by a new adaptive smoothing algorithm called regional mean denoising. For PVC, we propose a volume consistency-based iterative voxel-based correction algorithm in which denoised and delineated PET images guide the correction process during each iteration precisely. For PET image segmentation, we use affinity propagation (AP)-based iterative clustering method that helps the integration of PVC and denoising algorithms into the delineation process. Qualitative and quantitative results, obtained from phantoms, clinical, and pre-clinical data, show that the proposed framework provides an improved and joint solution for segmentation, denoising, and partial volume correction.

Robust Low-Dose CT Sinogram Preprocessing via Exploiting Noise-Generating Mechanism

Computed tomography (CT) image recovery from low-mAs acquisitions without adequate treatment is always severely degraded due to a number of physical factors. In this paper, we formulate the low-dose CT sinogram preprocessing as a standard maximum a posteriori (MAP) estimation, which takes full consideration of the statistical properties of the two intrinsic noise sources in low-dose CT, i.e., the X-ray photon statistics and the electronic noise background. In addition, instead of using a general image prior as found in the traditional sinogram recovery models, we design a new prior formulation to more rationally encode the piecewise-linear configurations underlying a sinogram than previously used ones, like the TV prior term. As compared with the previous methods, especially the MAP-based ones, both the likelihood/loss and prior/regularization terms in the proposed model are ameliorated in a more accurate manner and better comply with the statistical essence of the generation mechanism of a practical sinogram. We further construct an efficient alternating direction method of multipliers algorithm to solve the proposed MAP framework. Experiments on simulated and real low-dose CT data demonstrate the superiority of the proposed method according to both visual inspection and comprehensive quantitative performance evaluation.

Comparison Between Pre-Log and Post-Log Statistical Models in Ultra-Low-Dose CT Reconstruction

X-ray detectors in clinical computed tomography (CT) usually operate in current-integrating mode. Their complicated signal statistics often lead to intractable likelihood functions for practical use in model-based image reconstruction (MBIR). It is therefore desirable to design simplified statistical models without losing the essential factors. Depending on whether the CT transmission data are logarithmically transformed, pre-log and post-log models are two major categories of choices in CT MBIR. Both being approximations, it remains an open question whether one model can notably improve image quality over the other on real scanners. In this study, we develop and compare several pre-log and post-log MBIR algorithms under a unified framework. Their reconstruction accuracy based on simulation and clinical datasets are evaluated. The results show that pre-log MBIR can achieve notably better quantitative accuracy than post-log MBIR in ultra-low-dose CT, although in less extreme cases, post-log MBIR with handcrafted pre-processing remains a competitive alternative. Pre-log MBIR could play a growing role in emerging ultra-low-dose CT applications.

Fast analytical approach of application specific dose efficient spectrum selection for diagnostic CT imaging and PET attenuation correction

Computed tomography (CT) has been used for a variety of applications, two of which include diagnostic imaging and attenuation correction for PET or SPECT imaging. Ideally, the x-ray tube spectrum should be optimized for the specific application to minimize the patient radiation dose while still providing the necessary information. In this study, we proposed a projection-based analytic approach for the analysis of contrast, noise, and bias. Dose normalized contrast to noise ratio (CNRD), inverse noise normalized by dose (IND) and bias are used as evaluation metrics to determine the optimal x-ray spectrum. Our simulation investigated the dose efficiency of the x-ray spectrum ranging from 40 kVp to 200 kVp. Water cylinders with diameters of 15 cm, 24 cm, and 35 cm were used in the simulation to cover a variety of patient sizes. The effects of electronic noise and pre-patient copper filtration were also evaluated. A customized 24 cm CTDI-like phantom with 13 mm diameter inserts filled with iodine (10 mg ml^-1), tantalum (10 mg ml^-1), water, and PMMA was measured with both standard (1.5 mGy) and ultra-low (0.2 mGy) dose to verify the simulation results at tube voltages of 80, 100, 120, and 140 kVp. For contrast-enhanced diagnostic imaging, the simulation results indicated that for high dose without filtration, the optimal kVp for water contrast is approximately 100 kVp for a 15 cm water cylinder. However, the 60 kVp spectrum produces the highest CNRD for bone and iodine. The optimal kVp for tantalum has two selections: approximately 50 and 100 kVp. The kVp that maximizes CNRD increases when the object size increases. The trend in the CTDI phantom measurements agrees with the simulation results, which also agrees with previous studies. Copper filtration improved the dose efficiency for water and tantalum, but reduced the iodine and bone dose efficiency in a clinically-relevant range (70-140 kVp). Our study also shows that for CT-based attenuation correction applications for PET or SPECT, a higher-kVp spectrum with copper filtration is preferable. This method is developed based on filter back projection and does not require image reconstruction or Monte Carlo dose estimates; thus, it could potentially be used for patient-specific and task-based on-the-fly protocol optimization.

