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pro vyhledávání: '"A. A. Edidin"'
Semi-algebraic priors are ubiquitous in signal processing and machine learning. Prevalent examples include a) linear models where the signal lies in a low-dimensional subspace; b) sparse models where the signal can be represented by only a few coeffi
Externí odkaz:
http://arxiv.org/abs/2405.04354
The classical beltway problem entails recovering a set of points from their unordered pairwise distances on the circle. This problem can be viewed as a special case of the crystallographic phase retrieval problem of recovering a sparse signal from it
Externí odkaz:
http://arxiv.org/abs/2402.03787
The key ingredient to retrieving a signal from its Fourier magnitudes, namely, to solve the phase retrieval problem, is an effective prior on the sought signal. In this paper, we study the phase retrieval problem under the prior that the signal lies
Externí odkaz:
http://arxiv.org/abs/2311.08833
We consider the finite alphabet phase retrieval problem: recovering a signal whose entries lie in a small alphabet of possible values from its Fourier magnitudes. This problem arises in the celebrated technology of X-ray crystallography to determine
Externí odkaz:
http://arxiv.org/abs/2301.10647
Autor:
Bendory, Tamir, Edidin, Dan
Multi-reference alignment (MRA) is the problem of recovering a signal from its multiple noisy copies, each acted upon by a random group element. MRA is mainly motivated by single-particle cryo-electron microscopy (cryo-EM) that has recently joined X-
Externí odkaz:
http://arxiv.org/abs/2210.15727
Autor:
Bendory, Tamir, Edidin, Dan
The purpose of this article is to discuss recent advances in the growing field of phase retrieval, and to publicize open problems that we believe will be of interest to mathematicians in general, and algebraists in particular.
Externí odkaz:
http://arxiv.org/abs/2203.02774
We study the problem of recovering a signal $x\in\mathbb{C}^N$ from samples of its phaseless periodic short-time Fourier transform (STFT): the magnitude of the Fourier transform of the signal multiplied by a sliding window $w\in \mathbb{C}^W$. We sho
Externí odkaz:
http://arxiv.org/abs/2112.02836
We study the dihedral multi-reference alignment problem of estimating the orbit of a signal from multiple noisy observations of the signal, acted on by random elements of the dihedral group. We show that if the group elements are drawn from a generic
Externí odkaz:
http://arxiv.org/abs/2107.05262
Autor:
Dey, Papri, Edidin, Dan
Let ${\mathcal A} = \{A_{1},\dots,A_{r}\}$ be a collection of linear operators on ${\mathbb R}^m$. The degeneracy locus of ${\mathcal A}$ is defined as the set of points $x \in {\mathbb P}^{m-1}$ for which rank$([A_1 x \ \dots \ A_{r} x]) \\ \leq m-1
Externí odkaz:
http://arxiv.org/abs/2105.14970
The $q$-th order spectrum is a polynomial of degree $q$ in the entries of a signal $x\in\mathbb{C}^N$, which is invariant under circular shifts of the signal. For $q\geq 3$, this polynomial determines the signal uniquely, up to a circular shift, and
Externí odkaz:
http://arxiv.org/abs/2103.01551