A comparison of algebraic reconstruction techniques for a single-detector muon computed tomography system

OA158] Noise equivalent number of quanta (NEQ): A tool for choosing the optimal reconstruction algorithm in computed tomography (CT)

Convergence rate calculation of simultaneous iterative reconstruction technique algorithm for diffuse optical tomography image reconstruction: A feasibility study

In this paper, we developed an accelerated algorithm for the classical simultaneous iterative reconstruction technique (SIRT) method applied in CT image reconstruction. The proposed algorithm possesses the following two features. First, it can flexibly handle the image reconstruction problem where projection data is contaminated by Poisson noise. This property makes it successful in compensating the disadvantage of the typical algebraic reconstruction technique (ART) method. Second, we utilize Passty's proximal splitting framework to construct a row-action type accelerated iterative algorithm to minimize the cost function. The accelerating strategy makes it successful in compensating the disadvantage of the famous SIRT method. We proved that the new algorithm can achieve significant image quality with noise reduction in less than 10 iterations, while SIRT needs more than 200 iterations. Both digital phantom and clinical abdominal CT image were reconstructed for demonstrating the efficiency of the proposed method.

Algebraic Reconstruction Technique (ART) is an age-old method used for solving the problem of three-dimensional (3-D) reconstruction from projections in electron microscopy and radiology. In medical applications, direct 3-D reconstruction is at the forefront of investigation. The simultaneous iterative reconstruction technique (SIRT) is an ART-type algorithm with the potential of generating in a few iterations tomographic images of a quality comparable to that of convolution backprojection (CBP) methods. Pixel-based reconstruction (PBR) is similar to SIRT reconstruction, and it has been shown that PBR algorithms give better quality pictures compared to those produced by SIRT algorithms. In this work, we propose a few modifications to the PBR algorithms. The modified algorithms are shown to give better quality pictures compared to PBR algorithms. The PBR algorithm and the modified PBR algorithms are highly compute intensive, Not many attempts have been made to reconstruct objects in the true 3-D sense because of the high computational overhead. In this study, we have developed parallel two-dimensional (2-D) and 3-D reconstruction algorithms based on modified PBR. We attempt to solve the two problems encountered by the PBR and modified PBR algorithms, i.e., the long computational time and the large memory requirements, by parallelizing the algorithm on a multiprocessor system. We investigate the possible task and data partitioning schemes by exploiting the potential parallelism in the PBR algorithm subject to minimizing the memory requirement. We have implemented an extended hypercube (EH) architecture for the high-speed execution of the 3-D reconstruction algorithm using the commercially available fast floating point digital signal processor (DSP) chips as the processing elements (PEs) and dual-port random access memories (DPR) as channels between the PEs. We discuss and compare the performances of the PBR algorithm on an IBM 6000 RISC workstation, on a Silicon Graphics Indigo 2 workstation, and on an EH system. The results show that an EH(3,1) using DSP chips as PEs executes the modified PBR algorithm about 100 times faster than an LBM 6000 RISC workstation. We have executed the algorithms on a 4-node IBM SP2 parallel computer. The results show that execution time of the algorithm on an EH(3,1) is better than that of a 4-node IBM SP2 system. The speed-up of an EH(3,1) system with eight PEs and one network controller is approximately 7.85.

Optical projection tomography (OPT) is an advanced three-dimensional (3D) imaging technology, which uses the filtered backprojection (FBP) algorithm to recover the 3D volume with sufficient number of projections. As to in vivo imaging, it is urgent to reduce the number of projections because the acquisition time could be minimized. However, reconstructing from undersampled OPT data can lead to artifacts and the decline in image quality. The simultaneous iterative reconstruction technique (SIRT) is introduced to remove artifacts and improve the image quality. The image qualities reconstructed from FBP and SIRT separately are compared, and the structural similarity and peak signal-to-noise ratio are calculated. Through simulated phantoms and OPT data of in vivo zebrafish embryo, SIRT consistently outperforms FBP in terms of reduced artifacts and enhanced image contrast especially when the projection numbers are reduced. SIRT method can provide high-quality reconstruction with 50 or fewer projections, thereby significantly reducing the minimum acquisition time and light dose while maintaining reconstruction quality. Through optimization and GPU acceleration, the SIRT algorithm can converge faster so as to reduce the image processing time. To our knowledge, this is the first time one SIRT algorithm is used for reconstruction of sparse OPT data. The experimental results show that SIRT algorithm outperform FBP especially when the number of projections is reduced. In addition, SIRT performs better in the preservation of vascular signal, which is significant for the monitoring of angiogenesis.

