Related papers: Designing and using prior knowledge for phase retr…
The famous Fourier theorem states that, under some restrictions, any periodic function (or real world signal) can be obtained as a sum of sinusoids, and hence, a technique exists for decomposing a signal into its sinusoidal components. From…
Phase reconstruction, which estimates phase from a given amplitude spectrogram, is an active research field in acoustical signal processing with many applications including audio synthesis. To take advantage of rich knowledge from data,…
One of the most prominent challenges in the field of diffractive imaging is the phase retrieval (PR) problem: In order to reconstruct an object from its diffraction pattern, the inverse Fourier transform must be computed. This is only…
In the undersampled phase retrieval problem, the goal is to recover an $N$-dimensional complex signal $\mathbf{x}$ from only $M<N$ noisy intensity measurements without phase information. This problem has drawn a lot of attention to reduce…
Phase retrieval problems occur in a width range of applications in physics and engineering such as crystallography, astronomy, and laser optics. Common to all of them is the recovery of an unknown signal from the intensity of its Fourier…
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 $|\mathbf{\Phi} \mathbf{X}^\star|$, in which…
Phase retrieval aims to recover a signal from magnitude or power spectra measurements. It is often addressed by considering a minimization problem involving a quadratic cost function. We propose a different formulation based on Bregman…
Sparse modeling is one of the efficient techniques for imaging that allows recovering lost information. In this paper, we present a novel iterative phase-retrieval algorithm using a sparse representation of the object amplitude and phase.…
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…
This paper proposes a novel algorithm for image phase retrieval, i.e., for recovering complex-valued images from the amplitudes of noisy linear combinations (often the Fourier transform) of the sought complex images. The algorithm is…
By suitably generalizing the Fourier constraint projection in the difference map phasing algorithm, an object can be reconstructed from its diffraction pattern even when the latter has been incoherently averaged over a discrete group of…
Electronic wave functions of planar molecules can be reconstructed via inverse Fourier transform of angle-resolved photoelectron spectroscopy (ARPES) data, provided the phase of the electron wave in the detector plane is known. Since the…
We present the first phase retrieval algorithm guaranteed to solve the multidimensional phase retrieval problem in polynomial arithmetic complexity without prior information. The method successfully terminates in O(N log(N)) operations for…
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…
Reconstructing a signal from squared linear (rank-one quadratic) measurements is a challenging problem with important applications in optics and imaging, where it is known as phase retrieval. This paper proposes two new phase retrieval…
Anisotropic two-dimensional diffraction signals encode additional structural information, including atom-pair angular distributions, beyond conventional isotropic scattering. However, experimental constraints such as beam stops result in…
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…
Coherent diffraction imaging (CDI) for visualizing objects at atomic resolution has been realized as a promising tool for imaging single molecules. Drawbacks of CDI are associated with the difficulty of the numerical phase retrieval from…
Phase retrieval seeks to recover a signal x from the amplitude |Ax| of linear measurements. We cast the phase retrieval problem as a non-convex quadratic program over a complex phase vector and formulate a tractable relaxation (called…
In this paper, a new phase-retrieval algorithm from an X-ray schlieren image is proposed. The schlieren method allows phase-contrast imaging with an objective lens and a knife-edge filter placed at the back focal plane of the objective.…