相关论文: Recovery of Compactly Supported Functions from Spe…

We consider the problem of reconstructing one-dimensional point sources from their Fourier measurements in a bounded interval $[-\Omega, \Omega]$. This problem is known to be challenging in the regime where the spacing of the sources is…

This paper presents a simple method to recover phase information from regions of unresolvable fringe density, specifically, at the camera corners, where interference fringes are not resolved by the camera using Phase Shifting Interferometry…

We consider the problem of reconstructing a signal from under-determined modulo observations (or measurements). This observation model is inspired by a (relatively) less well-known imaging mechanism called modulo imaging, which can be used…

The reconstruction of high-dimensional sparse signals is a challenging task in a wide range of applications. In order to deal with high-dimensional problems, efficient sparse fast Fourier transform algorithms are essential tools. The second…

This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier…

Consider the task of recovering an unknown $n$-vector from phaseless linear measurements. This task is the phase retrieval problem. Through the technique of lifting, this nonconvex problem may be convexified into a semidefinite rank-one…

Coherent diffraction imaging (CDI) for visualizing objects at atomic resolution has been realized as a promising tool for imaging single molecules. Drawbacks of CDI are associated with the difficulty of the numerical phase retrieval from…

Through dedicated measurements in the optical regime we demonstrate that ptychography can be applied to reconstruct complex-valued object functions that vary with time from a sequence of spectral measurements. A probe pulse of approximately…

Fourier Ptychography (FP) is a recently proposed technique for large field of view and high resolution imaging. Specifically, FP captures a set of low resolution images under angularly varying illuminations and stitches them together in…

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…

We study the problem of recovering a signal $x\in\mathbb{C}^N$ from samples of its phaseless periodic short-time Fourier transform (STFT): the magnitude of the Fourier transform of the signal multiplied by a sliding window $w\in…

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…

Three-dimensional phase contrast imaging of multiply-scattering samples in X-ray and electron microscopy is extremely challenging, due to small numerical apertures, the unavailability of wavefront shaping optics, and the highly nonlinear…

Estimating quantum time-series such as the Loschmidt amplitude $f(t)=\langle\psi|\mathrm{e}^{-\mathrm{i}Ht}|\psi\rangle$ is central to spectroscopy, Hamiltonian analysis, and many phase-estimation algorithms. Direct estimation via the…

In this work, we present a novel centroiding method based on Fourier space Phase Fitting(FPF) for Point Spread Function(PSF) reconstruction. We generate two sets of simulations to test our method. The first set is generated by GalSim with…

We report a compact, cost-effective and field-portable lensless imaging platform for quantitative microscopy. In this platform, the object is placed on top of an image sensor chip without using any lens. We use a low-cost galvo scanner to…

A new method is developed for three-dimensional (3D) reconstruction of multi-material objects using propagation-based X-ray phase-contrast tomography (PB-CT) with phase retrieval via the contrast transfer function (CTF) formalism. The…

We provide sufficient conditions on a family of functions $(\phi_\alpha)_{\alpha\in A}:\mathbb{R}^d\to\mathbb{R}$ for sampling of multivariate bandlimited functions at certain nonuniform sequences of points in $\mathbb{R}^d$. We consider…

We consider the phase retrieval problem, in which the observer wishes to recover a $n$-dimensional real or complex signal $\mathbf{X}^\star$ from the (possibly noisy) observation of $|\mathbf{\Phi} \mathbf{X}^\star|$, in which…

We propose, analyze and realize a variational multiclass segmentation scheme that partitions a given image into multiple regions exhibiting specific properties. Our method determines multiple functions that encode the segmentation regions…