Related papers: Determination of compactly supported functions in …
Sparse-view computed tomography (SVCT) reconstruction aims to acquire CT images based on sparsely-sampled measurements. It allows the subjects exposed to less ionizing radiation, reducing the lifetime risk of developing cancers. Recent…
Implicit neural representations (INRs) have emerged as a powerful tool for solving inverse problems in computer vision and computational imaging. INRs represent images as continuous domain functions realized by a neural network taking…
We present novel microlocal and injectivity analyses of ellipsoid and hyperboloid Radon transforms. We introduce a new Radon transform, $R$, which defines the integrals of a compactly supported $L^2$ function, $f$, over ellipsoids and…
The light field reconstruction from the focal stack can be mathematically formulated as an ill-posed integral equation inversion problem. Although the previous research about this problem has made progress both in practice and theory, its…
We introduce a single-view reconstruction technique of volumetric fields in which multiple light scattering effects are omnipresent, such as in clouds. We model the unknown distribution of volumetric fields using an unconditional diffusion…
We study the inverse problem of unique recovery of a complex-valued scalar function $V:\mathcal M \times \mathbb C\to \mathbb C$, defined over a smooth compact Riemannian manifold $(\mathcal M,g)$ with smooth boundary, given the Dirichlet…
This paper addresses the electromagnetic inverse scattering problem of determining the location and shape of anisotropic objects from near-field data. We investigate both cases involving the Helmholtz equation and Maxwell's equations for…
In recent work [P. Grohs and M. Rathmair. Stable Gabor Phase Retrieval and Spectral Clustering. Communications on Pure and Applied Mathematics (2018)] the instabilities of the Gabor phase retrieval problem, i.e., the problem of…
Neural fields or implicit neural representations (INRs) have attracted significant attention in computer vision and imaging due to their efficient coordinate-based representation of images and 3D volumes. In this work, we introduce a…
This thesis is concerned with problems related to Synthetic Aperture Radar (SAR). The thesis is structured as follows: The first chapter explains what SAR is, and the physical and mathematical background is illuminated. The following…
We introduce a technique for recovering a sufficiently smooth function from its ray transform over a wide class of curves in a general region of Euclidean space. The method is based on a complexification of the underlying vector fields…
For a harmonic map $\mathcal{F}:\mathcal{Z} {\buildrel {\,harm\,} \over\longrightarrow} \mathcal{W}$ transforming the contour of a corner of the boundary $\partial\mathcal{Z}$ into a rectilinear segment of the boundary…
Synthesizing novel views from a single view image is a highly ill-posed problem. We discover an effective solution to reduce the learning ambiguity by expanding the single-view view synthesis problem to a multi-view setting. Specifically,…
Functions which are equivariant or invariant under the transformations of a compact linear group $G$ acting in an euclidean space $\real^n$, can profitably be studied as functions defined in the orbit space of the group. The orbit space is…
We study the problem of recovering an unknown compactly-supported multivariate function from samples of its Fourier transform that are acquired nonuniformly, i.e. not necessarily on a uniform Cartesian grid. Reconstruction problems of this…
In this paper, we focus on the approximation of smooth functions $f: [-\pi, \pi] \rightarrow \mathbb{C}$, up to an unresolvable global phase ambiguity, from a finite set of Short Time Fourier Transform (STFT) magnitude (i.e., spectrogram)…
We show that for an entire function $\varphi$ belonging to the Fock space ${\mathscr F}^2(\mathbb{C}^n)$ on the complex Euclidean space $\mathbb{C}^n$, the integral operator \begin{eqnarray*} S_{\varphi}F(z)=\int_{\mathbb{C}^n} F(w) e^{z…
The paper develops theory of covariant transform, which is inspired by the wavelet construction. It was observed that many interesting types of wavelets (or coherent states) arise from group representations which are not square integrable…
In this paper, we study random sampling on reproducing kernel space $V$, which is a range of an idempotent integral operator. Under certain decay condition on the integral kernel, we show that any element in $V$ can be approximated by an…
We study an Aganagic-Vafa brane supported on a special Lagrangian submanifold $\mathcal{L}$ in a non-compact toric Calabi-Yau threefold $\mathcal{X}$. From the perspective of geometric engineering, the Aganagic-Vafa branes give rise to a…