Forward Projection for Use with Iterative Reconstruction

This paper presents a three-dimensional method to reconstruct moving objects from cone-beam X-ray projections using an iterative reconstruction algorithm and a given motion vector field. For the image representation, adapted blobs are used, which can be implemented efficiently as basis functions. Iterative reconstruction requires the calculation of line integrals (forward projections) through the image volume, which are compared with the actual measurements to update the image volume. In the existence of a divergent motion vector field, a change in the volumes of the blobs has to be taken into account in the forward and backprojections. An efficient method to calculate the line integral through the adapted blobs is proposed. It solves the problem, how to compensate for the divergence in the motion vector field on a grid of basis functions. The method is evaluated on two phantoms, which are subject to three different known motions. Moreover, a motion-compensated filtered back-projection reconstruction method is used, and the reconstructed images are compared. Using the correct motion vector field with the iterative motion-compensated reconstruction, sharp images are obtained, with a quality that is significantly better than gated reconstructions.

With the development of computing technology, there is an increasing interest in iterative CT image reconstruction. To study iterative reconstruction algorithms, we have developed a software simulator IterCT in VC++ on PC and made it publicly available on the Internet. In the latest version of the simulator, we have implemented four representative iterative image reconstruction algorithms, which are expectation maximization (EM) method and its ordered-subset version (OSEM), the simultaneous algebraic reconstruction technique (SART) and its ordered-subset version (OSSART). The filtered backprojection method is included as the benchmark.

In recent several years, motivated by the need to reduce radiation doses in CT exams, all of the major CT manufacturers have commercialized different iterative image reconstruction techniques and these innovative techniques were used in clinical routines with increasing popularity. However, due to the intrinsic nonlinearity of these new techniques, the well accepted quantitative image quality assessment metrics such as spatial resolution and contrast to noise ratio are not sufficient to provide the needed quantitative metrics for assessing image quality and for guiding the CT scan protocol optimization. This symposium aims at providing a thorough update to AAPM community on what we have understood in the past for linear CT imaging system, what are the new challenges and opportunities offered by the nonlinear iterative image reconstruction, and what would be the future directions in quantitative image quality assessment that the AAPM community can work together to address the challenges and to adapt the nonlinear image reconstruction methods to routine clinical practice to improve patient care. Three invited speakers will lead the discussions in this symposium.Dr. Ke Li from the University of Wisconsin‐Madison will be presenting the new challenges introduced in model‐based iterative reconstruction (MBIR) method with a focus on how the nonlinear nature of the MBIR reconstruction poses challenges in quantitative image quality metrics such as spatial resolution, noise power spectrum, and the limitations of CNR in protocol optimization which eventually leads to the need of task‐based detectability index as the metric.Dr. Shuai Leng from Mayo Clinic will then present how the CNR metric is insufficient for nonlinear reconstruction algorithms, and how task based model observers can be used to more accurately quantify image quality, and to optimize imaging system and scanning protocols for nonlinear iterative image reconstruction algorithms based on specific imaging task. Practical considerations regarding the application of task based image quality metrics will also be discussed.Dr. Ehsan Samei from Duke University will start the symposium by summarizing a to‐be‐released AAPM Task Group report (TG 233: Performance Evaluation of Computed Tomography Systems). He will cover what has been understood and accepted for linear CT imaging system, what are the new challenges in CT image quality assessment introduced by the nonlinear iterative reconstruction (IR) techniques, and summarize both taskneutral and task‐based metrologies developed in TG 233 to partially address these challenges, and foresee additional challenges in the future. Learning Objectives: Understand the challenges in quantitative image quality assessment introduced by nonlinear iterative reconstruction techniques Understand the challenges and methods in noise performance assessment for nonlinear iterative reconstruction techniques Understand the challenges and methods in in spatial resolution assessment for nonlinear iterative reconstruction techniques Understand the challenges and methods in in task‐based observer performance assessment for nonlinear iterative reconstruction techniquesFunding support received from NIH and DOD; Funding support received from GE Healthcare; Funding support received from Siemens AX; Patent royalties received from GE Healthcare; S. Leng, R01 EB071095; U01 EB017185; E. Samei, Research grant, Siemens; Research grant, GE; K. Li, Funding from NIH, DOD and AAPM

