Related papers: A note on phase (norm) retrievable Real Hilbert sp…
The injectivity of ReLU layers in neural networks, the recovery of vectors from clipped or saturated measurements, and (real) phase retrieval in $\mathbb{R}^n$ allow for a similar problem formulation and characterization using frame theory.…
In this article, we propose and analyze an effective Hessian recovery strategy for the Lagrangian finite element of arbitrary order $k$. We prove that the proposed Hessian recovery preserves polynomials of degree $k+1$ on general…
Outer product frames are important objects in Hilbert space frame theory. But very little is known about them. In this paper, we make the first detailed study of the family of outer product frames induced directly by vector sequences. We…
Hyperspectral measurements from long range sensors can give a detailed picture of the items, materials, and chemicals in a scene but analysis can be difficult, slow, and expensive due to high spatial and spectral resolutions of…
Deep generative models such as diffusion and flow matching are powerful machine learning tools capable of learning and sampling from high-dimensional distributions. They are particularly useful when the training data appears to be…
Dense retrieval has been shown to be effective for retrieving relevant documents for Open Domain QA, surpassing popular sparse retrieval methods like BM25. REALM (Guu et al., 2020) is an end-to-end dense retrieval system that relies on MLM…
We present a new method for real- and complex-valued image reconstruction from two intensity measurements made in the Fourier plane: the Fourier magnitude of the unknown image, and the intensity of the interference pattern arising from…
In many scientific applications, the target probability distribution cannot be evaluated in closed form or sampled from directly. Instead, it can often be decomposed into multiple components, some of which are accessible only through…
We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…
The profusion of spectral bands generated by the acquisition process of hyperspectral images generally leads to high computational costs. Such difficulties arise in particular with nonlinear unmixing methods, which are naturally more…
Natural images tend to mostly consist of smooth regions with individual pixels having highly correlated spectra. This information can be exploited to recover hyperspectral images of natural scenes from their incomplete and noisy…
In this paper we consider the following problem of phase retrieval: Given a collection of real-valued band-limited functions $\{\psi_{\lambda}\}_{\lambda\in \Lambda}\subset L^2(\mathbb{R}^d)$ that constitutes a semi-discrete frame, we ask…
In this paper, we settle a long-standing problem on the connectivity of spaces of finite unit norm tight frames (FUNTFs), essentially affirming a conjecture first appearing in [Dykema and Strawn, 2003]. Our central technique involves…
Given $k:\mathbb{R}^n\setminus\{0\} \to \mathbb{R}^n$ a kernel of class $C^2$ and homogeneous of degree $1-n$, we prove existence and uniqueness of H\"older regular solutions for some non-linear transport equations with velocity fields…
We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for the Helmholtz equation in an exterior region in $\mathbb{R}^d,$ $d\geq 2$. In this region, we consider a hyperplane $X$ with sufficiently…
In this paper, a novel parallel hybrid iterative method is proposed for finding a common element of the set of solutions of a system of equilibrium problems, the set of solutions of variational inequalities for inverse strongly monotone…
While dense retrieval models, which embed queries and documents into a shared low-dimensional space, have gained widespread popularity, they were shown to exhibit important theoretical limitations and considerably lag behind traditional…
Let $(\Omega,\Sigma,\mu)$ be a measure space, and $1\leq p\leq \infty$. A subspace $E\subseteq L_p(\mu)$ is said to do stable phase retrieval (SPR) if there exists a constant $C\geq 1$ such that for any $f,g\in E$ we have $$…
We consider the problem of compressed sensing and of (real-valued) phase retrieval with random measurement matrix. We derive sharp asymptotics for the information-theoretically optimal performance and for the best known polynomial algorithm…
In the compressive phase retrieval problem, or phaseless compressed sensing, or compressed sensing from intensity only measurements, the goal is to reconstruct a sparse or approximately $k$-sparse vector $x \in \mathbb{R}^n$ given access to…