Noninvasive X-ray imaging of nanoscale three-dimensional objects, such as integrated circuits (ICs), generally requires two types of scanning: ptychographic, which is translational and returns estimates of the complex electromagnetic field through the IC; combined with a tomographic scan, which collects these complex field projections from multiple angles. Here, we present Attentional Ptycho-Tomography (APT), an approach to drastically reduce the amount of angular scanning, and thus the total acquisition time. APT is machine learning-based, utilizing axial self-Attention for Ptycho-Tomographic reconstruction. APT is trained to obtain accurate reconstructions of the ICs, despite the incompleteness of the measurements. The training process includes regularizing priors in the form of typical patterns found in IC interiors, and the physics of X-ray propagation through the IC. We show that APT with ×12 reduced angles achieves fidelity comparable to the gold standard Simultaneous Algebraic Reconstruction Technique (SART) with the original set of angles. When using the same set of reduced angles, then APT also outperforms Filtered Back Projection (FBP), Simultaneous Iterative Reconstruction Technique (SIRT) and SART. The time needed to compute the reconstruction is also reduced, because the trained neural network is a forward operation, unlike the iterative nature of these alternatives. Our experiments show that, without loss in quality, for a 4.48 × 93.2 × 3.92 µm3 IC (≃6 × 108 voxels), APT reduces the total data acquisition and computation time from 67.96 h to 38 min. We expect our physics-assisted and attention-utilizing machine learning framework to be applicable to other branches of nanoscale imaging, including materials science and biological imaging.

Gamma emission tomography (GET) detects fuel rods that emit gamma rays for potential use as verification tools in nuclear safeguards. In GET, iterative reconstruction algorithms are often used to reconstruct passive gamma-ray emitter source distributions. Generally, using noisy sinogram data, the iterative reconstruction algorithms increase the noise level on a reconstruction image with iterations. Thus, it is important to evaluate how performances of representative iterative reconstruction algorithms change with noisy sinogram data. The passive gamma-ray source distributions inside the mock-up of the water-water energetic reactor (WWER) fuel assembly having missing fuel rods were reconstructed by using the following algorithms: gradient method, steepest descent method, conjugate gradient reconstruction method, algebraic reconstruction technique, simultaneous iterative reconstruction technique, and maximum likelihood expectation maximization (MLEM). Consequently, MLEM algorithm yielded a higher contrast reconstruction image and was regarded as higher reliable algorithm to discriminate the fuel rods from the passive gamma-ray emitter source distribution.

To obtain useful knowledge and experience of CCERT under different excitation patterns, the image reconstruction performance of a 12-electrode CCERT sensor under five different excitation patterns (1-electrode excitation pattern, 2-electrode excitation pattern, 3-electrode excitation pattern, 4-electrode excitation pattern, and 5-electrode excitation pattern) are investigated and compared. A 12-electrode CCERT prototype, which can implement different excitation patterns, is developed to obtain the practical experiment data. Four typical image reconstruction algorithms (Linear Back Projection (LBP) algorithm, Landweber’s iteration algorithm, Algebraic Reconstruction Technique (ART) algorithm, and Simultaneous Iterative Reconstruction Technique (SIRT) algorithm) are introduced to investigate and compare the image reconstruction performance with the experimental data obtained from the CCERT prototype. Research results show that the 1-electrode excitation pattern and the 2-electrode excitation pattern have better global image reconstruction performance. These two excitation patterns are better choices, while the 3-electrode excitation pattern, the 4-electrode excitation pattern, and the 5-electrode excitation pattern are not recommended.

