Related papers: Phase Retrieval Versus Phaseless Reconstruction

Fraunhofer diffraction is a well-known phenomenon achieved with most wavelength even without lens. A single-shot intensity measurement of diffraction is generally considered inadequate to reconstruct the original light field, because the…

Phase retrieval is a well known ill-posed inverse problem where one tries to recover images given only the magnitude values of their Fourier transform as input. In recent years, new algorithms based on deep learning have been proposed,…

In this paper we consider the nonlinear inverse problem of phase retrieval in the context of dynamical sampling. Where phase retrieval deals with the recovery of signals & images from phaseless measurements, dynamical sampling was…

An important property of the phaseless far field patterns with incident plane waves is the translation invariance. Thus it is impossible to reconstruct the location of the underlying scatterers. By adding a reference point scatterer into…

Phase retrieval is the classical problem of recovering a signal $x^* \in \mathbb{R}^n$ from its noisy phaseless measurements $y_i = \langle a_i, x^* \rangle^2 + \zeta_i$ (where $\zeta_i$ denotes noise, and $a_i$ is the sensing vector) for…

Imaging 3D nano-structures at very high resolution is crucial in a variety of scientific fields. However, due to fundamental limitations of light propagation we can only measure the object indirectly via 2D intensity measurements of the 3D…

This paper discusses the connection between the phase retrieval problem and permutation invariant embeddings. We show that the real phase retrieval problem for $\mathbb{R}^d/O(1)$ is equivalent to Euclidean embeddings of the quotient space…

Fourier phase retrieval is a classical problem that deals with the recovery of an image from the amplitude measurements of its Fourier coefficients. Conventional methods solve this problem via iterative (alternating) minimization by…

We consider the recovery of a (real- or complex-valued) signal from magnitude-only measurements, known as phase retrieval. We formulate phase retrieval as a convex optimization problem, which we call PhaseMax. Unlike other convex methods…

The problem of identifying models of post-disaster reconstruction is an issue that has been dealt with in depth in a number of works, mostly dedicated to individual cases or to the comparison of models. There are also a number of works that…

We study convex relaxation algorithms for phase retrieval on imaging problems. We show that structural assumptions on the signal and the observations, such as sparsity, smoothness or positivity, can be exploited to both speed-up convergence…

The generalized phase retrieval problem over compact groups aims to recover a set of matrices -- representing an unknown signal -- from their associated Gram matrices. This framework generalizes the classical phase retrieval problem, which…

Zernike's phase contrast microscopy (PCM) is among the most widely used techniques for observing phase objects, but it lacks quantitative nature, as it cannot directly provide phase information. Current methods for computationally…

We address the problem of phase retrieval (PR) from quantized measurements. The goal is to reconstruct a signal from quadratic measurements encoded with a finite precision, which is indeed the case in many practical applications. We develop…

If the phase retrieval problem can be solved by a method similar to that of solving a system of linear equations under the context of FFT, the time complexity of computer based phase retrieval algorithm would be reduced. Here I present such…

The paper considers the phase retrieval problem in N-dimensional complex vector spaces. It provides two sets of deterministic measurement vectors which guarantee signal recovery for all signals, excluding only a specific subspace and a…

CDI is a lensless imaging technique that enables atomic-resolution imaging of non-crystalline specimens and their dynamics. However, its broader implementation has been hindered by the instability and ill-posedness of its reconstruction…

In many applications, signals are measured according to a linear process, but the phases of these measurements are often unreliable or not available. To reconstruct the signal, one must perform a process known as phase retrieval. This paper…

We consider a recently proposed convex formulation, known as the PhaseMax method, for solving the phase retrieval problem. Using the replica method from statistical mechanics, we analyze the performance of PhaseMax in the high-dimensional…

Phase retrieval is the problem of reconstructing images from magnitude-only measurements. In many real-world applications the problem is underdetermined. When training data is available, generative models allow optimization in a…