A Simple Low-dose X-ray CT Simulation from High-dose Scan

Low-dose X-ray computed tomography (CT) simulation from high-dose scan is required in optimizing radiation dose to patients. In this study, we propose a simple low-dose CT simulation strategy in sinogram domain using the raw data from high-dose scan. Specially, a relationship between the incident fluxes of low- and high- dose scans is first determined according to the repeated projection measurements and analysis. Second, the incident flux level of the simulated low-dose scan is generated by properly scaling the incident flux level of high-dose scan via the determined relationship in the first step. Third, the low-dose CT transmission data by energy integrating detection is simulated by adding a statistically independent Poisson noise distribution plus a statistically independent Gaussian noise distribution. Finally, a filtered back-projection (FBP) algorithm is implemented to reconstruct the resultant low-dose CT images. The present low-dose simulation strategy is verified on the simulations and real scans by comparing it with the existing low-dose CT simulation tool. Experimental results demonstrated that the present low-dose CT simulation strategy can generate accurate low-dose CT sinogram data from high-dose scan in terms of qualitative and quantitative measurements.

Noise correlation in CBCT projection data and its application for noise reduction in low-dose CBCT

PURPOSE

To study the noise correlation properties of cone-beam CT (CBCT) projection data and to incorporate the noise correlation information to a statistics-based projection restoration algorithm for noise reduction in low-dose CBCT.

METHODS

In this study, the authors systematically investigated the noise correlation properties among detector bins of CBCT projection data by analyzing repeated projection measurements. The measurements were performed on a TrueBeam onboard CBCT imaging system with a 4030CB flat panel detector. An anthropomorphic male pelvis phantom was used to acquire 500 repeated projection data at six different dose levels from 0.1 to 1.6 mAs per projection at three fixed angles. To minimize the influence of the lag effect, lag correction was performed on the consecutively acquired projection data. The noise correlation coefficient between detector bin pairs was calculated from the corrected projection data. The noise correlation among CBCT projection data was then incorporated into the covariance matrix of the penalized weighted least-squares (PWLS) criterion for noise reduction of low-dose CBCT.

RESULTS

The analyses of the repeated measurements show that noise correlation coefficients are nonzero between the nearest neighboring bins of CBCT projection data. The average noise correlation coefficients for the first- and second-order neighbors are 0.20 and 0.06, respectively. The noise correlation coefficients are independent of the dose level. Reconstruction of the pelvis phantom shows that the PWLS criterion with consideration of noise correlation (PWLS-Cor) results in a lower noise level as compared to the PWLS criterion without considering the noise correlation (PWLS-Dia) at the matched resolution. At the 2.0 mm resolution level in the axial-plane noise resolution tradeoff analysis, the noise level of the PWLS-Cor reconstruction is 6.3% lower than that of the PWLS-Dia reconstruction.

CONCLUSIONS

Noise is correlated among nearest neighboring detector bins of CBCT projection data. An accurate noise model of CBCT projection data can improve the performance of the statistics-based projection restoration algorithm for low-dose CBCT.

