Related papers: Phase Unwrapping and One-Dimensional Sign Problems
Signal transduction and cell function are governed by the spatiotemporal organization of membrane-associated molecules. Despite significant advances in visualizing molecular distributions by 3D light microscopy, cell biologists still have…
We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…
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.…
Materials with nanoscale phase separation are considered. These materials are formed by a mixture of several phases, so that inside one phase there exist nanosize inclusions of other phases, with random shapes and random spatial locations.…
We present a deterministic framework for three-dimensional beam shaping that enables versatile control of intensity and phase, pixel-by-pixel, across multiple axial planes. Conventional multi-plane holographic techniques typically rely on…
Phase aberrations, despite degrading ultrasound images, also encode valuable information about the spatial distribution of the speed of sound in tissue. In pulse-echo ultrasound, we can quantify them by exploiting speckle correlations.…
We present an exactly solvable mean-field-like theory of correlated ternary sequences which are actually systems with two independent parameters. Depending on the values of these parameters, the variance on the average number of any given…
The role of phase in neural sequence models remains poorly understood. To isolate this question, we introduce PRISM, a complex-valued encoder that enforces a unit-norm constraint ($|z| = 1$) and replaces attention with gated spectral…
Various hand-crafted features representations of bio-signals rely primarily on the amplitude or power of the signal in specific frequency bands. The phase component is often discarded as it is more sample specific, and thus more sensitive…
This paper considers the question of recovering the phase of an object from intensity-only measurements, a problem which naturally appears in X-ray crystallography and related disciplines. We study a physically realistic setup where one can…
We consider the geometry associated to the ambiguities of the one-dimensional Fourier phase retrieval problem for vectors in ${\mathbb C}^{N+1}$. Our first result states that the space of signals has a finite covering (which we call the…
In most current approaches of speech processing, information is extracted from the magnitude spectrum. However recent perceptual studies have underlined the importance of the phase component. The goal of this paper is to investigate the…
Understanding phase diagrams is essential for material selection and design, as they provide a comprehensive representation of the thermodynamics of mixtures. This work delivers a broad and systematic overview of possible ternary phase…
Deep unfolding is a method of growing popularity that fuses iterative optimization algorithms with tools from neural networks to efficiently solve a range of tasks in machine learning, signal and image processing, and communication systems.…
We treat the problem of characterizing in a systematic way the qualitative features of two-dimensional dynamical systems. To that end, we construct a representation of the topological features of phase portraits by means of diagrams that…
The so-called method of phase synchronization has been advocated in a number of papers as a way of decoupling a system of linear second-order differential equations by a linear transformation of coordinates and velocities. This is a rather…
We describe a procedure for alleviating the fermion sign problem in which phase fluctuations are explicitly subtracted from the Boltzmann factor. Several ans\"atze for fluctuations are designed and compared. In the absence of a sufficiently…
Phase transitions in combinatorial problems have recently been shown to be useful in locating "hard" instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been…
We study a $U(1)\times U(1)$ system with short-range interactions and mutual $\theta=2\pi/3$ statistics in (2+1) dimensions. We are able to reformulate the model to eliminate the sign problem, and perform a Monte Carlo study. We find a…
In recent years, the mathematical and algorithmic aspects of the phase retrieval problem have received considerable attention. Many papers in this area mention crystallography as a principal application. In crystallography, the signal to be…