Related papers: Multiscale Phase Retrieval
We study information theoretic limits of recovering an unknown $n$ dimensional, complex signal vector $\mathbf{x}_\star$ with unit norm from $m$ magnitude-only measurements of the form $y_i = |(\mathbf{A} \mathbf{x}_\star)_i|^2, \; i = 1,2…
We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…
Phase retrieval (PR) concerns the recovery of complex phases from complex magnitudes. We identify the connection between the difficulty level and the number and variety of symmetries in PR problems. We focus on the most difficult far-field…
Context. The next generation of space-borne instruments dedicated to the direct detection of exoplanets requires unprecedented levels of wavefront control precision. Coronagraphic wavefront sensing techniques for these instruments must…
On-chip holographic video is a convenient way to monitor biological samples simultaneously at high spatial resolution and over a wide field-of-view. However, due to the limited readout rate of digital detector arrays, one often faces a…
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…
The phase unwrapping plays a key role in obtaining a ground-truth phase of the wrapped phase. High-accurate unwrapped phases are demanded in various research fields such as optical holography, optical diffraction tomography, and magnetic…
The hybrid interferometer integrating an optical parametric amplifier and a beam splitter has the potential to outperform the SU(1,1) interferometer. However, photon loss remains a critical limitation for practical implementation. To…
Recovering a signal from its Fourier intensity underlies many important applications, including lensless imaging and imaging through scattering media. Conventional algorithms for retrieving the phase suffer when noise is present but display…
Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear…
Digital holography is one of the most widely used label-free microscopy techniques in biomedical imaging. Recovery of the missing phase information of a hologram is an important step in holographic image reconstruction. Here we demonstrate…
Ptychography is an enabling coherent diffraction imaging technique for both fundamental and applied sciences. Its applications in optical microscopy, however, fall short for its low imaging throughput and limited resolution. Here, we report…
We answer a number of open problems concerning phase retrieval and phase retrieval by projections. In particular, one main theorem classifies phase retrieval by projections via collections of sequences of vectors allowing norm retrieval.…
Interference of light fields plays an important role in various high-precision measurement schemes. It has been shown that super resolving phase measurements beyond the standard coherent state limit can be obtained either by using maximally…
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…
Phase-sensitive coherent imaging exploits changes in the phases of backscattered light to observe tiny alterations of scattering structures or variations of the refractive index. But moving scatterers or a fluctuating refractive index…
We present a reconstruction technique for simultaneous retrieval of absorption and phase shifting properties of an object recorded by in-line holography. The routine is experimentally tested by applying it to optical holograms of a pure…
A new numerically and experimentally tested measurement method for the local electrical light field including its phase is presented. The method is based on Self Referencing Interferograms (SRI) such as shearing interferograms. The complex…
Quantitative phase imaging (QPI) enables visualization and quantitative extraction of the optical phase information of transparent samples. However, conventional QPI techniques typically rely on multi-frame acquisition or complex…
A new method for phase recovery from a single two-beam interferogram is presented. Conventional approaches, relying on trigonometric inversion followed by phase unfolding and unwrapping, are hindered by discontinuities typically addressed…