Statistical image reconstruction for low-dose CT using nonlocal means-based regularization

Low-dose computed tomography (CT) imaging without sacrifice of clinical tasks is desirable due to the growing concerns about excessive radiation exposure to the patients. One common strategy to achieve low-dose CT imaging is to lower the milliampere-second (mAs) setting in data scanning protocol. However, the reconstructed CT images by the conventional filtered back-projection (FBP) method from the low-mAs acquisitions may be severely degraded due to the excessive noise. Statistical image reconstruction (SIR) methods have shown potentials to significantly improve the reconstructed image quality from the low-mAs acquisitions, wherein the regularization plays a critical role and an established family of regularizations is based on the Markov random field (MRF) model. Inspired by the success of nonlocal means (NLM) in image processing applications, in this work, we propose to explore the NLM-based regularization for SIR to reconstruct low-dose CT images from low-mAs acquisitions. Experimental results with both digital and physical phantoms consistently demonstrated that SIR with the NLM-based regularization can achieve more gains than SIR with the well-known Gaussian MRF regularization or the generalized Gaussian MRF regularization and the conventional FBP method, in terms of image noise reduction and resolution preservation.

Soft-tissue imaging with C-arm cone-beam CT using statistical reconstruction

The potential for statistical image reconstruction methods such as penalized-likelihood (PL) to improve C-arm cone-beam CT (CBCT) soft-tissue visualization for intraoperative imaging over conventional filtered backprojection (FBP) is assessed in this work by making a fair comparison in relation to soft-tissue performance. A prototype mobile C-arm was used to scan anthropomorphic head and abdomen phantoms as well as a cadaveric torso at doses substantially lower than typical values in diagnostic CT, and the effects of dose reduction via tube current reduction and sparse sampling were also compared. Matched spatial resolution between PL and FBP was determined by the edge spread function of low-contrast (∼ 40-80 HU) spheres in the phantoms, which were representative of soft-tissue imaging tasks. PL using the non-quadratic Huber penalty was found to substantially reduce noise relative to FBP, especially at lower spatial resolution where PL provides a contrast-to-noise ratio increase up to 1.4-2.2 × over FBP at 50% dose reduction across all objects. Comparison of sampling strategies indicates that soft-tissue imaging benefits from fully sampled acquisitions at dose above ∼ 1.7 mGy and benefits from 50% sparsity at dose below ∼ 1.0 mGy. Therefore, an appropriate sampling strategy along with the improved low-contrast visualization offered by statistical reconstruction demonstrates the potential for extending intraoperative C-arm CBCT to applications in soft-tissue interventions in neurosurgery as well as thoracic and abdominal surgeries by overcoming conventional tradeoffs in noise, spatial resolution, and dose.

Accurate sparse-projection image reconstruction via nonlocal TV regularization

Sparse-projection image reconstruction is a useful approach to lower the radiation dose; however, the incompleteness of projection data will cause degeneration of imaging quality. As a typical compressive sensing method, total variation has obtained great attention on this problem. Suffering from the theoretical imperfection, total variation will produce blocky effect on smooth regions and blur edges. To overcome this problem, in this paper, we introduce the nonlocal total variation into sparse-projection image reconstruction and formulate the minimization problem with new nonlocal total variation norm. The qualitative and quantitative analyses of numerical as well as clinical results demonstrate the validity of the proposed method. Comparing to other existing methods, our method more efficiently suppresses artifacts caused by low-rank reconstruction and reserves structure information better.

