Limited-angle tomography is a highly ill-posed linear inverse problem. It arises in many applications, such as digital breast tomosynthesis. Reconstructions from limited-angle data typically suffer from severe stretching of features along the central direction of projections, leading to poor separation between slices perpendicular to the central direction. A new method is introduced, based on machine learning and geometry, producing an estimate for interfaces between regions of different X-ray attenuation. The estimate can be presented on top of the reconstruction, indicating more reliably the true form and extent of features. The method uses directional edge detection, implemented using complex wavelets and enhanced with morphological operations. By using machine learning, the visible part of the wavefront set is first extracted and then extended to the full domain, filling in the parts of the wavefront set that would otherwise be hidden due to the lack of measurement directions.
Here we present new joint reconstruction and regularization techniques inspired by ideas in microlocal analysis and lambda tomography, for the simultaneous reconstruction of the attenuation coefficient and electron density from X-ray transmission (i.e., X-ray CT) and backscattered data (assumed to be primarily Compton scattered). To demonstrate our theory and reconstruction methods, we consider the "parallel line segment" acquisition geometry of Webber and Miller ("Compton scattering tomography in translational geometries." Inverse Problems 36, no. 2 (2020): 025007), which is motivated by syst…
We present a Machine Learning-based method for tomographic reconstruction of dense layered objects, with range of projection angles limited to $\pm $10$^\circ$. Whereas previous approaches to phase tomography generally require two steps, first to retrieve phase projections from intensity projections and then perform tomographic reconstruction on the retrieved phase projections, in our work a physics-informed pre-processor followed by a Deep Neural Network (DNN) conduct the three-dimensional reconstruction directly from the intensity projections. We demonstrate this single-step method experimen…
Shenzhen University（深圳大学）；University of Delaware（特拉华大学）；Chongqing University（重庆大学）；Chongqing University of Science and Technology（重庆科技大学）
In this paper, we first propose a variational model for the limited-angle computed tomography (CT) image reconstruction and then convert the model into an end-to-end deep network.We use the penalty method to solve the model and divide it into three iterative subproblems, where the first subproblem completes the sinograms by utilizing the prior information of sinograms in the frequency domain and the second refines the CT images by using the prior information of CT images in the spatial domain, and the last merges the outputs of the first two subproblems. In each iteration, we use the convoluti…
Dispersion is a common phenomenon in optics due to the frequency dependence of the refractive index in polychromatic light. This issue, if left untreated in optical coherence tomography (OCT) imaging, leads to signal broadening of the coherence length and deterioration of the axial resolution. We report a new numeric method for the systematic dispersion compensation in a spectral-domain (SD) OCT for imaging the iridocorneal angle of human cadaver eyes. The dispersion compensation for our OCT system is calculated by an automated iterative process that minimizes the wavenumber-dependent variance…
Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希-亚历山大大学）；Siemens Healthcare GmbH（西门子医疗有限公司）；Shanghai Jiao Tong University（上海交通大学）；Erlangen Graduate School in Advanced Optical Technologies (SAOT)（埃尔朗根先进光学技术研究生院（SAOT））
Robustness of deep learning methods for limited angle tomography is challenged by two major factors: a) due to insufficient training data the network may not generalize well to unseen data; b) deep learning methods are sensitive to noise. Thus, generating reconstructed images directly from a neural network appears inadequate. We propose to constrain the reconstructed images to be consistent with the measured projection data, while the unmeasured information is complemented by learning based methods. For this purpose, a data consistent artifact reduction (DCAR) method is introduced: First, a pr…
Massachusetts Institute of Technology（麻省理工学院）；Sandia National Laboratory（桑迪亚国家实验室）
Limited-angle X-ray tomography reconstruction is an ill-conditioned inverse problem in general. Especially when the projection angles are limited and the measurements are taken in a photon-limited condition, reconstructions from classical algorithms such as filtered backprojection may lose fidelity and acquire artifacts due to the missing-cone problem. To obtain satisfactory reconstruction results, prior assumptions, such as total variation minimization and nonlocal image similarity, are usually incorporated within the reconstruction algorithm. In this work, we introduce deep neural networks t…
University of Helsinki（赫尔辛基大学）；University of Modena and Reggio Emilia（摩德纳-雷焦艾米利亚大学）
