Iterative Image Reconstruction with Under-Sampled Data Assisted by a Neural Network.

To improve image quality and reduce imaging dose in CBCT for radiation therapy applications and to realize near real-time image reconstruction based on use of a fast convergence iterative algorithm and acceleration by multi-GPUs. An iterative image reconstruction that sought to minimize a weighted least squares cost function that employed total variation (TV) regularization was employed to mitigate projection data incompleteness and noise. To achieve rapid 3D image reconstruction (< 1 min), a highly optimized multiple-GPU implementation of the algorithm was developed. The convergence rate and reconstruction accuracy were evaluated using a modified 3D Shepp-Logan digital phantom and a Catphan-600 physical phantom. The reconstructed images were compared with the clinical FDK reconstruction results. Digital phantom studies showed that only 15 iterations and 60 iterations are needed to achieve algorithm convergence for 360-view and 60-view cases, respectively. The RMSE was reduced to 10-4 and 10-2, respectively, by using 15 iterations for each case. Our algorithm required 5.4s to complete one iteration for the 60-view case using one Tesla C2075 GPU. The few-view study indicated that our iterative algorithm has great potential to reduce the imaging dose and preserve good image quality. For the physical Catphan studies, the images obtained from the iterative algorithm possessed better spatial resolution and higher SNRs than those obtained from by use of a clinical FDK reconstruction algorithm. We have developed a fast convergence iterative algorithm for CBCT image reconstruction. The developed algorithm yielded images with better spatial resolution and higher SNR than those produced by a commercial FDK tool. In addition, from the few-view study, the iterative algorithm has shown great potential for significantly reducing imaging dose. We expect that the developed reconstruction approach will facilitate applications including IGART and patient daily CBCT-based treatment localization.

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

There are occasions, perhaps due to hardware constraints, or to speed-up data acquisition, when it is helpful to be able to reconstruct a photoacoustic image from an under-sampled or incomplete data set. Here, we will show how Deep Learning can be used to improve image reconstruction in such cases. Deep Learning is a type of machine learning in which a multi-layered neural network is trained from a set of examples to perform a task. Convolutional Neural Networks (CNNs), a type of deep neural network in which one or more layers perform convolutions, have seen spectacular success in recent years in tasks as diverse as image classification, language processing and game playing. In this work, a series of CNNs were trained to perform the steps of an iterative, gradient-based, image reconstruction algorithm from under-sampled data. This has two advantages: first, the iterative reconstruction is accelerated by learning more efficient updates for each iterate; second, the CNNs effectively learn a prior from the training data set, meaning that it is not necessary to make potentially unrealistic regularising assumptions about the image sparsity or smoothness, for instance. In addition, we show an example in which the CNNs learn to remove artifacts that arise when a slow but accurate acoustic model is replaced by a fast but approximate model. Reconstructions from simulated as well as in vivo data will be shown.

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 propose a hybrid dynamical system as a continuous analog to the block-iterative multiplicative algebraic reconstruction technique (BI-MART), which is a well-known iterative image reconstruction algorithm for computed tomography. The hybrid system is described by a switched nonlinear system with a piecewise smooth vector field or differential equation and, for consistent inverse problems, the convergence of non-negatively constrained solutions to a globally stable equilibrium is guaranteed by the Lyapunov theorem. Namely, we can prove theoretically that a weighted Kullback-Leibler divergence measure can be a common Lyapunov function for the switched system. We show that discretizing the differential equation by using the first-order approximation (Euler's method) based on the geometric multiplicative calculus leads to the same iterative formula of the BI-MART with the scaling parameter as a time-step of numerical discretization. The present paper is the first to reveal that a kind of iterative image reconstruction algorithm is constructed by the discretization of a continuous-time dynamical system for solving tomographic inverse problems. Iterative algorithms with not only the Euler method but also the Runge-Kutta methods of lower-orders applied for discretizing the continuous-time system can be used for image reconstruction. A numerical example showing the characteristics of the discretized iterative methods is presented.

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.

An approach to Magnetic Resonance (MR) image reconstruction from undersampled data is proposed. Undersampling artifacts are removed using an iterative thresholding algorithm applied to nonlinearly transformed image block arrays. Each block array is transformed using kernel principal component analysis where the contribution of each image block to the transform depends in a nonlinear fashion on the distance to other image blocks. Elimination of undersampling artifacts is achieved by conventional principal component analysis in the nonlinear transform domain, projection onto the main components and back-mapping into the image domain. Iterative image reconstruction is performed by interleaving the proposed undersampling artifact removal step and gradient updates enforcing consistency with acquired k-space data. The algorithm is evaluated using retrospectively undersampled MR cardiac cine data and compared to k-t SPARSE-SENSE, block matching with spatial Fourier filtering and k-t ℓ1-SPIRiT reconstruction. Evaluation of image quality and root-mean-squared-error (RMSE) reveal improved image reconstruction for up to 8-fold undersampled data with the proposed approach relative to k-t SPARSE-SENSE, block matching with spatial Fourier filtering and k-t ℓ1-SPIRiT. In conclusion, block matching and kernel methods can be used for effective removal of undersampling artifacts in MR image reconstruction and outperform methods using standard compressed sensing and ℓ1-regularized parallel imaging methods.

