Related papers: Phase retrieval for wavelet transforms
Recovering an unknown complex signal from the magnitude of linear combinations of the signal is referred to as phase retrieval. We present an exact performance analysis of a recently proposed convex-optimization-formulation for this…
The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier transform, naturally arises in various fields of physics, such as astronomy, radar, speech recognition, quantum mechanics and,…
In this paper, we propose a new non-convex algorithm for solving the phase retrieval problem, i.e., the reconstruction of a signal $ \vx\in\H^n $ ($\H=\R$ or $\C$) from phaseless samples $ b_j=\abs{\langle \va_j, \vx\rangle } $, $…
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…
Phase retrieval in inline holography is a fundamental yet ill-posed inverse problem due to the nonlinear coupling between amplitude and phase in coherent imaging. We present a novel off-the-shelf solution that leverages a diffusion model…
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…
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…
The one-dimensional phase retrieval problem consists in the recovery of a complex-valued signal from its Fourier intensity. Due to the well-known ambiguousness of this problem, the determination of the original signal within the extensive…
This contribution proposes a two stage strategy to allow for phase retrieval in state of the art sub-Nyquist sampling schemes for sparse multiband signals. The proposed strategy is based on data acquisition via modulated wideband converters…
The phase retrieval from multi-frequency intensity (power) observations is considered. The object to be reconstructed is complex-valued. A novel algorithm is presented that accomplishes both the object phase (absolute phase) retrieval and…
The problem of retrieving phase information from amplitude measurements alone has appeared in many scientific disciplines over the last century. PhaseLift is a recently introduced algorithm for phase recovery that is computationally…
High-throughput computational imaging requires efficient processing algorithms to retrieve multi-dimensional and multi-scale information. In computational phase imaging, phase retrieval (PR) is required to reconstruct both amplitude and…
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 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…
In the data analysis of oscillatory systems, methods based on phase reconstruction are widely used to characterize phase-locking properties and inferring the phase dynamics. The main component in these studies is an extraction of the phase…
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,…
In the reconstruction process of unknown multiple scattering objects in inverse medium scattering problems, the first important step is to effectively locate some approximate domains that contain all inhomogeneous media. Without such an…
We address the problem of reconstructing phase-shifting objects from their single shot in-line holograms. We show that a phase-shifting object cannot be reliably recovered from its in-line hologram by non-iterative reconstruction routines,…
We study the convolutional phase retrieval problem, of recovering an unknown signal $\mathbf x \in \mathbb C^n $ from $m$ measurements consisting of the magnitude of its cyclic convolution with a given kernel $\mathbf a \in \mathbb C^m $.…
The problem of recovering a signal from its Fourier magnitude is of paramount importance in various fields of engineering and applied physics. Due to the absence of Fourier phase information, some form of additional information is required…