Quantifying the Importance of the Statistical Assumption in Statistical X-ray CT Image Reconstruction

Statistical image reconstruction (SIR) is a promising approach to reducing radiation dose in clinical computerized tomography (CT) scans. Clinical CT scanners use energy-integrating detectors. The CT signal follows a compound Poisson distribution, its probability density function (PDF) does not have an analytical form hence cannot be used in an SIR method. The goal of this work is to quantify the effects of using an approximate statistical assumption in SIR methods for clinical CT applications. We apply a pseudo-Ideal Observer (pIO) to simulated CT projection data of the fanbeam geometry at different dose levels. The simulation models the polychromatic X-ray tube spectrum, the effects of the bowtie filter, and the energy-integrating detectors. The pIO uses a pseudo likelihood function (pLF) to calculate the pseudo likelihood ratio, which is the decision variable used by the pIO in a binary detection task. The pLF is an approximation to the true LF of the underlying data. The pIO has inferior performance than the IO unless the pLF coincides with the LF; this performance difference quantifies the closeness between the pseudo likelihood and the exact one. Using lesion detectability in a signal known exactly, background known exactly binary detection task as a figure-of-merit, our results show that at down to 0.1% of a reference tube current level I0, the pIO that uses a Poisson approximation, or a matched variance Gaussian approximation in either the transmission or the line integral domain, achieves 99% the performance of the IO. The constant variance Gaussian approximation has only 70%-80% of the IO performance. At tube currents lower than 0.1% I0, the performance difference is more substantial. We conclude that at current clinical dose levels, it is important to account for the mean-dependent variance in CT projection data in SIR problem formulation, the exact PDF of the CT signal is not as important.

Low-mAs X-ray CT image reconstruction by adaptive-weighted TV-constrained penalized re-weighted least-squares

BACKGROUND

The negative effects of X-ray exposure, such as inducing genetic and cancerous diseases, has arisen more attentions.

OBJECTIVE

This paper aims to investigate a penalized re-weighted least-square (PRWLS) strategy for low-mAs X-ray computed tomography image reconstruction by incorporating an adaptive weighted total variation (AwTV) penalty term and a noise variance model of projection data.

METHODS

An AwTV penalty is introduced in the objective function by considering both piecewise constant property and local nearby intensity similarity of the desired image. Furthermore, the weight of data fidelity term in the objective function is determined by our recent study on modeling variance estimation of projection data in the presence of electronic background noise.

RESULTS

The presented AwTV-PRWLS algorithm can achieve the highest full-width-at-half-maximum (FWHM) measurement, for data conditions of (1) full-view 10 mA acquisition and (2) sparse-view 80 mA acquisition. In comparison between the AwTV/TV-PRWLS strategies and the previous reported AwTV/TV-projection onto convex sets (AwTV/TV-POCS) approaches, the former can gain in terms of FWHM for data condition (1), but cannot gain for the data condition (2).

CONCLUSIONS

In the case of full-view 10 mA projection data, the presented AwTV-PRWLS shows potential improvement. However, in the case of sparse-view 80 mA projection data, the AwTV/TV-POCS shows advantage over the PRWLS strategies.

Regularized multidirections and multiscales anisotropic diffusion for sinogram restoration of low-dosed computed tomography

Although most of existing anisotropic diffusion (AD) methods are supported by prefect mathematical theories, they still lead to smoothed edges and anatomy details (EADs). They are caused by not considering the discrete nature of digital signal. In order to improve the performance of AD in sinogram restoration of low-dosed computed tomography (LDCT), we propose a new AD method, named regularized multidirections and multiscales anisotropic diffusion (RMDMS-AD), by extending AD to regularized AD (RAD) in multidirections and multiscales. Since the multidirections can reduce the discrete errors to the maximum extent, meanwhile multiscales and RAD make searching neighborhood of solution be as large as possible which can get more optimal solution to AD, the new proposed method can improve the performance of AD both in denoising and in stability of solution. Moreover, the discrete errors and ill-posed solutions occur mostly near the EADs; the RMDMS-AD will also preserve EADs well. Comparing the proposed new method to existing AD methods using real sinogram, the new method shows good performance in EADs preserving while denoising and suppressing artifacts.

