We describe and examine an algorithm for tomographic image reconstruction where prior knowledge about the solution is available in the form of training images. We first construct a nonnegative dictionary based on prototype elements from the training images; this problem is formulated as a regularized non-negative matrix factorization. Incorporating the dictionary as a prior in a convex reconstruction problem, we then find an approximate solution with a sparse representation in the dictionary. The dictionary is applied to non-overlapping patches of the image, which reduces the computational complexity compared to other algorithms. Computational experiments clarify the choice and interplay of the model parameters and the regularization parameters, and we show that in few-projection low-dose settings our algorithm is competitive with total variation regularization and tends to include more texture and more correct edges.
Technical University of Denmark（丹麦技术大学）；Tufts University（塔夫茨大学）
We consider tomographic reconstruction using priors in the form of a dictionary learned from training images. The reconstruction has two stages: first we construct a tensor dictionary prior from our training data, and then we pose the reconstruction problem in terms of recovering the expansion coefficients in that dictionary. Our approach differs from past approaches in that a) we use a third-order tensor representation for our images and b) we recast the reconstruction problem using the tensor formulation. The dictionary learning problem is presented as a non-negative tensor factorization pro…
In this paper we present a new two-level iterative algorithm for tomographic image reconstruction. The algorithm uses a regularization technique, which we call edge-preserving Laplacian, that preserves sharp edges between objects while damping spurious oscillations in the areas where the reconstructed image is smooth. Our numerical simulations demonstrate that the proposed method outperforms total variation (TV) regularization and it is competitive with the combined TV-L2 penalty. Obtained reconstructed images show increased signal-to-noise ratio and visually appealing structural features. Com…
We present a novel approach to handle ring artifacts correction in compressed sensing tomographic reconstruction. The correction is part of the reconstruction process, which differs from classical sinogram pre-processing and image post-processing techniques. The principle of compressed sensing tomographic reconstruction is presented. Then, we show that the ring artifacts correction can be integrated in the reconstruction problem formalism. We provide numerical results for both simulated and real data. This technique is included in the PyHST2 code which is used at the European Synchrotron Radia…
In this paper, we consider the problem of feature reconstruction from incomplete x-ray CT data. Such problems occurs, e.g., as a result of dose reduction in the context medical imaging. Since image reconstruction from incomplete data is a severely ill-posed problem, the reconstructed images may suffer from characteristic artefacts or missing features, and significantly complicate subsequent image processing tasks (e.g., edge detection or segmentation). In this paper, we introduce a novel framework for the robust reconstruction of convolutional image features directly from CT data, without the …
This paper deals with a method of tomographic reconstruction of radially symmetric objects from a single radiograph, in order to study the behavior of shocked material. The usual tomographic reconstruction algorithms such as generalized inverse or filtered back-projection cannot be applied here because data are very noisy and the inverse problem associated to single view tomographic reconstruction is highly unstable. In order to improve the reconstruction, we propose here to add some a priori assumptions on the looked after object. One of these assumptions is that the object is binary and cons…
Okinawa Institute of Science and Technology (OIST)（冲绳科学技术大学院大学）
Limited data and low dose constraints are common problems in a variety of tomographic reconstruction paradigms which lead to noisy and incomplete data. Over the past few years sinogram denoising has become an essential pre-processing step for low dose Computed Tomographic (CT) reconstructions. We propose a novel sinogram denoising algorithm inspired by the modern field of signal processing on graphs. Graph based methods often perform better than standard filtering operations since they can exploit the signal structure. This makes the sinogram an ideal candidate for graph based denoising since …
ETH Zurich（苏黎世联邦理工学院）；Paul Scherrer Institute（保罗·谢勒研究所）
This work introduces and characterizes a fast parameterless filter based on the Helgason-Ludwig consistency conditions, used to improve the accuracy of analytical reconstructions of tomographic undersampled datasets. The filter, acting in the Radon domain, extrapolates intermediate projections between those existing. The resulting sinogram, doubled in views, is then reconstructed by a standard analytical method. Experiments with simulated data prove that the peak-signal-to-noise ratio of the results computed by filtered backprojection is improved up to 5-6 dB, if the filter is used prior to re…
Hybrid adiabatic quantum computing for tomographic image reconstruction -- opportunities and limitations