Low-dose computed tomography (CT) has attracted much attention in clinical applications since X-ray radiations can cause serious health risks to patients. Sparse-view CT imaging is one of the major ways to reduce radiation dose. However, if reconstructing the sparse-view CT images with conventional filtered backprojection (FBP) algorithm, image quality may be significantly degraded due to the severe streaking artifacts. Therefore, iterative sparse-view CT image reconstruction (IR) algorithms have been developed and utilized to improve image quality. One drawback of using the IR algorithms is they usually spend long computation time. Additionally, adjusting and optimizing the hyper-parameters that are needed during iteration procedures is also time-consuming, some- times may even depend on individual experience. These potential drawbacks strongly limit the wide applications of IR algorithms. Aiming at partially overcome such difficulties, in the present work, we propose a deep iterative reconstruction (DIR) framework to generalize the conventional IR algorithms by mapping them into the deep neural network (DNN) technique. With this proposed DIR algorithms, the prior term, the data fidelity term, and the hyper-parameters can all be represented and learned by network. By doing so, some generalized iterative models can be used to perform high quality sparse-view CT image reconstructions. Numerical experiments based on clinical patient data demonstrated that the proposed DIR algorithms can mitigate the streaking artifacts more effectively while well preserving the subtle structures.

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.

BackgroundHybrid imaging combines nuclear medicine imaging such as single photon emission computed tomography (SPECT) or positron emission tomography (PET) with computed tomography (CT). Through this hybrid design, scanned patients accumulate radiation exposure from both applications. Imaging modalities have been the subject of long-term optimization efforts, focusing on diagnostic applications. It was the aim of this study to investigate the influence of an iterative CT image reconstruction algorithm (ASIR) on the image quality of the low-dose CT images.Methodology/Principal FindingsExaminations were performed with a SPECT-CT scanner with standardized CT and SPECT-phantom geometries and CT protocols with systematically reduced X-ray tube currents. Analyses included image quality with respect to photon flux. Results were compared to the standard FBP reconstructed images. The general impact of the CT-based attenuation maps used during SPECT reconstruction was examined for two SPECT phantoms. Using ASIR for image reconstructions, image noise was reduced compared to FBP reconstructions for the same X-ray tube current. The Hounsfield unit (HU) values reconstructed by ASIR were correlated to the FBP HU values(R2 ≥ 0.88) and the contrast-to-noise ratio (CNR) was improved by ASIR. However, for a phantom with increased attenuation, the HU values shifted for low X-ray tube currents I ≤ 60 mA (p ≤ 0.04). In addition, the shift of the HU values was observed within the attenuation corrected SPECT images for very low X-ray tube currents (I ≤ 20 mA, p ≤ 0.001).Conclusion/SignificanceIn general, the decrease in X-ray tube current up to 30 mA in combination with ASIR led to a reduction of CT-related radiation exposure without a significant decrease in image quality.

Modelling the forward projection or reprojection, that is defined as the operation that transforms a 3D volume into series of 2D set of line integrals, is of interest in several medical imaging applications as iterative tomographic reconstruction (X-ray, Computed Tomography [CT], Positron Emission Tomography [PET], Single Photon Emission Computed Tomography [SPECT]), dose-calculation in radiotherapy and 3D-display volume-rendering. As forward projection is becoming widely used, iterative reconstruction algorithms and their characteristics may affect the reconstruction quality; its accuracy and performance needs more attention. The aim of this chapter is to show the importance of the modelling of the forward projection in the accuracy of medical tomographic data (CT, SPECT and PET) reconstructed with iterative algorithms. Therefore, we first present a brief overview on the iterative algorithms used in tomographic reconstruction in medical imaging. Second, we focus on the projection operators. Concepts and implementation of the most popular projection operators are discussed in detail. Performance of the computer implementations is shown using the well-known Shepp_Logan phantom. In order to avoid possibly confounding perspective effects implied by fan or cone-beam, this study is performed in parallel acquisition geometry.

In limited-angle tomography, the system of imaging equations is underdetermined, and a naïve reconstruction may not have any practical values. Additional information is needed to augment the data so that a useful image can be reconstructed. This additional information is usually implemented as a Bayesian term in the objective function for an iterative optimization procedure. The state-of-the-art augmented information is the total variation (TV) norm of the image. The TV norm enforces a smooth image with sharp edges. The novelty of this paper is a new Bayesian term that is in the form of a neural network. This neural network is a classifier trained by images reconstructed by full and limited-angle projections. The impact of the proposed method is that the information provided by the neural network contains more features of the images than the TV norm and better reconstruction is expected. Computer simulations are carried out and presented.

In limited-angle tomography, the system of imaging equations is underdetermined, and a naïve reconstruction may not have any practical values. Additional information is needed to augment the data so that a useful image can be reconstructed. This additional information is usually implemented as a Bayesian term in the objective function for an iterative optimization procedure. The state-of-the-art augmented information is the total variation (TV) norm of the image. The TV norm enforces a smooth image with sharp edges. The novelty of this paper is a new Bayesian term that is in the form of a neural network. This neural network is a classifier trained by images reconstructed by full and limited-angle projections. The impact of the proposed method is that the information provided by the neural network contains more features of the images than the TV norm and better reconstruction is expected. Computer simulations are carried out and presented.

In practical applications of tomographic imaging, there are often challenges for image reconstruction due to under-sampling and insufficient data. In computed tomography (CT), for example, image reconstruction from few views would enable rapid scanning with a reduced x-ray dose delivered to the patient. Limited-angle problems are also of practical significance in CT. In this work, we develop and investigate an iterative image reconstruction algorithm based on the minimization of the image total variation (TV) that applies to divergent-beam CT. Numerical demonstrations of our TV algorithm are performed with various insufficient data problems in fan-beam CT. The TV algorithm can be generalized to cone-beam CT as well as other tomographic imaging modalities.

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.