Limited-data tomography, to which electromagnetic geotomography belongs, is analyzed in this paper. In this technique, a discrete forward projection model may be expressed by a rank-deficient system of linear equations whose the nullspace is non-trivial. This means that some image components may fall into the nullspace, and hence the minimal-norm least-square solution, to which many image reconstructions methods converge, may be different from the true one. The Algebraic Reconstruction Technique (ART), Simultaneous Iterative Reconstruction Technique (SIRT), or Conjugate Gradients Least Squares (CGLS) are examples of such methods. In this paper, we deal with the question of how to partially recover the missing image components. First, we analyze the advantages of using the iterative Tikhonov regularization and the Maximum A Posteriori (MAP) algorithm with Gibbs prior. Then, we conclude that the missing (nullspace) image components can be partially recovered if the MAP algorithm is implemented through a multigrid technique. The results, which are presented for synthetic noise-free and noisy data, demonstrate the validity of our assumption. The problem of estimating the regularization and scaling parameters in the MAP algorithm is also addressed.

Nuclear magnetic resonance imaging (MRI) has become the gold standard for many imaging applications. It is routinely used to detect diseases and tissue pathologies due to its superior soft tissue contrast and high spatial resolution. Unlike other imaging techniques such as X-rays, computed tomography, it does not harm patients with ionising radiation.However, MRIs are expensive and only a small portion of patients who would benefit from them can access them. The pursuit of higher sensitivity has generated a trend towards increasing the already large static magnetic field. This has improved imaging quality but has made this technology more expensive and further hindered MRI accessibility. The main cost driver of MRI machines is the strong magnet.The collection of techniques being developed to overcome the intrinsic low NMR sensitivity has fostered interest in low field (LF) MRI to improve cost-effectiveness of MRI. First, the purchase and operational cost of LF systems is relatively low. Second, they are more compatible with other instrumentation which enables versatile concepts such as application-specific open systems and intraoperative imaging. LF systems can offer a wide range of configurations by using permanent magnets. Third, the small fringe field lowers the risk to patients and workers and makes the magnet easier to site. Fourth, artefacts which rely on the strength of field are reduced, as well as the specific absorption rate (SAR) in tissues.Ultra-low field (ULF) MRI systems employ field strengths lower than 10 mT. These systems can complement the advantages of LF systems mentioned above with additional potential benefits. The requirement of homogeneity in ULF is relaxed extensively. It is possible to adjust the strength and direction of the measurement field, allowing flexibility in pulse sequences. Moreover, ULF systems operate in the low kHz frequency range, avoiding the need for radio frequency (RF) noise shielding and enhancing T1-weighted contrast.Most ULF MRI research concentrates on using expensive and fragile sensors, produces the magnetic fields through resistive coils and employs linear gradient fields for encoding. Although ULF systems are important low-cost and portable MRI candidates, they still need considerable space to generate linear fields and need expensive and bulky high permeability shielding to suppress ambient noise.This PhD project develops two major solutions towards a portable and low-cost ULF MRI system: a software gradiometer based on machine learning for ambient noise cancellation and a fast iterative algorithm with total variation (TV) regularisation for image reconstruction. In addition, a concept for a dynamical permanent magnet array (PMA) ULF MRI system is proposed with nonlinear 3D spatial encoding.First, I introduce an experimental setup as a platform for evaluating the MR signal in the ULF regime using a Helmholtz coil as a framework. It is composed of a measurement field, an NMR console, a transmit and receive coil, and a shielding box. The NMR signal is successfully acquired and analysed in partial shielding and full shielding. The results suggest that partial shielding of ULF MRI instruments has the potential to generate a strong signal. This system is built for a subsequent study on noise cancellation presented in following chapter.The second study is a convolutional neural network (CNN) based software gradiometer for background noise cancellation. It includes three ambient noise monitoring coils which are placed away from the NMR sensing coil. The noise induced in the sensing coils is estimated using machine learning. The results show that the software gradiometer reduces ambient noise and can be used to relax shielding requirements, thereby reducing the size and weight of the shielding box.The concept of using small magnets for 3D-spatial encoding in dynamical PMA based ULF MRI is described. It uses small rectangular permanent magnets to generate a 3D-spatial encoding field. The encoding magnets move along an optimised trajectory to achieve an encoding matrix with a low condition number. A prototype of the 3D-spatial encoding has been built and its feasibility tested. The described encoding system can reduce the volume and energy requirements and improve the portability of ULF MRI systems.Finally, iterative imaging reconstruction algorithms for ULF MR are studied. The current state-of-the-art methods are evaluated, which includes Simultaneous Iterative Reconstruction Technique (ART/SIRT), Conjugate Gradient Least Squares (CGLS), and the Chambolle-Pock (CP) algorithms. A dynamic weight Column Action Reconstruction Technique (dwCART) method is proposed and applied to image reconstruction with TV regularisation in the setting of undersampling. In the absence of having a finalised prototype to acquire real ULF MRI imaging data, the methods are tested on CT models (using both simulated and real CT data). The dwCART algorithm performed best on the tested CT problems. It paves the way for fast and accurate imaging with the PMA-based ULF MRI system.