PIRPLE: a penalized-likelihood framework for incorporation of prior images in CT reconstruction

Over the course of diagnosis and treatment, it is common for a number of imaging studies to be acquired. Such imaging sequences can provide substantial patient-specific prior knowledge about the anatomy that can be incorporated into a prior-image-based tomographic reconstruction for improved image quality and better dose utilization. We present a general methodology using a model-based reconstruction approach including formulations of the measurement noise that also integrates prior images. This penalized-likelihood technique adopts a sparsity enforcing penalty that incorporates prior information yet allows for change between the current reconstruction and the prior image. Moreover, since prior images are generally not registered with the current image volume, we present a modified model-based approach that seeks a joint registration of the prior image in addition to the reconstruction of projection data. We demonstrate that the combined prior-image- and model-based technique outperforms methods that ignore the prior data or lack a noise model. Moreover, we demonstrate the importance of registration for prior-image-based reconstruction methods and show that the prior-image-registered penalized-likelihood estimation (PIRPLE) approach can maintain a high level of image quality in the presence of noisy and undersampled projection data.

Modelling the physics in the iterative reconstruction for transmission computed tomography

There is an increasing interest in iterative reconstruction (IR) as a key tool to improve quality and increase applicability of x-ray CT imaging. IR has the ability to significantly reduce patient dose; it provides the flexibility to reconstruct images from arbitrary x-ray system geometries and allows one to include detailed models of photon transport and detection physics to accurately correct for a wide variety of image degrading effects. This paper reviews discretization issues and modelling of finite spatial resolution, Compton scatter in the scanned object, data noise and the energy spectrum. The widespread implementation of IR with a highly accurate model-based correction, however, still requires significant effort. In addition, new hardware will provide new opportunities and challenges to improve CT with new modelling.

Modelling the physics in the iterative reconstruction for transmission computed tomography

There is an increasing interest in iterative reconstruction (IR) as a key tool to improve quality and increase applicability of x-ray CT imaging. IR has the ability to significantly reduce patient dose; it provides the flexibility to reconstruct images from arbitrary x-ray system geometries and allows one to include detailed models of photon transport and detection physics to accurately correct for a wide variety of image degrading effects. This paper reviews discretization issues and modelling of finite spatial resolution, Compton scatter in the scanned object, data noise and the energy spectrum. The widespread implementation of IR with a highly accurate model-based correction, however, still requires significant effort. In addition, new hardware will provide new opportunities and challenges to improve CT with new modelling.

Radiation dose reduction of chest CT with iterative reconstruction in image space - Part I: studies on image quality using dual source CT

OBJECTIVE

To determine whether the image quality (IQ) is improved with iterative reconstruction in image space (IRIS), and whether IRIS can be used for radiation reduction in chest CT.

MATERIALS AND METHODS

Standard dose chest CT (SDCT) in 50 patients and low dose chest CT (LDCT) in another 50 patients were performed, using a dual-source CT, with 120 kVp and same reference mAs (50 mAs for SDCT and 25 mAs for LDCT) employed to both tubes by modifying a dual-energy scan mode. Full-dose data were obtained by combining the data from both tubes and half-dose data were separated from a single tube. These were reconstructed by using a filtered back projection (FBP) and IRIS: full-dose FBP (F-FBP); full-dose IRIS (F-IRIS); half-dose FBP (H-FBP) and half-dose IRIS (H-IRIS). Objective noise was measured. The subjective IQ was evaluated by radiologists for the followings: noise, contrast and sharpness of mediastinum and lung.

RESULTS

Objective noise was significantly lower in H-IRIS than in F-FBP (p < 0.01). In both SDCT and LDCT, the IQ scores were highest in F-IRIS, followed by F-FBP, H-IRIS and H-FBP, except those for sharpness of mediastinum, which tended to be higher in FBP. When comparing CT images between the same dose and different reconstruction (F-IRIS/F-FBP and H-IRIS/H-FBP) algorithms, scores tended to be higher in IRIS than in FBP, being more distinct in half-dose images. However, despite the use of IRIS, the scores were lower in H-IRIS than in F-FBP.

CONCLUSION

IRIS generally helps improve the IQ, being more distinct at the reduced radiation. However, reduced radiation by half results in IQ decrease even when using IRIS in chest CT.