In this paper, a unified framework of iterative algebraic reconstruction for emission computed tomography (ECT) and its application to positron emission tomography (PET) is presented. The unified framework is based on an algebraic image restoration model and contains conventional iterative algebraic reconstruction algorithms: ART, SIRT, Landweber iteration (LWB), the generalized Landweber iteration (GLWB), the steepest descent method (STP), as well as iterative filtered backprojection (IFBP) reconstruction algorithms: Chang's method, Walters' method, and a modified iterative MAP. The framework provides an effective tool to systematically study conventional iterative algebraic algorithms and IFBP algorithms. Based on this framework, conventional iterative algebraic algorithms and IFBP algorithms are generalized. It is shown from the algebraic point of view that IFBP algorithms are not only excellent methods for correction of attenuation (either uniform or nonuniform) but are also good general iterative reconstruction algorithms (they can be applied to either attenuated or attenuation-free projections and converge very fast). The convergence behavior of iterative algebraic algorithms is discussed and insight is drawn into the fast convergence property of IFBP algorithms. A simulated PET system is used to evaluate IFBP algorithms and LWB in comparison with the maximum likelihood estimation via expectation maximization algorithm (MLE-EM) and the filtered backprojection (FBP) algorithm. The simulation results indicate that for both attenuation-free projection and attenuated projection cases IFBP algorithms have a significant computational advantage over LWB and MLE-EM, and have performance advantages over FBP in terms of contrast recovery and/or noise-to-signal ratios (NSRs) in regions of interest.

BackgroundIterative computed tomography (CT) image reconstruction shows high potential for the preservation of image quality in diagnostic CT while reducing patients’ exposure; it has become available for low-dose CT (LD-CT) in high-end hybrid imaging systems (e.g. single-photon emission computed tomography [SPECT]-CT).PurposeTo examine the effect of an iterative CT reconstruction algorithm on image quality, image noise, detectability, and the reader’s confidence for LD-CT data by a subjective assessment.Material and MethodsThe LD-CT data were validated for 40 patients examined by an abdominal hybrid SPECT-CT (U = 120 kV, I = 40 mA, pitch = 1.375). LD-CT was reconstructed using either filtered back projection (FBP) or an iterative image reconstruction algorithm (Adaptive Statistical Iterative Reconstruction [ASIR]®) with different parameters (ASIR levels 50% and 100%). The data were validated by two independent blinded readers using a scoring system for image quality, image noise, detectability, and reader confidence, for a predefined set of 16 anatomic substructures.ResultsThe image quality was significantly improved by iterative reconstruction of the LD-CT data compared with FBP (P ≤ 0.0001). While detectability increased in only 2/16 structures (P ≤ 0.03), the reader’s confidence increased significantly due to iterative reconstruction (P ≤ 0.002). Meanwhile, at the ASIR level of 100%, the detectability in bone structure was highly reduced (P = 0.003).ConclusionAn ASIR level of 50% represents a good compromise in abdominal LD-CT image reconstruction. The specific ASIR level improved image quality (reduced image noise) and reader confidence, while preserving detectability of bone structure.

We evaluated the feasibility of sub-millisievert (mSv) coronary CT angiography (CCTA) using low tube voltage, prospective ECG gating, and a knowledge-based iterative model reconstruction algorithm. Twenty-four non-obese healthy subjects (M:F 13:11; mean age 50.2±7.8years) were enrolled. Three sets of CT images were reconstructed using three different reconstruction methods: filtered back projection (FBP), iterative reconstruction (IR), and knowledge-based iterative model reconstruction (IMR). The scanning parameters were as follows: step-and-shoot axial scanning, 80kVp, and 200mAs. On the three sets of CT images, the attenuation and image noise values were measured at the aortic root. The signal-to-noise ratio (SNR) and the contrast-to-noise ratio (CNR) were calculated at the proximal right coronary artery and the left main coronary artery. The qualitative image quality of the CCTA with IMR was assessed using a 4-point grading scale (grade 1, poor; grade 4, excellent). The mean radiation dose of the CCTA was 0.89±0.09mSv. The attenuation values with IMR were not different from those of other reconstruction methods. The image noise with IMR was significantly lower than with IR and FBP. Compared to FBP, the noise reduction rate of IMR was 69%. The SNR and CNR of CCTA with IMR were significantly higher than with FBP or IR. On the qualitative analysis with IMR, all included segments were diagnostic (grades 2, 3, and 4), and the mean image quality score was 3.6±0.6. In conclusion, CCTA with low tube voltage, prospective ECG gating, and an IMR algorithm might be a feasible method that allows for sub-millisievert radiation doses and good image quality when used with non-obese subjects.

