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3D reconstruction from 2D images is a central problem in computer vision. Recent works have been focusing on reconstruction directly from a single image. It is well known however that only one image cannot provide enough information for…

We introduce Patchwork, a new general-purpose shape representation capable of modeling 2D and 3D geometry with a small number of parameters. Patchwork is grounded in a rigorous mathematical framework, providing provable complexity bounds…

Diffusion models have become the most popular approach to deep generative modeling of images, largely due to their empirical performance and reliability. From a theoretical standpoint, a number of recent works have studied the iteration…

This paper analyzes the nonlinear correspondence between the reflectivity profile (model) and the plane wave impulse response at the boundary (data) for a three-dimensional half space consisting of a sequence of homogeneous horizontal…

The problem of diffraction of a waveguide mode by a thin Neumann screen is considered. The incident mode is assumed to have frequency close to the cut-off. The problem is reduced to a propagation problem on a branched surface and then is…

Using i.i.d. data to estimate a high-dimensional distribution in Wasserstein distance is a fundamental instance of the curse of dimensionality. We explore how structural knowledge about the data-generating process which gives rise to the…

While perspective is a well-studied topic in art, it is generally taken for granted in images. However, for the recent wave of high-quality image synthesis methods such as latent diffusion models, perspective accuracy is not an explicit…

Deep neural networks give state-of-the-art accuracy for reconstructing images from few and noisy measurements, a problem arising for example in accelerated magnetic resonance imaging (MRI). However, recent works have raised concerns that…

A theory for multiple scattering of elastic waves is presented in a random medium bounded by two ideal free surfaces, whose horizontal size is infinite and whose transverse size is smaller than the mean free path of the waves. This geometry…

Ptychography is a computational method of microscopy that recovers high-resolution transmission images of samples from a series of diffraction patterns. While conventional phase retrieval algorithms can iteratively recover the images, they…

Electrical impedance tomography is an imaging modality for extracting information on the conductivity distribution inside a physical body from boundary measurements of current and voltage. In many practical applications, it is a priori…

Ptychography, as an essential tool for high-resolution and nondestructive material characterization, presents a challenging large-scale nonlinear and non-convex inverse problem; however, its intrinsic photon statistics create clear…

We consider wave propagation problems over 2-dimensional domains with piecewise-linear boundaries, possibly including scatterers. We assume that the wave speed is constant, and that the initial conditions and forcing terms are radially…

Resonant scattering of plane waves by a periodic slab under conditions close to those that support a guided mode is accompanied by sharp transmission anomalies. For two-dimensional structures, we establish sufficient conditions, involving…

We study the backward scatterings of plane waves by reciprocal scatterers and reveal that $n$-fold ($n\geq3$) rotation symmetry is sufficient to secure invariant backscattering for arbitrarily-polarized incident plane waves. It is further…

Ptychographic Coherent Diffractive Imaging enables diffraction-limited imaging of nanoscale structures at extreme ultraviolet and x-ray wavelengths, where high-quality image-forming optics are not available. However, its reliance on a set…

Desert mirages were simulated in the laboratory by heating a flat surface of sand. This showed that a boundary layer of air, of only a few millimeters immediately covering a heated surface has nearly the same thickness over a wide range of…

An appealing requirement from the well-known diffraction tomography (DT) exists for success reconstruction from few-view and limited-angle data. Inspired by the well-known compressive sensing (CS), the accurate super-resolution…

We are concerned with the inverse scattering problem of extracting the geometric structures of an unknown/inaccessible inhomogeneous medium by using the corresponding acoustic far-field measurement. Using the intrinsic geometric properties…

Limited-angle electron tomography aims to reconstruct 3D shapes from 2D projections of Transmission Electron Microscopy (TEM) within a restricted range and number of tilting angles, but it suffers from the missing-wedge problem that causes…