Variance analysis of x-ray CT sinograms in the presence of electronic noise background

PURPOSE

Low-dose x-ray computed tomography (CT) is clinically desired. Accurate noise modeling is a fundamental issue for low-dose CT image reconstruction via statistics-based sinogram restoration or statistical iterative image reconstruction. In this paper, the authors analyzed the statistical moments of low-dose CT data in the presence of electronic noise background.

METHODS

The authors first studied the statistical moment properties of detected signals in CT transmission domain, where the noise of detected signals is considered as quanta fluctuation upon electronic noise background. Then the authors derived, via the Taylor expansion, a new formula for the mean-variance relationship of the detected signals in CT sinogram domain, wherein the image formation becomes a linear operation between the sinogram data and the unknown image, rather than a nonlinear operation in the CT transmission domain. To get insight into the derived new formula by experiments, an anthropomorphic torso phantom was scanned repeatedly by a commercial CT scanner at five different mAs levels from 100 down to 17.

RESULTS

The results demonstrated that the electronic noise background is significant when low-mAs (or low-dose) scan is performed.

CONCLUSIONS

The influence of the electronic noise background should be considered in low-dose CT imaging.

Iterative reconstruction methods in X-ray CT

Iterative reconstruction (IR) methods have recently re-emerged in transmission x-ray computed tomography (CT). They were successfully used in the early years of CT, but given up when the amount of measured data increased because of the higher computational demands of IR compared to analytical methods. The availability of large computational capacities in normal workstations and the ongoing efforts towards lower doses in CT have changed the situation; IR has become a hot topic for all major vendors of clinical CT systems in the past 5 years. This review strives to provide information on IR methods and aims at interested physicists and physicians already active in the field of CT. We give an overview on the terminology used and an introduction to the most important algorithmic concepts including references for further reading. As a practical example, details on a model-based iterative reconstruction algorithm implemented on a modern graphics adapter (GPU) are presented, followed by application examples for several dedicated CT scanners in order to demonstrate the performance and potential of iterative reconstruction methods. Finally, some general thoughts regarding the advantages and disadvantages of IR methods as well as open points for research in this field are discussed.

Dose reduction in abdominal computed tomography: intraindividual comparison of image quality of full-dose standard and half-dose iterative reconstructions with dual-source computed tomography

OBJECTIVES

We sought to evaluate the image quality of iterative reconstruction in image space (IRIS) in half-dose (HD) datasets compared with full-dose (FD) and HD filtered back projection (FBP) reconstruction in abdominal computed tomography (CT).

MATERIALS AND METHODS

To acquire data with FD and HD simultaneously, contrast-enhanced abdominal CT was performed with a dual-source CT system, both tubes operating at 120 kV, 100 ref.mAs, and pitch 0.8. Three different image datasets were reconstructed from the raw data: Standard FD images applying FBP which served as reference, HD images applying FBP and HD images applying IRIS. For the HD data sets, only data from 1 tube detector-system was used. Quantitative image quality analysis was performed by measuring image noise in tissue and air. Qualitative image quality was evaluated according to the European Guidelines on Quality criteria for CT. Additional assessment of artifacts, lesion conspicuity, and edge sharpness was performed.

RESULTS

: Image noise in soft tissue was substantially decreased in HD-IRIS (-3.4 HU, -22%) and increased in HD-FBP (+6.2 HU, +39%) images when compared with the reference (mean noise, 15.9 HU). No significant differences between the FD-FBP and HD-IRIS images were found for the visually sharp anatomic reproduction, overall diagnostic acceptability (P = 0.923), lesion conspicuity (P = 0.592), and edge sharpness (P = 0.589), while HD-FBP was rated inferior. Streak artifacts and beam hardening was significantly more prominent in HD-FBP while HD-IRIS images exhibited a slightly different noise pattern.

CONCLUSIONS

Direct intrapatient comparison of standard FD body protocols and HD-IRIS reconstruction suggest that the latest iterative reconstruction algorithms allow for approximately 50% dose reduction without deterioration of the high image quality necessary for confident diagnosis.