Phase Retrieval: Uniqueness and Stability

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, speech ...

Small changes at single nodes can shift global network dynamics

Understanding the sensitivity of a system's behavior with respect to
parameter changes is essential for many applications. This sensitivity may be
desired - for instance in the brain, where a large re ...

Dual-Frequency Quantum Phase Estimation Mitigates the Spectral Leakage of Quantum Algorithms

Quantum phase estimation is an important component in diverse quantum
algorithms. However, it suffers from spectral leakage, when the reciprocal of
the record length is not an integer multiple of the ...

Phase Retrieval for $L^2([-π,π])$ via the Provably Accurate and Noise Robust Numerical Inversion of Spectrogram Measurements

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 Transfor ...

Phase-Modulated Rapid-Scanning Fluorescence-Detected Two-Dimensional Electronic Spectroscopy

We present a rapid-scanning approach to fluorescence-detected two-dimensional
electronic spectroscopy that combines acousto-optic phase-modulation with
digital lock-in detection. The approach shifts t ...

Phase and amplitude dynamics of coupled oscillator systems on complex networks

We investigated the locking behaviors of coupled limit-cycle oscillators with
phase and amplitude dynamics. We focused on how the dynamics are affected by
inhomogeneous coupling strength and by angula ...

Information Theory

Functional Analysis

Optimization and Control

Math Numerical Analysis

Statistics Theory

Phase Retrieval via Wirtinger Flow: Theory and Algorithms

We study the problem of recovering the phase from magnitude measurements;
specifically, we wish to reconstruct a complex-valued signal x of C^n about
which we have phaseless samples of the form y_r = ...

Construction of optimal spectral methods in phase retrieval

We consider the phase retrieval problem, in which the observer wishes to
recover a $n$-dimensional real or complex signal $\mathbf{X}^\star$ from the
(possibly noisy) observation of $|\mathbf{\Phi} \m ...

Quantum limits on phase-preserving linear amplifiers

The purpose of a phase-preserving linear amplifier is to make a small signal
larger, regardless of its phase, so that it can be perceived by instruments
incapable of resolving the original signal, whi ...

Evaluating phase synchronization methods in fMRI: a comparison study and new approaches

In recent years there has been growing interest in measuring time-varying
functional connectivity between different brain regions using resting-state
functional magnetic resonance imaging (rs-fMRI) da ...