Friedrich-Alexander Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希-亚历山大大学）；Siemens Healthineers GmbH（西门子医疗有限公司）；Siemens Medical Solutions USA, Inc（美国西门子医疗解决方案公司）
IIT Bombay（印度理工学院孟买分校）；IITB-Monash Research Academy（印度理工学院孟买分校-莫纳什研究学院）；Monash University（莫纳什大学）
Recent research in tomographic reconstruction is motivated by the need to efficiently recover detailed anatomy from limited measurements. One of the ways to compensate for the increasingly sparse sets of measurements is to exploit the information from templates, i.e., prior data available in the form of already reconstructed, structurally similar images. Towards this, previous work has exploited using a set of global and patch based dictionary priors. In this paper, we propose a global prior to improve both the speed and quality of tomographic reconstruction within a Compressive Sensing framew…
ETH Zurich（苏黎世联邦理工学院）；Paul Scherrer Institute（保罗谢尔研究所）
The performance of an iterative reconstruction algorithm for X-ray tomography is strongly determined by the features of the used forward and backprojector. For this reason, a large number of studies has focused on the to design of projectors with increasingly higher accuracy and speed. To what extent the accuracy of an iterative algorithm is affected by the mathematical affinity and the similarity between the actual implementation of the forward and backprojection, referred here as "coupling projector-backprojector", has been an overlooked aspect so far. The experimental study presented here s…
LMT-Cachan (ENS de Cachan/CNRS/UPMC/PRES UniverSud Paris)（卡尚力学与技术实验室（卡尚高等师范学校/法国国家科学研究中心/皮埃尔与玛丽·居里大学/巴黎南大大学联盟））
Tomographic reconstruction of a binary image from few projections is considered. A novel {\em heuristic} algorithm is proposed, the central element of which is a nonlinear transformation $ψ(p)=\log(p/(1-p))$ of the probability $p$ that a pixel of the sought image be 1-valued. It consists of backprojections based on $ψ(p)$ and iterative corrections. Application of this algorithm to a series of artificial test cases leads to exact binary reconstructions, (i.e recovery of the binary image for each single pixel) from the knowledge of projection data over a few directions. Images up to $10^6$ pixel…
Samsung Research America（三星美国研究院）；Argonne National Laboratory（阿贡国家实验室）；Northwestern University（西北大学）；Purdue University（普渡大学）
In many computed tomography (CT) imaging applications, it is important to rapidly collect data from an object that is moving or changing with time. Tomographic acquisition is generally assumed to be step-and-shoot, where the object is rotated to each desired angle, and a view is taken. However, step-and-shoot acquisition is slow and can waste photons, so in practice fly-scanning is done where the object is continuously rotated while collecting data. However, this can result in motion-blurred views and consequently reconstructions with severe motion artifacts. In this paper, we introduce CodEx,…
Rensselaer Polytechnic Institute（伦斯勒理工学院）；Southeast University（东南大学）；Fudan University（复旦大学）；University of Massachusetts Lowell（马萨诸塞大学洛厄尔分校）；The University of Hong Kong（香港大学）
Tomographic image reconstruction with deep learning is an emerging field, but a recent landmark study reveals that several deep reconstruction networks are unstable for computed tomography (CT) and magnetic resonance imaging (MRI). Specifically, three kinds of instabilities were reported: (1) strong image artefacts from tiny perturbations, (2) small features missing in a deeply reconstructed image, and (3) decreased imaging performance with increased input data. On the other hand, compressed sensing (CS) inspired reconstruction methods do not suffer from these instabilities because of their bu…
Southern Illinois University Carbondale（南伊利诺伊大学卡本代尔分校）
In this paper, we investigated a C-arm tomographic technique as a new three dimensional (3D) kidney imaging method for nephrolithiasis and kidney stone detection over view angle less than 180o. Our C-arm tomographic technique provides a series of two dimensional (2D) images with a single scan over 40o view angle. Experimental studies were performed with a kidney phantom that was formed from a pig kidney with two embedded kidney stones. Different reconstruction methods were developed for C-arm tomographic technique to generate 3D kidney information including: point by point back projection (BP)…
University of Southern Denmark（南丹麦大学）；Newtec Engineering A/S（Newtec工程公司）；Mads Clausen Institute（马德斯·克劳森研究所）
A novel method, utilizing convolutional neural networks (CNNs), is proposed to reconstruct hyperspectral cubes from computed tomography imaging spectrometer (CTIS) images. Current reconstruction algorithms are usually subject to long reconstruction times and mediocre precision in cases of a large number of spectral channels. The constructed CNNs deliver higher precision and shorter reconstruction time than a sparse expectation maximization algorithm. In addition, the network can handle two different types of real-world images at the same time -- specifically ColorChecker and carrot spectral im…
Indian Institute of Technology Bombay（印度理工学院孟买分校）；Monash University（莫纳什大学）
