Related papers: Uniqueness transition in noisy phase retrieval
Phase contrast imaging seeks to reconstruct the complex refractive index of an unknown sample from scattering intensities, measured for example under illumination with coherent X-rays. By incorporating refraction, this method yields…
X-ray single particle imaging involves the measurement of a large number of noisy diffraction patterns of isolated objects in random orientations. The missing information about these patterns is then computationally recovered in order to…
This paper is aimed at developing a better understanding of the structure of the information that in contained in galaxy surveys, so as to find optimal ways to combine observables from such surveys. We first show how Jaynes' Maximal Entropy…
We propose a patch-based singular value shrinkage method for diffusion magnetic resonance image estimation targeted at low signal to noise ratio and accelerated acquisitions. It operates on the complex data resulting from a sensitivity…
Optical phase-modulated fringe-patterns are usually digitized with XxY pixels and 8 bits/pixel (or higher) gray-levels. The digitized 8 bits/pixel are raw-data bits, not Shannon information bits. Here we show that noisy fringe-patterns…
Quantum noise in a model of singly resonant frequency doubling including phase mismatch and driving in the harmonic mode is analyzed. The general formulae about the fixed points and their stability as well as the squeezing spectra…
Ptychography has risen as a reference X-ray imaging technique: it achieves resolutions of one billionth of a meter, macroscopic field of view, or the capability to retrieve chemical or magnetic contrast, among other features. A…
The realm of classical phase retrieval concerns itself with the arduous task of recovering a signal from its Fourier magnitude measurements, which are fraught with inherent ambiguities. A single-exposure intensity measurement is commonly…
To recover a low rank structure from a noisy matrix, truncated singular value decomposition has been extensively used and studied. Recent studies suggested that the signal can be better estimated by shrinking the singular values. We pursue…
In photoacoustic imaging the objective is to determine the optical properties of biological tissue from boundary measurement of the generated acoustic wave. Here, we propose a restriction to piecewise constant media parameters. Precisely we…
Phase imaging and wavefront reconstruction from noisy observations of complex exponent is a topic of this paper. It is a highly non-linear problem because the exponent is a 2{\pi}-periodic function of phase. The reconstruction of phase and…
Ptychography is a computational imaging technique that aims to reconstruct the object of interest from a set of diffraction patterns. Each of these is obtained by a localized illumination of the object, which is shifted after each…
A geometric form of information theory allows for reasonable, i.e. probabilistic, evidence-ranking based, and generalized noise-level dependent, classifications of the crystallographic and quasicrystallographic symmetries in noisy digital…
We address the denoising of images contaminated with multiplicative noise, e.g. speckle noise. Classical ways to solve such problems are filtering, statistical (Bayesian) methods, variational methods, and methods that convert the…
X-ray phase contrast imaging holds great promise for improving the visibility of light-element materials such as soft tissues and tumors. Single-mask differential phase contrastnimaging method stands out as a simple and effective approach…
We present fundamental limits on the reliable classification of linear and affine subspaces from noisy, linear features. Drawing an analogy between discrimination among subspaces and communication over vector wireless channels, we propose…
This paper studies the phase-only reconstruction problem of recovering a complex-valued signal $\textbf{x}$ in $\mathbb{C}^d$ from the phase of $\textbf{Ax}$ where $\textbf{A}$ is a given measurement matrix in $\mathbb{C}^{m\times d}$. The…
A simple model for image formation in linear shift-invariant systems is considered, in which both the detected signal and the noise variance are varying slowly compared to the point-spread function of the system. It is shown that within the…
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 the recovery of the phase information of a signal from…
We present a general linear algorithm for measuring the surface mass density 1-\kappa from the observable reduced shear g=\gamma/(1-\kappa) in the strong lensing regime. We show that in general, the observed polarization field can be…