164 Citations
STABILITY OF FRAMES WHICH GIVE PHASE RETRIEVAL
- Mathematics
- 2015
In this paper we study the property of phase retrievability by redundant sysems of vectors under perturbations of the frame set. Specifically we show that if a set F of m vectors in the complex…
Strong convexity of affine phase retrieval
- MathematicsArXiv
- 2022
The recovery of a signal from the intensity measurements with some entries being known in advance is termed as affine phase retrieval . In this paper, we prove that a natural least squares formulation…
Stability of Phase Retrieval Problem
- Mathematics2019 13th International conference on Sampling Theory and Applications (SampTA)
- 2019
A new method based on the frame order statistics is proposed, which can be used to establish stability of the measurement maps for other classes of frames, namely, frames with independent frame vectors satisfying bounded fourth moment assumption and frames with no independence assumptions.
Phase Retrieval via Wirtinger Flow: Theory and Algorithms
- Computer ScienceIEEE Transactions on Information Theory
- 2015
This paper develops a nonconvex formulation of the phase retrieval problem as well as a concrete solution algorithm that is shown to rigorously allow the exact retrieval of phase information from a nearly minimal number of random measurements.
Phase retrieval for affine groups over prime fields
- Mathematics
- 2021
. We study phase retrieval for group frames arising from permutation representations, focusing on the action of the affine group of a finite field. We investigate various versions of the phase retrieval…
The Mathematics of Phase Retrieval
- Physics
- 2019
The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier transform, naturally arises in various fields of physics, such as astronomy, radar,…
Phase Retrieval for Binary Signals: Box Relaxation and Uniqueness
- Computer ScienceArXiv
- 2019
Focusing on binary signals, it is shown that a box relaxation to the binary constraint is equivalent to the original problem and proved that binary signals can be recovered uniquely up to trivial ambiguities under certain conditions.
The Algebraic Approach to Phase Retrieval and Explicit Inversion at the Identifiability Threshold
- Mathematics, Computer ScienceArXiv
- 2014
It is verified that a certain number of generic rank-one or generic linear measurements are sufficient to enable signal reconstruction for generic signals, and slightly more generic measurements yield reconstructability for all signals.
References
SHOWING 1-10 OF 18 REFERENCES
Stable phase retrieval with low-redundancy frames
- MathematicsAdv. Comput. Math.
- 2015
This work shows that for complex vectors in d dimensions, 4d−4 suitably chosen frame vectors are sufficient to uniquely determine each signal, up to an overall unimodular constant, from the magnitudes of its frame coefficients.
Algebraic Reconstruction Bounds and Explicit Inversion for Phase Retrieval at the Identifiability Threshold
- Mathematics, Computer ScienceAISTATS
- 2014
It is verified that a certain number of generic rank-one or generic linear measurements are sufficient to enable signal reconstruction for generic signals, and slightly more generic measurements yield reconstructability for all signals.
Basic algebraic geometry
- Mathematics
- 1974
The second volume of Shafarevich's introductory book on algebraic geometry focuses on schemes, complex algebraic varieties and complex manifolds. As with first volume the author has revised the text…
Quantum Tomography under Prior Information
- Economics, Mathematics
- 2013
We provide a detailed analysis of the question: how many measurement settings or outcomes are needed in order to identify an unknown quantum state which is constrained by prior information? We show…
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
- Mathematics
- 1992
Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: Does the The denominator is taking on this, book interested. This book for…
Ideals, Varieties, and Algorithms
- Mathematics
- 1997
(here, > is the Maple prompt). Once the Groebner package is loaded, you can perform the division algorithm, compute Groebner bases, and carry out a variety of other commands described below. In…
Discriminants, Resultants, and Multidimensional Determinants
- Mathematics
- 1994
Preface.- Introduction.- General Discriminants and Resultants.- Projective Dual Varieties and General Discriminants.- The Cayley Method of Studying Discriminants.- Associated Varieties and General…