Related papers: Phase retrieval from multiple-window short-time Fo…
We propose a time-varying graph signal recovery method for estimating the true time-varying graph signal from corrupted observations by leveraging dynamic graphs. Most of the conventional methods for time-varying graph signal recovery have…
In this paper we prove two results regarding reconstruction from magnitudes of frame coefficients (the so called "phase retrieval problem"). First we show that phase retrievability as an algebraic property implies that nonlinear maps are…
In this paper, we aim to reconstruct an n-dimensional real vector from m phaseless measurements corrupted by an additive noise. We extend the noiseless framework developed in [15], based on mirror descent (or Bregman gradient descent), to…
We study nonconvex optimization for phase retrieval and the more general problem of semidefinite low-rank matrix sensing; in particular, we focus on the global nonconvex landscape of overparametrized versions of the nonsmooth amplitude…
In the context of the phase retrieval problem, it is known that certain natural classes of measurements, such as Fourier measurements and random Bernoulli measurements, do not lead to the unique reconstruction of all possible signals, even…
Phase retrieval aims at recovering a complex-valued signal from magnitude-only measurements, which attracts much attention since it has numerous applications in many disciplines. However, phase recovery involves solving a system of…
One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in signals on weighted graphs. To do so, we need to account for the intrinsic geometric…
Recently Fourier Ptychography (FP) has attracted great attention, due to its marked effectiveness in leveraging snapshot numbers for spatial resolution in large field-of-view imaging. To acquire high signal-to-noise-ratio (SNR) images under…
Phase retrieval is the nonlinear inverse problem of recovering a true signal from its Fourier magnitude measurements. It arises in many applications such as astronomical imaging, X-Ray crystallography, microscopy, and more. The problem is…
We propose a new algorithm to learn a dictionary for reconstructing and sparsely encoding signals from measurements without phase. Specifically, we consider the task of estimating a two-dimensional image from squared-magnitude measurements…
This paper discusses the noisy phase retrieval problem: recovering a complex image signal with independent noise from quadratic measurements. Inspired by the dark fringes shown in the measured images of the array detector, a novel phase…
This paper is concerned with stable phase retrieval for a family of phase retrieval models we name "locally stable and conditionally connected" (LSCC) measurement schemes. For every signal $f$, we associate a corresponding weighted graph…
We consider the problem of estimating a signal from noisy circularly-translated versions of itself, called multireference alignment (MRA). One natural approach to MRA could be to estimate the shifts of the observations first, and infer the…
We study the problem of stable reconstruction of the short-time Fourier transform from samples taken from trajectories in $\R^2$. We first consider the interplay between relative density of the trajectory and the reconstruction property.…
Measurements achieved with ptychographic imaging are a special case of diffraction measurements. They are generated by illuminating small parts of a sample with, e.g., a focused X-ray beam. By shifting the sample, a set of far-field…
We propose an optimization-based method for reconstructing a time-domain signal from a low-dimensional spectral representation such as a mel-spectrogram. Phase reconstruction has been studied to reconstruct a time-domain signal from the…
Analyzing the internal loss characteristics and multimodedness of (integrated) optical devices can prove difficult. One technique to recover this information is to Fourier transform the transmission spectrum of optical components. This…
In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts the recovery of the phase information of a signal from…
Ptychography, a special case of the phase retrieval problem, is a popular method in modern imaging. Its measurements are based on the shifts of a locally supported window function. In general, direct recovery of an object from such…
Time-resolved facade pressure fields are essential for the wind-resistant design and aerodynamic assessment of high-rise buildings. However, dense instrumentation is costly and often impractical, and sensor outages can further reduce data…