Related papers: Phase field methods for binary recovery

We treat the inverse problem of determining material losses, such as cavities, in a conducting body, by performing electrostatic measurements at the boundary. We develop a numerical approach, based on variational methods, to reconstruct the…

We introduce a numerical framework for reconstructing the potential in two dimensional semilinear elliptic PDEs with power type nonlinearities from the nonlinear Dirichlet to Neumann map. By applying higher order linearization method, we…

Several strategies in phase retrieval are unified by an iterative "difference map" constructed from a pair of elementary projections and a single real parameter $\beta$. For the standard application in optics, where the two projections…

In this paper, we propose the SPR (sparse phase retrieval) method, which is a new phase retrieval method for coherent x-ray diffraction imaging (CXDI). Conventional phase retrieval methods effectively solve the problem for high…

We derive a set of ptychography phase-retrieval iterative engines based on proximal algorithms originally developed in convex optimization theory, and discuss their connections with existing ones. The use of proximal operator creates a…

While characterization of coherent wavefields is essential to laser, x-ray and electron imaging, sensors measure the squared magnitude of the field, rather than the field itself. Holography or phase retrieval must be used to characterize…

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,…

A general mathematical framework and recovery algorithm is presented for the holographic phase retrieval problem. In this problem, which arises in holographic coherent diffraction imaging, a "reference" portion of the signal to be recovered…

The need for an efficient method of integration of a dense normal field is inspired by several computer vision tasks, such as shape-from-shading, photometric stereo, deflectometry, etc. Inspired by edge-preserving methods from image…

The quantum-mechanical D-dimensional inverse square potential is analyzed using field-theoretic renormalization techniques. A solution is presented for both the bound-state and scattering sectors of the theory using cutoff and dimensional…

We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…

The inverse problem of Kohn-Sham density functional theory (DFT) is often solved in an effort to benchmark and design approximate exchange-correlation potentials. The forward and inverse problems of DFT rely on the same equations but the…

Most deep learning-based models for speech enhancement have mainly focused on estimating the magnitude of spectrogram while reusing the phase from noisy speech for reconstruction. This is due to the difficulty of estimating the phase of…

We apply the stationary phase method developed in (Assier, Shanin \& Korolkov, QJMAM, 76(1), 2022) to the problem of wave diffraction by a quarter-plane. The wave field is written as a double Fourier transform of an unknown spectral…

Signals and images with discontinuities appear in many problems in such diverse areas as biology, medicine, mechanics, and electrical engineering. The concrete data are often discrete, indirect and noisy measurements of some quantities…

We address the problem of super-resolution of point sources from binary measurements, where random projections of the blurred measurement of the actual signal are encoded using only the sign information. The threshold used for binary…

Most methods tackling the phase retrieval problem of magnitude-only antenna measurements suffer from unrealistic sampling requirements, from unfeasible computational complexities, and, most severely, from the lacking reliability of…

In many signal processing problems arising in practical applications, we wish to reconstruct an unknown signal from its phaseless measurements with respect to a frame. This inverse problem is known as the phase retrieval problem. For each…

Phase retrieval is one of the most challenging processes in many interferometry techniques. To promote the phase retrieval, Xu et. al [X. Xu, Y. Wang, Y. Xu, W. Jin. 2016] proposed a method based on dual-wavelength interferometry. However,…

Phase recovery (PR) refers to calculating the phase of the light field from its intensity measurements. As exemplified from quantitative phase imaging and coherent diffraction imaging to adaptive optics, PR is essential for reconstructing…