Related papers: Enforcing uniqueness in one-dimensional phase retr…

We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…

The identification of sampling sets that enable unique signal recovery is fundamental to many applications in signal processing and remains a central problem in mathematical analysis. Recent studies in the mathematical literature,…

The problem of signal recovery from the autocorrelation, or equivalently, the magnitudes of the Fourier transform, is of paramount importance in various fields of engineering. In this work, for one-dimensional signals, we give conditions,…

A signal recovery problem is considered, where the same binary testing problem is posed over multiple, independent data streams. The goal is to identify all signals, i.e., streams where the alternative hypothesis is correct, and noises,…

In this work we consider the problem of reconstruction of a signal from the magnitude of its Fourier transform, also known as phase retrieval. The problem arises in many areas of astronomy, crystallography, optics, and coherent diffraction…

We study phase retrieval from magnitude measurements of an unknown signal as an algebraic estimation problem. Indeed, phase retrieval from rank-one and more general linear measurements can be treated in an algebraic way. It is verified that…

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…

The coherent radiation emitted by an electron bunch provides a diagnostic signal that can be used to estimate its longitudinal distribution. Commonly only the amplitude of the intensity spectrum can be measured and the associated phase must…

Inverse analysis, such as model calibration, often suffers from a lack of informative data in complex real-world scenarios. The standard remedy, designing new experimental setups, is often costly and time-consuming, while readily available…

We give a way to recover time-dependent singular coefficients of the wave-equation in the one-dimensional case.

Context: Several approaches to estimate frequency, phase and amplitude errors in time series analyses were reported in the literature, but they are either time consuming to compute, grossly overestimating the error, or are based on…

Phase retrieval refers to recovering a signal from its Fourier magnitude. This problem arises naturally in many scientific applications, such as ultra-short laser pulse characterization and diffraction imaging. Unfortunately, phase…

In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts to recover the phase information of a signal from the…

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 work, we investigate the shape identification and coefficient determination associated with two time-dependent partial differential equations in two dimensions. We consider the inverse problems of determining a convex polygonal…

Resonances are common in wave physics and their full and rigorous characterization is crucial to correctly tailor the response of a system in both time and frequency domains. However, they have been conventionally described by the quality…

Compression of the sign information of discrete cosine transform coefficients is an intractable problem in image compression schemes due to the equiprobable occurrence of the sign bits. To overcome this difficulty, we propose an efficient…

This paper considers the recovery of continuous time signals from the magnitude of its samples. It uses a combination of structured modulation and oversampling and provides sufficient conditions on the signal and the sampling system such…

The problem of recovering coefficients in a diffusion equation is one of the basic inverse problems. Perhaps the most important term is the one that couples the length and time scales and is often referred to as {\it the\/} diffusion…

We report an iterative algorithm to retrieve accurate real space information from gas phase ultrafast diffraction measurements with missing data at low momentum transfer. The algorithm operates in a manner similar to phase retrieval…