We describe a fast forward and back projector pair based on inverse Fourier rebinning for use in iterative image reconstruction for fully 3-D positron emission tomography (PET). The projector pair is used as part of a factored system matrix that takes into account detector-pair response by using shift-variant sinogram blur kernels, thereby combining the computational advantages of Fourier rebinning with iterative reconstruction using accurate system models. The forward projector consists of a 2-D projector, which maps 3-D images into 2-D direct sinograms, followed by exact inverse rebinning which maps the 2-D into fully 3-D sinograms. The back projector is implemented as the transpose of the forward projector and differs from the true exact rebinning operator in the sense that it does not require reprojection to compute missing lines of response (LORs). We compensate for two types of inaccuracies that arise in a cylindrical PET scanner when using inverse Fourier rebinning: 1) nonuniform radial sampling and 2) nonconstant oblique angles in the radial direction in a single oblique sinogram. We examine the effects of these corrections on sinogram accuracy and reconstructed image quality. We evaluate performance of the new projector pair for maximum a posteriori (MAP) reconstruction of simulated and in vivo data. The new projector results in only a small loss in resolution towards the edge of the field-of-view when compared to the fully 3-D geometric projector and requires an order of magnitude less computation.

To explore the application value of the reconstruction algorithm based on an iterative algorithm in the analysis of CT image and analyze the therapeutic effect of honey-fried Herba Ephedrae combined with Western medicine on acute exacerbation chronic obstructive pulmonary disease (AECOPD), a total of 96 AECOPD patients admitted to our hospital from January 2018 to December 2019 were selected as research subjects. According to a different treatment method, the subjects were divided into a control group (Ctrl group, conventional therapy) and an observation group (OG, conventional therapy + honey-fried Herba Ephedrae), with 48 in each group. The CT image algorithm was established based on the iterative algorithm, and the CT dose indexes of the reconstruction algorithm and the Filtered Back Projection (FBP) algorithm under the same conditions were compared ( P < 0.05 ). After using CT to confirm the diagnosis of the subjects, the difference in indicators of forced expiratory volume in one second (FEV1), forced expiratory volume in one second to forced vital capacity ratio (FEV1%), and forced vital capacity (FVC), inflammatory factors of serum interleukin-8 (IL-8), serum interleukin-10 (IL-10), and tumor necrosis factor (TNF-α), the bronchial wall area, and the total treatment efficiency before and after different treatment was analyzed. The results suggested that the Computed Tomography Dose Index (CTDI) of iterative reconstruction (IR) algorithm when scanning different parts was higher than that of the FBP algorithm. The pulmonary function indexes and the expression of IL-8 and TNF-α in the OG were higher than those in the Ctrl group ( P < 0.05 ); the bronchial wall area, bronchial wall area percentage, and IL-10 expression in the OG were all lower than those in the Ctrl group ( P < 0.05 ). The effectiveness and improvement rates of the Ctrl group were 47.92% and 25%, respectively, significantly lower than those in the OG group, 56.25% and 31.25% ( P < 0.05 ), and the total efficiency of the observation group was 87.5%, which was significantly higher than that in the Ctrl group (72.92%) ( P < 0.05 ). In conclusion, based on the iterative algorithm, a CT reconstruction algorithm with better noise reduction performance was established, and the use of honey-fried Herba Ephedrae combined with Western medicine can improve the effective rate of treatment.

To evaluate the image quality produced by six different iterative reconstruction (IR) algorithms in four CT systems in the setting of brain CT, using different radiation dose levels and iterative image optimisation levels. An image quality phantom, supplied with a bone mimicking annulus, was examined using four CT systems from different vendors and four radiation dose levels. Acquisitions were reconstructed using conventional filtered back-projection (FBP), three levels of statistical IR and, when available, a model-based IR algorithm. The evaluated image quality parameters were CT numbers, uniformity, noise, noise-power spectra, low-contrast resolution and spatial resolution. Compared with FBP, noise reduction was achieved by all six IR algorithms at all radiation dose levels, with further improvement seen at higher IR levels. Noise-power spectra revealed changes in noise distribution relative to the FBP for most statistical IR algorithms, especially the two model-based IR algorithms. Compared with FBP, variable degrees of improvements were seen in both objective and subjective low-contrast resolutions for all IR algorithms. Spatial resolution was improved with both model-based IR algorithms and one of the statistical IR algorithms. The four statistical IR algorithms evaluated in the study all improved the general image quality compared with FBP, with improvement seen for most or all evaluated quality criteria. Further improvement was achieved with one of the model-based IR algorithms. The six evaluated IR algorithms all improve the image quality in brain CT but show different strengths and weaknesses.

In this paper, we analyze the propagation of noise in iterative image reconstruction algorithms. We derive theoretical expressions for the general form of preconditioned gradient algorithms with line searches. The results are applicable to a wide range of iterative reconstruction problems, such as emission tomography, transmission tomography, and image restoration. A unique contribution of this paper compared to the previous work is that the line search is explicitly modeled and we do not use the approximation that the gradient of the objective function is zero. As a result, the accuracy of the theoretical prediction is significantly improved.