The need for tomographic reconstruction from sparse measurements arises when the measurement process is potentially harmful, needs to be rapid, or is uneconomical. In such cases, prior information from previous longitudinal scans of the same or similar objects helps to reconstruct the current object whilst requiring significantly fewer `updating' measurements. However, a significant limitation of all prior-based methods is the possible dominance of the prior over the reconstruction of new localised information that has evolved within the test object. In this paper, we improve the state of the …
Tomographic Reconstruction and Regularisation with Search Space Expansion and Total Variation
School of Computing & Mathematical Sciences, University of Greenwich（格林威治大学计算与数学科学学院）；Department of Computing, Goldsmiths College, University of London（伦敦大学金史密斯学院计算机系）
This paper describes a novel approach to partially reconstruct high-resolution 4D light fields from a stack of differently focused photographs taken with a fixed camera. First, a focus map is calculated from this stack using a simple approach combining gradient detection and region expansion with graph-cut. Then, this focus map is converted into a depth map thanks to the calibration of the camera. We proceed after this with the tomographic reconstruction of the epipolar images by back-projecting the focused regions of the scene only. We call it masked back-projection. The angles of back-projec…
Deep learning affords enormous opportunities to augment the armamentarium of biomedical imaging, albeit its design and implementation have potential flaws. Fundamentally, most deep learning models are driven entirely by data without consideration of any prior knowledge, which dramatically increases the complexity of neural networks and limits the application scope and model generalizability. Here we establish a geometry-informed deep learning framework for ultra-sparse 3D tomographic image reconstruction. We introduce a novel mechanism for integrating geometric priors of the imaging system. We…
Yale University（耶鲁大学）；Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）
Limited view tomographic reconstruction aims to reconstruct a tomographic image from a limited number of sinogram or projection views arising from sparse view or limited angle acquisitions that reduce radiation dose or shorten scanning time. However, such a reconstruction suffers from high noise and severe artifacts due to the incompleteness of sinogram. To derive quality reconstruction, previous state-of-the-art methods use UNet-like neural architectures to directly predict the full view reconstruction from limited view data; but these methods leave the deep network architecture issue largely…
Johns Hopkins University（约翰斯·霍普金斯大学）；Okinawa Institute of Science and Technology（冲绳科学技术大学院大学）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
Sparsity exploiting image reconstruction (SER) methods have been extensively used with Total Variation (TV) regularization for tomographic reconstructions. Local TV methods fail to preserve texture details and often create additional artefacts due to over-smoothing. Non-Local TV (NLTV) methods have been proposed as a solution to this but they either lack continuous updates due to computational constraints or limit the locality to a small region. In this paper, we propose Adaptive Graph-based TV (AGTV). The proposed method goes beyond spatial similarity between different regions of an image bei…
IIT Bombay（孟买印度理工学院）；Monash University（莫纳什大学）；IITB-Monash Research Academy（IITB-莫纳什研究院）
Low-dose tomography is highly preferred in medical procedures for its reduced radiation risk when compared to standard-dose Computed Tomography (CT). However, the lower the intensity of X-rays, the higher the acquisition noise and hence the reconstructions suffer from artefacts. A large body of work has focussed on improving the algorithms to minimize these artefacts. In this work, we propose two new techniques, rescaled non-linear least squares and Poisson-Gaussian convolution, that reconstruct the underlying image making use of an accurate or near-accurate statistical model of the noise in t…
High-Quality Tomographic Image Reconstruction Integrating Neural Networks and Mathematical Optimization
Department of Data Science, Friedrich-Alexander-Universität Erlangen-Nürnberg Erlangen-Nürnberg（数据科学系，埃朗根-纽伦堡大学）；Department of Mathematics, Linköping University（数学系，利德斯堡大学）；Electric Power Systems unit, RISE - Research Institutes of Sweden（电力系统单元，瑞典研究机构）
Tomographic SAR Reconstruction for Forest Height Estimation
University of Cambridge（剑桥大学）；United Nations Office for Outer Space Affairs（联合国外层空间事务厅）；UK Department for Energy Security and Net Zero（英国能源安全与净零部）；INSEC TEC；Drexel University（卓克索大学）
本文提出直接由二维 SLC SAR 图像利用深度学习估计森林冠层高度，并评估 SLC 数量影响；结果表明绕过完整层析处理会使误差增加 16%–21%。
IIT Bombay（印度理工学院孟买分校）；Monash University（莫纳什大学）；IITB-Monash Research Academy（印度理工学院孟买分校-莫纳什大学研究院）
The need for tomographic reconstruction from sparse measurements arises when the measurement process is potentially harmful, needs to be rapid, or is uneconomical. In such cases, information from previous longitudinal scans of the same object helps to reconstruct the current object while requiring significantly fewer updating measurements. Our work is based on longitudinal data acquisition scenarios where we wish to study new changes that evolve within an object over time, such as in repeated scanning for disease monitoring, or in tomography-guided surgical procedures. While this is easily fea…