We propose a novel convolutional neural network (CNN), called $Ψ$DONet, designed for learning pseudodifferential operators ($Ψ$DOs) in the context of linear inverse problems. Our starting point is the Iterative Soft Thresholding Algorithm (ISTA), a well-known algorithm to solve sparsity-promoting minimization problems. We show that, under rather general assumptions on the forward operator, the unfolded iterations of ISTA can be interpreted as the successive layers of a CNN, which in turn provides fairly general network architectures that, for a specific choice of the parameters involved, allow…
We propose a novel intensity diffraction tomography (IDT) reconstruction algorithm based on the split-step non-paraxial (SSNP) model for recovering the 3D refractive index (RI) distribution of multiple-scattering biological samples. High-quality IDT reconstruction requires high-angle illumination to encode both low- and high- spatial frequency information of the 3D biological sample. We show that our SSNP model can more accurately compute multiple scattering from high-angle illumination compared to paraxial approximation-based multiple-scattering models. We apply this SSNP model to both sequen…
Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔朗根-纽伦堡弗里德里希-亚历山大大学）；Spallation Neutron Source Science Center（散裂中子源科学中心）；Institute of High Energy Physics, Chinese Academy of Sciences（中国科学院高能物理研究所）；University of Science and Technology of China（中国科学技术大学）
In transmission X-ray microscopy (TXM) systems, the rotation of a scanned sample might be restricted to a limited angular range to avoid collision to other system parts or high attenuation at certain tilting angles. Image reconstruction from such limited angle data suffers from artifacts due to missing data. In this work, deep learning is applied to limited angle reconstruction in TXMs for the first time. With the challenge to obtain sufficient real data for training, training a deep neural network from synthetic data is investigated. Particularly, the U-Net, the state-of-the-art neural networ…
Computed Tomography (CT) is a non-invasive imaging modality with applications ranging from healthcare to security. It reconstructs cross-sectional images of an object using a collection of projection data collected at different angles. Conventional methods, such as FBP, require that the projection data be uniformly acquired over the complete angular range. In some applications, it is not possible to acquire such data. Security is one such domain where non-rotational scanning configurations are being developed which violate the complete data assumption. Conventional methods produce images from …
Attentional Ptycho-Tomography (APT) for three-dimensional nanoscale X-ray imaging with minimal data acquisition and computation time
Argonne National Laboratory（阿贡国家实验室）；Massachusetts Institute of Technology（麻省理工学院）；Singapore-MIT Alliance for Research and Technology (SMART) Centre（新加坡-麻省理工研究与技术联盟（SMART）中心）；University of California, Berkeley（加州大学伯克利分校）
Computed Tomography (CT) is an imaging technique where information about an object are collected at different angles (called projections or scans). Then the cross-sectional image showing the internal structure of the slice is produced by solving an inverse problem. Limited by certain factors such as radiation dosage, projection angles, the produced images can be noisy or contain artifacts. Inspired by the success of transformer for natural language processing, the core idea of this preliminary study is to consider a projection of tomography as a word token, and the whole scan of the cross-sect…
Circular cone-beam (CCB) Computed Tomography (CT) has become an integral part of industrial quality control, materials science and medical imaging. The need to acquire and process each scan in a short time naturally leads to trade-offs between speed and reconstruction quality, creating a need for fast reconstruction algorithms capable of creating accurate reconstructions from limited data. In this paper we introduce the Neural Network Feldkamp-Davis-Kress (NN-FDK) algorithm. This algorithm adds a machine learning component to the FDK algorithm to improve its reconstruction accuracy while maint…
Graz University of Technology（格拉茨技术大学）；Johannes Kepler University Linz（约翰内斯·开普勒林茨大学）
In the past decades, Computed Tomography (CT) has established itself as one of the most important imaging techniques in medicine. Today, the applicability of CT is only limited by the deposited radiation dose, reduction of which manifests in noisy or incomplete measurements. Thus, the need for robust reconstruction algorithms arises. In this work, we learn a parametric regularizer with a global receptive field by maximizing it's likelihood on reference CT data. Due to this unsupervised learning strategy, our trained regularizer truly represents higher-level domain statistics, which we empirica…
AI-driven projection tomography with multicore fibre-optic cell rotation
Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；TU Dresden（德累斯顿工业大学）；Max Planck Institute for the Science of Light（马克斯·普朗克光科学研究所）；Max Planck-Zentrum für Physik und Medizin（马克斯·普朗克物理与医学中心）
