相关论文: Explicit Frames for Deterministic Phase Retrieval …
In this paper, we consider the phase retrieval problem in which one aims to recover a signal from the magnitudes of affine measurements. Let $\{{\mathbf a}_j\}_{j=1}^m \subset {\mathbb H}^d$ and ${\mathbf b}=(b_1, \ldots,…
An important yet challenging problem in understanding indoor scene is recovering indoor frame structure from a monocular image. It is more difficult when occlusions and illumination vary, and object boundaries are weak. To overcome these…
In this work, we present some new results for compressed sensing and phase retrieval. For compressed sensing, it is shown that if the unknown $n$-dimensional vector can be expressed as a linear combination of $s$ unknown Vandermonde vectors…
Fraunhofer diffraction is a well-known phenomenon achieved with most wavelength even without lens. A single-shot intensity measurement of diffraction is generally considered inadequate to reconstruct the original light field, because the…
Fourier phase retrieval is a classical problem that deals with the recovery of an image from the amplitude measurements of its Fourier coefficients. Conventional methods solve this problem via iterative (alternating) minimization by…
This note formulates a deterministic recovery result for vectors $x$ from quadratic measurements of the form $(Ax)_i \overline{(Ax)_j}$ for some left-invertible $A$. Recovery is exact, or stable in the noisy case, when the couples $(i,j)$…
Phase retrieval seeks to recover a complex signal from amplitude-only measurements, a challenging nonlinear inverse problem. Current theory and algorithms often ignore signal priors. By contrast, we evaluate here a variety of image priors…
This paper pioneers the integration of learning optimization into measurement matrix design for phase retrieval. We introduce the Deep Learning-based Measurement Matrix for Phase Retrieval (DLMMPR) algorithm, which parameterizes the…
Recovering a signal up to a unimodular constant from the magnitudes of linear measurements has been popular and well studied in recent years. However, numerous unsolved problems regarding phase retrieval still exist. Given a phase retrieval…
We generalize the short-time Fourier transform (STFT) formalism for radial velocity extraction to cases where the underlying spectral components are unknown. The method factorizes a spectroscopic time series into principal spectra and…
We demonstrate that a sparse signal can be estimated from the phase of complex random measurements, in a "phase-only compressive sensing" (PO-CS) scenario. With high probability and up to a global unknown amplitude, we can perfectly recover…
This paper investigates how to recover parameters of a linear time invariant system from values and derivatives of its transfer function matrix, along several particular directions at a prescribed set of points in the complex plane, in…
We consider the problem of recovering a complex vector $\mathbf{x}\in \mathbb{C}^n$ from $m$ quadratic measurements $\{\langle A_i\mathbf{x}, \mathbf{x}\rangle\}_{i=1}^m$. This problem, known as quadratic feasibility, encompasses the well…
Generally, phase retrieval problem can be viewed as the reconstruction of a function/signal from only the magnitude of the linear measurements. These measurements can be, for example, the Fourier transform of the density function.…
This paper proposes a new framework to regularize the highly ill-posed and non-linear phase retrieval problem through deep generative priors using simple gradient descent algorithm. We experimentally show effectiveness of proposed algorithm…
The recovery of a signal from the intensity measurements with some entries being known in advance is termed as {\em affine phase retrieval}. In this paper, we prove that a natural least squares formulation for the affine phase retrieval is…
In matrix recovery from random linear measurements, one is interested in recovering an unknown $M$-by-$N$ matrix $X_0$ from $n<MN$ measurements $y_i=Tr(A_i^T X_0)$ where each $A_i$ is an $M$-by-$N$ measurement matrix with i.i.d random…
A new phase-coherent technique for the calibration of polarimetric data is presented. Similar to the one-dimensional form of convolution, data are multiplied by the response function in the frequency domain. Therefore, the system response…
We realize dual-polarization full-field recovery using intensity only measurements and phase retrieval techniques based on dispersive elements. 30-Gbaud QPSK waveforms are transmitted over 520-km standard single-mode fiber and equalized…
Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine…