Related papers: Lecture Notes on Computerized Tomography
The limited angle Radon transform is notoriously difficult to invert due to its ill-posedness. In this work, we give a mathematical explanation that data-driven approaches can stably reconstruct more information compared to traditional…
X-ray computed tomography (CT) reveals the materials' internal structures non-destructively from a tilt series of projected images. Filtered back projection (FBP) is a widely-adopted reconstruction algorithm in CT owing to its small…
Promoted by the advent of coherent synchrotron light sources, phase contrast tomography allows to resolve three-dimensional variations of an unknown sample's complex refractive index from scattering intensities recorded at different…
These notes were compiled as lecture notes for a course developed and taught at the University of the Southern California. They should be accessible to a typical engineering graduate student with a strong background in Applied Mathematics.…
The monograph contains a systematic treatment of a circle of problems in analysis and integral geometry related to inversion of the Radon transform on the space of real rectangular matrices. This transform assigns to a function $f$ on the…
Assume you encounter an inverse problem that shall be solved for a large number of data, but no ground-truth data is available. To emulate this encounter, in this study, we assume it is unknown how to solve the imaging problem of Computed…
Neutron Computed Tomography (CT) is an increasingly utilised non-destructive analysis tool in material science, palaeontology, and cultural heritage. With the development of new neutron imaging facilities (such as DINGO, ANSTO, Australia)…
Classical methods for X-ray computed tomography are based on the assumption that the X-ray source intensity is known, but in practice, the intensity is measured and hence uncertain. Under normal operating conditions, when the exposure time…
Representation learning has been a critical topic in machine learning. In Click-through Rate Prediction, most features are represented as embedding vectors and learned simultaneously with other parameters in the model. With the development…
Cone beam computed tomography (CBCT) is an important imaging technology widely used in medical scenarios, such as diagnosis and preoperative planning. Using fewer projection views to reconstruct CT, also known as sparse-view reconstruction,…
Low dose computed tomography (LDCT) has attracted more and more attention in routine clinical diagnosis assessment, therapy planning, etc., which can reduce the dose of X-ray radiation to patients. However, the noise caused by low X-ray…
Unlike previous works, this open data collection consists of X-ray cone-beam (CB) computed tomography (CT) datasets specifically designed for machine learning applications and high cone-angle artefact reduction. Forty-two walnuts were…
Tomography deals with the reconstruction of objects from their projections, acquired along a range of angles. Discrete tomography is concerned with objects that consist of a small number of materials, which makes it possible to compute…
Performing X-ray computed tomography (CT) examinations with less radiation has recently received increasing interest: in medical imaging this means less (potentially harmful) radiation for the patient; in non-destructive testing of…
Radon Transformation is generally used to construct optical image (like CT image) from the projection data in biomedical imaging. In this paper, the concept of Radon Transformation is implemented to reconstruct Electrical Impedance…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
Using projections on the (generalized) eigenvectors associated to matrices that characterize the topological structure, several authors have constructed generalizations of the Fourier transform on graphs. By exploring mappings of the…
These are lecture notes that arose from a representation theory course given by the first author to the remaining six authors in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students,…
X-ray computed tomography is a powerful tool for volumetric imaging, where three-dimensional (3D) images are generated from a large number of individual X-ray projection images. Collecting the required number of low noise projection images…
Time-resolved high-resolution X-ray Computed Tomography (4D $\mu$CT) is an imaging technique that offers insight into the evolution of dynamic processes inside materials that are opaque to visible light. Conventional tomographic…