Related papers: Designing and using prior knowledge for phase retr…
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…
We consider the phase retrieval problem for signals that belong to a union of subspaces. We assume that amplitude measurements of the signal of length $n$ are observed after passing it through a random $m \times n$ measurement matrix. We…
In this paper we tackle the problem of recovering the phase of complex linear measurements when only magnitude information is available and we control the input. We are motivated by the recent development of dedicated optics-based hardware…
Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…
In this paper, we develop a novel phase retrieval approach to reconstruct x-ray differential phase shift induced by an object. A primary advantage of our approach is a higher-order accuracy over that with the conventional linear…
The ability of a radar to discriminate in both range and Doppler velocity is completely characterized by the ambiguity function (AF) of its transmit waveform. Mathematically, it is obtained by correlating the waveform with its…
In this paper, we introduce two symmetric directed graphs depending on supports of signals and windows, and we show that the connectivity of those graphs provides either necessary and sufficient conditions to phase retrieval of a signal…
The classical phase retrieval problem involves estimating a signal from its Fourier magnitudes (power spectrum) by leveraging prior information about the desired signal. This paper extends the problem to compact groups, addressing the…
Even though image signals are typically defined on a regular two-dimensional grid, there also exist many scenarios where this is not the case and the amplitude of the image signal only is available for a non-regular subset of pixel…
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 $.…
Phase reconstruction is important in transmission electron microscopy for structural studies. We describe electron Fourier ptychography and its application to phase reconstruction of both radiation-resistant and beam-sensitive materials. We…
We address the problem of signal reconstruction from intensity measurements with respect to a measurement frame. This non-convex inverse problem is known as phase retrieval. The case considered in this paper concerns phaseless measurements…
We address the problem of super-resolution frequency recovery using prior knowledge of the structure of a spectrally sparse, undersampled signal. In many applications of interest, some structure information about the signal spectrum is…
We improve a phase retrieval approach that uses correlation-based measurements with compactly supported measurement masks [27]. The improved algorithm admits deterministic measurement constructions together with a robust, fast recovery…
Phase retrieval is the numerical procedure of recovering a complex-valued signal from knowledge about its amplitude and some additional information. Here, an indirect registration procedure, based on the large deformation diffeomorphic…
In this work we analyze the problem of phase retrieval from Fourier measurements with random diffraction patterns. To this end, we consider the recently introduced PhaseLift algorithm, which expresses the problem in the language of convex…
This paper presents a method for reconstructing an acoustic source located in a two-layered medium from multi-frequency phased or phaseless far-field patterns measured on the upper hemisphere. The interface between the two media is assumed…
Fourier phase retrieval is a classical problem of restoring a signal only from the measured magnitude of its Fourier transform. Although Fienup-type algorithms, which use prior knowledge in both spatial and Fourier domains, have been widely…
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 consider the problem of reconstructing two signals from the autocorrelation and cross-correlation measurements. This inverse problem is a fundamental one in signal processing, and arises in many applications, including phase retrieval…