Iterative image reconstruction in photoacoustic tomography using Kaiser-Bessel windows

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.

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.

Photoacoustic computed tomography (PACT) has emerged as a unique and promising technology for multiscale biomedical imaging. To fully realize its potential for various preclinical and clinical applications, development of systems with high imaging speed, reasonable cost, and manageable data flow are needed. Sparse-sampling PACT with advanced reconstruction algorithms, such as compressed-sensing reconstruction, has shown potential as a solution to this challenge. However, most such algorithms require iterative reconstruction and thus intense computation, which may lead to excessively long image reconstruction times. Here, we developed a principal component analysis (PCA)-based PACT (PCA-PACT) that can rapidly reconstruct high-quality, three-dimensional (3-D) PACT images with sparsely sampled data without requiring an iterative process. In vivo images of the vasculature of a human hand were obtained, thus validating the PCA-PACT method. The results showed that, compared with the back-projection (BP) method, PCA-PACT required ∼50% fewer measurements and ∼40% less time for image reconstruction, and the imaging quality was almost the same as that for BP with full sampling. In addition, compared with compressed sensing-based PACT, PCA-PACT had approximately sevenfold faster imaging speed with higher imaging accuracy. This work suggests a promising approach for low-cost, 3-D, rapid PACT for various biomedical applications.

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.

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.

Photoacoustic computed tomography (PACT) is an emerging computed imaging modality that exploits optical contrast and ultrasonic detection principles to form images of the absorbed optical energy density within tissue. The PACT reconstruction problem corresponds to a time-domain inverse source problem, where the initial pressure distribution is recovered from the wavefield recorded on a measurement aperture located outside the support of the source. A major challenge in transcranial PACT brain imaging is to compensate for aberrations in the measured photoacoustic data due to their propagation through the skull. The transmission of ultrasonic waves through the skull induces strong changes to the photoacoustic wavefield through the processes of absorption, scattering, and longitudinal-to-shear wave mode conversion. To properly account for these effects, a wave equation-based inversion method should be employed that can model the heterogeneous elastic properties of the medium.

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.

Photoacoustic computed tomography (PACT), also known as optoacoustic tomography or thermoacoustic tomography, is an emerging biomedical imaging technique that combines optical absorption contrast with ultrasound detection principles. Recently, a novel analytic image reconstruction formula has been proposed that operates on a data function expressed in the temporal frequency and spatial domains. The validity the formula has been demonstrated for a two-dimensional (2D) circular measurement geometry. In this study, computer simulation studies are conducted to validate the reconstruction formula for a three-dimensional (3D) spherical measurement geometry. This formula provides new insights into how the spatial frequency components of the sought-after object function can be explicitly determined by the temporal frequency components of the data function measured with a 2D circular or 3D spherical measurement geometry in PACT. Comparing with existing Fourier transform-based reconstruction formulas, the reconstruction formula possesses a simple structure that requires no computation of series expansions or multi-dimensional interpolation in Fourier space.

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

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.

Reducing radiation dose and enhancing imaging quality of 4DCT for radiation therapy using iterative reconstruction algorithms

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.

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.

Image segmentation is important in improving the diagnostic capability of ultrasound computed tomography (USCT) and photoacoustic computed tomography (PACT), as it can be included in the image reconstruction process to improve image quality and quantification abilities. Segmenting the imaged object out of the background using image domain methods is easily complicated by low contrast, noise, and artifacts in the reconstructed image. Here, we introduce a new signal domain object segmentation method for USCT and PACT which does not require image reconstruction beforehand and is automatic, robust, computationally efficient, accurate, and straightforward. We first establish the relationship between the time-of-flight of the received first arrival waves and the object's boundary which is described by ellipse equations. Then, we show that the ellipses are tangent to the boundary. By looking for tangent points on the common tangent of neighboring ellipses, the boundary can be approximated with high fidelity. Imaging experiments of human fingers and mice cross-sections showed that our method provided equivalent or better segmentations than the optimal ones by active contours. In summary, our method greatly reduces the overall complexity of object segmentation and shows great potential in eliminating user dependency without sacrificing segmentation accuracy. The method can be further seamlessly incorporated into algorithms for other processing purposes in USCT and PACT, such as high-quality image reconstruction.