相关论文: Stable Gabor Phase Retrieval and Spectral Clusteri…
The phase retrieval problem has a long history and is an important problem in many areas of optics. Theoretical understanding of phase retrieval is still limited and fundamental questions such as uniqueness and stability of the recovered…
For 2D compressible Euler equations of isentropic gas, we prove the structural stability of mixed Riemann configurations containing centered rarefaction waves and surfaces of discontinuities (such as shock waves or vortex sheets), by…
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 $\fc$ of $m$ vectors in the complex Hilbert space of dimension n allows for…
For the optical testing of a large mirror with a long radius of curvature, it is generally necessary to use a single-shot phase-shifting interferometer to take several measurements because the influence of air turbulence on air…
X-ray ptychography is one of the versatile techniques for nanometer resolution imaging. The magnitude of the diffraction patterns is recorded on a detector and the phase of the diffraction patterns is estimated using phase retrieval…
Signal recovery from nonlinear measurements involves solving an iterative optimization problem. In this paper, we present a framework to optimize the sensing parameters to improve the quality of the signal recovered by the given iterative…
Reconstruction of multidimensional signals from the samples of their partial derivatives is known to be a standard problem in inverse theory. Such and similar problems routinely arise in numerous areas of applied sciences, including optical…
Optical spectroscopy the measurement of electromagnetic spectra is fundamental to various scientific domains and serves as the building block of numerous technologies. Computational spectrometry is an emerging field that employs an array of…
We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…
We develop a fast phase retrieval method which can utilize a large class of local phaseless correlation-based measurements in order to recover a given signal ${\bf x} \in \mathbb{C}^d$ (up to an unknown global phase) in near-linear…
In recent years, the mathematical and algorithmic aspects of the phase retrieval problem have received considerable attention. Many papers in this area mention crystallography as a principal application. In crystallography, the signal to be…
We consider the inverse problem of reconstructing the scattering and absorption coefficients using boundary measurements for a time dependent radiative transfer equation (RTE). As the measurement is mostly polluted by errors, both…
The rapid rise in inverter-based renewable resources has heightened concerns over subsynchronous resonance and oscillations, thereby challenging grid stability. This paper reviews approaches to identify and mitigate these issues, focusing…
Flux calibration of spectra in reverberation mapping (RM) is most often performed by assuming the flux constancy of some specified narrow emission lines, which stem from an extended region that is sometimes partially spatially resolved, in…
This paper addresses three-dimensional signal distortion and image reconstruction issues in x-ray Bragg coherent diffraction imaging (BCDI) in the event of a general non-orthogonal orientation of the area detector with respect to the…
The problem of recovering a pair of signals from their blind phaseless short-time Fourier transform measurements arises in several important phase retrieval applications, including ptychography and ultra-short pulse characterization. In…
Several strategies in phase retrieval are unified by an iterative "difference map" constructed from a pair of elementary projections and a single real parameter $\beta$. For the standard application in optics, where the two projections…
We propose and demonstrate a new phase retrieval method for imaging through random media. Although methods to recover the Fourier amplitude through random distortions are well established, recovery of the Fourier phase has been a more…
We consider the inverse problem of determining the fragmentation rate from noisy measurements in the growth-fragmentation equation. We use Fourier transform theory on locally compact groups to treat this problem for general fragmentation…
We prove that low-rank matrices can be recovered efficiently from a small number of measurements that are sampled from orbits of a certain matrix group. As a special case, our theory makes statements about the phase retrieval problem. Here,…