Related papers: On The 2D Phase Retrieval Problem
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…
We consider the phase retrieval problem of reconstructing a $n$-dimensional real or complex signal $\mathbf{X}^{\star}$ from $m$ (possibly noisy) observations $Y_\mu = | \sum_{i=1}^n \Phi_{\mu i} X^{\star}_i/\sqrt{n}|$, for a large class of…
We study the problem of recovering the phase from magnitude measurements; specifically, we wish to reconstruct a complex-valued signal x of C^n about which we have phaseless samples of the form y_r = |< a_r,x >|^2, r = 1,2,...,m (knowledge…
We will give several surprising equivalences and consequences of weak phase retrieval. These results give a complete understanding of the difference between weak phase retrieval and phase retrieval. We also answer two longstanding open…
Phase unwrapping is the process of recovering a continuous phase signal from an original signal wrapped in the ($-\pi$,$\pi$] interval. It is a critical step of coherent signal processing, with applications such as synthetic aperture radar,…
We introduce and discuss a new approach to the phase retrieval of fields radiated by continuous aperture sources having a circular support, which is of interest in many applications including the detection of shape deformations on reflector…
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…
In this paper, we consider the uniqueness of STFT phase retrieval with two window functions. We show that a complex-valued locally integrable nonseparable signal is uniquely determined up to a global phase by phaseless samples of its short…
We consider the task of recovering two real or complex $m$-vectors from phaseless Fourier measurements of their circular convolution. Our method is a novel convex relaxation that is based on a lifted matrix recovery formulation that allows…
As a new type of series expansion, the so-called one-dimensional adaptive Fourier decomposition (AFD) and its variations (1D-AFDs) have effective applications in signal analysis and system identification. The 1D-AFDs have considerable…
The main result of this paper states that phase retrieval in infinite-dimensional Hilbert spaces is never uniformly stable, in sharp contrast to the finite dimensional setting in which phase retrieval is always stable. This leads us 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…
The recovery of an unknown signal from its linear measurements is a fundamental problem spanning numerous scientific and engineering disciplines. Commonly, prior knowledge suggests that the underlying signal resides within a known algebraic…
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 finite alphabet phase retrieval problem: recovering a signal whose entries lie in a small alphabet of possible values from its Fourier magnitudes. This problem arises in the celebrated technology of X-ray crystallography to…
We consider the phase retrieval problem in which one tries to reconstruct a function from the modulus of its wavelet transform. We study the unicity and stability of the reconstruction. In the case where the wavelets are Cauchy wavelets, we…
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…
This paper develops a mathematical theory of super-resolution. Broadly speaking, super-resolution is the problem of recovering the fine details of an object---the high end of its spectrum---from coarse scale information only---from samples…
Exact reconstruction of an image from measurements of its Discrete Fourier Transform (DFT) typically requires all DFT coefficients to be available. However, incorporating the prior assumption that the image contains only integer values…
In this paper, we address the problem of computing the dimension of data space in phase retrieval problem. Starting from the quadratic formulation of the phase retrieval,the analysis is performed in two steps. First, we exploit the lifting…