The use of transmission electron tomography for three dimensional morphology analysis of nanostructured materials has grown significantly in recent years due to the improved robustness of automated image collection, alignment and reconstruction routines. Although the amount of published 3D electron tomography data has increased accordingly, in many cases the data is used purely for visualization purposes, due to the difficulty of making quantitative measurements from the as-reconstructed data. This is due to the traditionally difficult step of segmentation of the 3D image volume, which has been hindered due to noise, artifacts and lack of necessary image detail or sharpness. In this work the Simultaneous Iterative Reconstruction Technique (SIRT) is used to reconstruct High Angle Annular Dark Field-Scanning Transmission Electron Microscopy (HAADF-STEM) tomography data. The number of SIRT iterations is varied to optimize the reconstruction for segmentation. In particular, signal to noise ratio, signal to artifact ratio, and image blur are identified as parameters which each contribute to the suitability of the reconstruction for segmentation. The Expectation Maximization/ Maximization of Posterior Marginals image segmentation algorithm is applied to the SIRT reconstructions, and the resulting Average Intensity Projection (AIP) of the segmented image stack is compared to the raw tomography projection data.

Electron tomography based on a total variation minimization reconstruction technique

Examples of extracting meaningful information from image projection data using tomographic reconstruction techniques can be found in many areas of science. Within the photochemical dynamics community, tomography allows for complete three-dimensional (3D) charged particle momentum distributions to be reconstructed following a photodissociation or photoionization event. This permits highly differential velocity- and angle-resolved measurements to be made simultaneously. However, the generalized tomographic reconstruction strategies typically adopted for use with photochemical imaging-based around the Fourier-slice theorem and filtered back-projection algorithms-are not optimized for these specific types of problems. Here, we discuss pre-existing alternative strategies-namely, the simultaneous iterative reconstruction technique and Hankel Transform Reconstruction (HTR)-and introduce them in the context of velocity-map imaging applications. We demonstrate the clear advantages they afford, and how they can perform considerably better than approaches commonly adopted at present. Most notably, with HTR we can set a bound on the minimum number of projections required to reliably reconstruct 3D photoproduct distributions. This bound is significantly lower than what is currently accepted and will help make tomographic imaging far more accessible and efficient for many experimentalists working in the field of photochemical dynamics.

Progressive Stochastic Reconstruction Technique (PSRT) for cryo electron tomography.

Denoising reconstruction techniques can introduce nonlinear properties into computed tomography (CT) systems. These nonlinear algorithms introduce distortion which affects the assessment of the resolution of the system. The purpose of the present study was to decouple and investigate amplitude modulation and waveform distortion in reconstruction algorithms in CT. The methodology developed by Wells, J. R. and Dobbins, J. T. III [Frequency response and distortion properties of nonlinear image processing algorithms and the importance of imaging context. Med. Phys. 40, 091906 (2013)] was adapted to CT reconstruction algorithms. The CT simulating program ASTRA Toolbox© for MATLAB™ was used for the reconstruction of the sinusoidal wave functions. Filtered back projection and the simultaneous iterative reconstruction technique were investigated with simple nonlinear mechanisms: a median filter and a non-negative constraint, respectively. The native reconstruction algorithms were not free from nonlinear waveform distortion, however, none of the metrics showed any dependence on the contrast-to-noise ratio (CNR). Furthermore, the algorithms including nonlinear mechanisms showed a clear and specific CNR dependence, indicating the necessity for distortion analysis in nonlinear CT reconstruction.