Electrical capacitance tomography (ECT) is used to obtain information about the distribution of a mixture of dielectric materials inside a vessel or pipe. ECT has several advantages over other reconstruction algorithms and has found many applications in the industrial fields. However, there are some difficulties with image reconstruction in ECT: The relationship between the permittivity distribution and measured capacitance is nonlinear. And inverse problem is ill-posed so that the inverse solution is sensitive to measurement error. To cope with these difficulties iterative image reconstruction algorithms have been developed. In general, the iterative reconstruction algorithms in ECT have comparatively good-quality in reconstructed images but result in intensive computational burden. This paper presents the iterative image reconstruction algorithm for ECT that can enhance the speed of image reconstruction without degradation in the quality of reconstructed image. The main contribution of the proposed algorithm is new weighting matrices, which are obtained by the interpolation of the grouped electrical field centre lines (EFCLs). Extensive simulation results have demonstrated that proposed algorithm provides improved reconstruction performance in terms of computational time and image quality.

Image reconstruction with under-sampled data is usually achieved by an iterative algorithm, which minimizes an objective function. The objective function commonly contains a data fidelity term and one or more Bayesian terms. A popular Bayesian term is the total variation (TV) norm of the image. This paper suggests an addition Bayesian term that is generated by a neural network. This neural network is essentially a classifier. This classifier can recognize the artifacts caused by the incomplete data. This classifier is trained by patient images reconstructed by complete and incomplete data sets. This newly introduced Bayesian term is referred to as the CNN score, which is a real number in (-∞, ∞). Patient studies show the good correlation between the CNN score and the severeness of the artifacts due to the incomplete measurements. A neural network can extract features from images that are suffering from incomplete measurements and convert the features into a CNN score. An iterative image reconstruction algorithm can be developed to minimize this CNN score to suppress the artifacts in the reconstructed image.

3D or multi-dimensional medical image reconstruction is attracting more and more attention in modern era. Rapid volumetric image reconstruction is of paramount importance to clinicians for prompt diagnosis and analysis of complex tissue alternations. However, due to a high demand on computation for either the analytical or iterative image reconstruction algorithms, it is almost impossible to meet the requirement of real-time reconstruction. On the other hand, with high computing capability and broad banding characteristic, recently multi-core processors provide a new possibility and hopeful start for some of the most computation-demanding applications, such as medical imaging, digital media and entertainment equipment. This study aims to parallelize an analytical 3D CT image reconstruction algorithm, the so-called FDK method, and to implement it on an existing multi-core platform system, towards a real-time 3D medical image reconstruction. In this paper, the parallelization of the 3D image reconstruction algorithm, the coding optimizations and a comparative result of run time savings are described.

Rapid system and hardware development of X-ray computed tomography (CT) technologies has been accompanied by equally exciting advances in image reconstruction algorithms. Of the two reconstruction algorithms, analytical and iterative, iterative reconstruction (IR) algorithms have become a clinically viable option in CT imaging. The first CT scanners in the early 1970s used IR algorithms, but lack of computation power prevented their clinical use. In 2009, the first IR algorithms became commercially available and replaced conventionally established analytical algorithms as filtered back projection. Since then, IR has played a vital role in the field of radiology. Although all available IR algorithms share the common mechanism of artifact reduction and/or potential for radiation dose reduction, the magnitude of these effects depends upon specific IR algorithms. IR reconstructs images by iteratively optimizing an objective function. The objective function typically consists of a data integrity term and a regularization term. Therefore, different regularization priors are used in IR algorithms. This paper will briefly look at the overall evolution of CT image reconstruction and the regularization priors used in IR algorithms. Finally, a discussion is presented based on the reality of various reconstruction methodologies at a glance to find the preferred one. Consequently, we will present anticipation towards future advancements in this domain.

Iterative image reconstruction for positron emission tomography (PET) can improve image quality by using spatial regularization that penalizes image intensity difference between neighboring pixels. Themost commonly used quadratic penalty often over-smoothes edges and small objects in reconstructed images. Non-quadratic penalties can preserve edges but may introduce piece-wise constant blocky artifacts. The results are also sensitive to the hyper-parameter that controls the shape of the penalty function. This paper presents a robust regularization for iterative image reconstruction by using neighborhood patches instead of individual pixels in formulating the non-quadratic penalties. An optimization transfer algorithm is developed for the corresponding optimization problem. Computer simulations show that the proposed patch-based regularization can achieve better contrast recovery for small objects compared with quadratic regularization, and is more robust to the hyper-parameter than the conventional pixel-based non-quadratic regularization.