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We reconstruct 3D deformable object through time, in the context of a live pottery making process where the crafter molds the object. Because the object suffers from heavy hand interaction, and is being deformed, classical techniques cannot…
We consider the one-phase Stefan problem describing the evolution of melting ice. On the one hand, we focus on understanding the evolution of the free boundary near isolated singular points, and we establish for the first time upper and…
We propose inverse renormalization group transformations to construct approximate configurations for lattice volumes that have not yet been accessed by supercomputers or large-scale simulations in the study of spin glasses. Specifically,…
Image restoration is a class of important tasks that emerges from a wide range of scientific disciplines. It has been noticed that most practical images can be modeled as a composition from a sparse singularity set (edges) where the image…
The two-dimensional Radon transform of the Wigner quasiprobability is introduced in canonical form and the functions playing a role in its inversion are discussed. The transformation properties of this Radon transform with respect to…
Normally one assumes isolated surface singularities to be normal. The purpose of this paper is to show that it can be useful to look at nonnormal singularities. By deforming them interesting normal singularities can be constructed, such as…
Hyperspectral neutron computed tomography enables 3D non-destructive imaging of the spectral characteristics of materials. In traditional hyperspectral reconstruction, the data for each neutron wavelength bin is reconstructed separately.…
High density implants such as metals often lead to serious artifacts in the reconstructed CT images which hampers the accuracy of image based diagnosis and treatment planning. In this paper, we propose a novel wavelet frame based CT image…
This paper introduces a new approach for the automated reconstruction - reassembly of fragmented objects having one surface near to plane, on the basis of the 3D representation of their constituent fragments. The whole process starts by 3D…
We present new higher-order quadratures for a family of boundary integral operators re-derived using the approach introduced in [Kublik, Tanushev, and Tsai - J. Comp. Phys. 247: 279-311, 2013]. In this formulation, a boundary integral over…
Random Reshuffling (RR) is an algorithm for minimizing finite-sum functions that utilizes iterative gradient descent steps in conjunction with data reshuffling. Often contrasted with its sibling Stochastic Gradient Descent (SGD), RR is…
The modern imaging techniques of Positron Emission Tomography and of Single Photon Emission Computed Tomography are not only two of the most important tools for studying the functional characteristics of the brain, but they now also play a…
A weak wild arithmetic quotient singularity arises from the quotient of a smooth arithmetic surface by a finite group action, where the inertia group of a point on a closed characteristic p fiber is a p-group acting with smallest possible…
Modern tomography involves gathering projection data from multiple directions and feeding them into a software algorithm for tomographic reconstruction. We focus our study on image reconstruction from Radon data in the setting of…
This paper considers the reconstruction problem in Acousto-Electrical Tomography, i.e., the problem of estimating a spatially varying conductivity in a bounded domain from measurements of the internal power densities resulting from…
We prove partial regularity of weakly stationary harmonic maps with (partially) free boundary data on manifolds where the domain metric may degenerate or become singular along the free boundary at the rate $d^\alpha$ for the distance…
This paper presents several new algorithms for the regularized reconstruction of a surface from its measured gradient field. By taking a matrix-algebraic approach, we establish general framework for the regularized reconstruction problem…
An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…
In the realm of robotics, numerous downstream robotics tasks leverage machine learning methods for processing, modeling, or synthesizing data. Often, this data comprises variables that inherently carry geometric constraints, such as the…
Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the…