ToNNO: Tomographic Reconstruction of a Neural Network's Output for Weakly Supervised Segmentation of 3D Medical Images
TheraPanacea；University of Crete（克里特大学）；IACM, FORTH（FORTH 应用与计算数学研究所）；Archimedes, Athena RC（雅典研究中心阿基米德研究所）；CentraleSupélec, University of Paris-Saclay（中央理工-高等电力学院，巴黎-萨克雷大学）
Sun Yat-sen University（中山大学）；China Three Gorges University（三峡大学）；The First People’s Hospital of Yichang（宜昌市第一人民医院）
Decreasing projection views to lower X-ray radiation dose usually leads to severe streak artifacts. To improve image quality from sparse-view data, a Multi-domain Integrative Swin Transformer network (MIST-net) was developed in this article. First, MIST-net incorporated lavish domain features from data, residual-data, image, and residual-image using flexible network architectures, where residual-data and residual-image sub-network was considered as data consistency module to eliminate interpolation and reconstruction errors. Second, a trainable edge enhancement filter was incorporated to detec…
High-resolution tomographic reconstruction of optical absorbance through scattering media using neural fields
School of Information Science and Technology, ShanghaiTech University（上海科技大学信息科学与技术学院）；School of Physical Science and Technology, ShanghaiTech University（上海科技大学物理科学与技术学院）；Institute of Mathematical Science, ShanghaiTech University（上海科技大学数学科学研究所）；School of Mathematics, University of Birmingham（伯明翰大学数学学院）
Massachusetts Institute of Technology（麻省理工学院）；qiTech, Inc.（qiTech公司）
We propose a noise-resilient deep reconstruction algorithm for X-ray tomography. Our approach shows strong noise resilience without obtaining noisy training examples. The advantages of our framework may further enable low-photon tomographic imaging.
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Tomographic reconstruction recovers an unknown image given its projections from different angles. State-of-the-art methods addressing this problem assume the angles associated with the projections are known a-priori. Given this knowledge, the reconstruction process is straightforward as it can be formulated as a convex problem. Here, we tackle a more challenging setting: 1) the projection angles are unknown, 2) they are drawn from an unknown probability distribution. In this set-up our goal is to recover the image and the projection angle distribution using an unsupervised adversarial learning…
Deep learning (DL) has shown unprecedented performance for many image analysis and image enhancement tasks. Yet, solving large-scale inverse problems like tomographic reconstruction remains challenging for DL. These problems involve non-local and space-variant integral transforms between the input and output domains, for which no efficient neural network models have been found. A prior attempt to solve such problems with supervised learning relied on a brute-force fully connected network and applied it to reconstruction for a $128^4$ system matrix size. This cannot practically scale to realist…
Institute of Biological and Medical Imaging, Helmholtz Zentrum Munich（慕尼黑亥姆霍兹中心生物与医学成像研究所）；Technical University Munich（慕尼黑工业大学）
Objective:Optoacoustic (photoacoustic) tomography is aimed at reconstructing maps of the initial pressure rise induced by the absorption of light pulses in tissue. In practice, due to inaccurate assumptions in the forward model, noise and other experimental factors, the images are often afflicted by artifacts, occasionally manifested as negative values. The aim of the work is to develop an inversion method which reduces the occurrence of negative values and improves the quantitative performance of optoacoustic imaging. Methods: We present a novel method for optoacoustic tomography based on an …
Pennsylvania State University（宾夕法尼亚州立大学）；U.S. Naval Research Laboratory（美国海军研究实验室）
Any image recovery algorithm attempts to achieve the highest quality reconstruction in a timely manner. The former can be achieved in several ways, among which are by incorporating Bayesian priors that exploit natural image tendencies to cue in on relevant phenomena. The Hierarchical Bayesian MAP (HB-MAP) is one such approach which is known to produce compelling results albeit at a substantial computational cost. We look to provide further analysis and insights into what makes the HB-MAP work. While retaining the proficient nature of HB-MAP's Type-I estimation, we propose a stochastic approxim…
X$^{2}$-Gaussian: 4D Radiative Gaussian Splatting for Continuous-time Tomographic Reconstruction
The Chinese University of Hong Kong（香港中文大学）；Johns Hopkins University（约翰霍普金斯大学）；The Australian National University（澳大利亚国立大学）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
University of Southern Denmark（南丹麦大学）；Newtec Engineering A/S（Newtec工程公司）；Mads Clausen Institute（马德斯·克劳森研究所）
We present a simple but novel hybrid approach to hyperspectral data cube reconstruction from computed tomography imaging spectrometry (CTIS) images that sequentially combines neural networks and the iterative Expectation Maximization (EM) algorithm. We train and test the ability of the method to reconstruct data cubes of $100\times100\times25$ and $100\times100\times100$ voxels, corresponding to 25 and 100 spectral channels, from simulated CTIS images generated by our CTIS simulator. The hybrid approach utilizes the inherent strength of the Convolutional Neural Network (CNN) with regard to noi…
