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Kinematic diffraction is well suited for a mathematical approach via measures, which has substantially been developed since the discovery of quasicrystals. The need for further insight emerged from the question of which distributions of…
We propose a convolutional neural network (CNN) approach that works synergistically with physics-based reconstruction methods to reduce artifacts in accelerated MRI. Given reconstructed coil k-spaces, our network predicts a k-space…
Approximation theory plays an important role in image processing, especially image deconvolution and decomposition. For piecewise smooth images, there are many methods that have been developed over the past thirty years. The goal of this…
Distance transforms are a central tool in shape analysis, morphometry, and curve evolution problems. This work describes and investigates an artifact present in distance maps computed from sampled signals. Namely, sampling reflects through…
Focused ion beams (FIBs) are widely used in nanofabrication for applications such as circuit repair, ultra-thin lamella preparation, strain engineering, and quantum device prototyping. Although the lateral spread of the ion beam is often…
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…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
The degenerate parabolic Generalized Porous Medium Equation (GPME) poses numerical challenges due to self-sharpening and its sharp corner solutions. For these problems, we show results for two subclasses of the GPME with differentiable…
We propose approaches based on deep learning to localize objects in images when only a small training dataset is available and the images have low quality. That applies to many problems in medical image processing, and in particular to the…
Hyperbolic metamaterials are materials in which at least one principal dielectric constant is negative. We describe the refractive index surface, and the resulting refraction effects, for a biaxial hyperbolic metamaterial, with principal…
A wave-packet time evolution method, based on the split-operator technique, is developed to investigate the scattering of quasi-particles at a normal-superconductor interface of arbitrary profile and shape. As a practical application, we…
Spreading uniform and dense layers is of paramount importance to creating high-quality components using powder bed additive manufacturing (AM). Blade-like tools are often employed for spreading powder metal feedstocks, especially in laser…
In this study, we present a methodology to predict the macroscopic yield surface of metals and metallic alloys with general crystallographic textures. In previous work, we have established the use of partially input convex neural networks…
Scatter can account for large errors in cone-beam CT (CBCT) due to its wide field of view, and its complicated nature makes its compensation difficult. Iterative polyenergetic reconstruction algorithms offer the potential to provide…
A sparsity-exploiting algorithm intended for few-view Single Photon Emission Computed Tomography (SPECT) reconstruction is proposed and characterized. The algorithm models the object as piecewise constant subject to a blurring operation. To…
Spectral computed tomography (CT) is an emerging technology capable of providing high chemical specificity, which is crucial for many applications such as detecting threats in luggage. This type of application requires both fast and…
Multi-spectral computed tomography is an emerging technology for the non-destructive identification of object materials and the study of their physical properties. Applications of this technology can be found in various scientific and…
The integral-field unit (IFU) spectrometers on board the James Webb Space Telescope (JWST) undersample the nearly diffraction-limited point spread function provided by the telescope optics. This undersampling produces large oscillating…
We study the geometrical characteristic of quasi-static fractures in disordered media, using iterated conformal maps to determine the evolution of the fracture pattern. This method allows an efficient and accurate solution of the Lam\'e…
Cone-beam CT (CBCT) employs a flat-panel detector to achieve three-dimensional imaging with high spatial resolution. However, CBCT is susceptible to scatter during data acquisition, which introduces CT value bias and reduced tissue contrast…