Related papers: Phase Retrieval with Random Phase Illumination
Inspired by the quantum computing algorithms for Linear Algebra problems [HHL,TaShma] we study how the simulation on a classical computer of this type of "Phase Estimation algorithms" performs when we apply it to solve the Eigen-Problem of…
We consider the problem of phase retrieval, namely, recovery of a signal from the magnitude of its Fourier transform, or of any other linear transform. Due to the loss of the Fourier phase information, this problem is ill-posed. Therefore,…
Recovering an unknown complex signal from the magnitude of linear combinations of the signal is referred to as phase retrieval. We present an exact performance analysis of a recently proposed convex-optimization-formulation for this…
Phase-rectified signal averaging (PRSA) is a widely used algorithm to analyze nonstationary biomedical time series. The method operates by identifying hinge points in the time series according to prescribed rules, extracting segments…
X-ray ptychography utilizes overlapping illuminations to reconstruct the object's phase and absorption signal with spatial resolutions much smaller than the focus size. Usually, the illumination overlap is chosen to be between 50% and 60%…
Wavefront sensing involves estimating the phase and intensity of light, enabling a wide range of imaging applications, from adaptive optics and astronomy to biomedical imaging. Since conventional image sensors can only measure the spatial…
Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in…
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 consider the problem of recovering a $K$-sparse complex signal $x$ from $m$ intensity measurements. We propose the PhaseCode algorithm, and show that in the noiseless case, PhaseCode can recover an arbitrarily-close-to-one fraction of…
Hyperspectral super-resolution refers to the problem of fusing a hyperspectral image (HSI) and a multispectral image (MSI) to produce a super-resolution image (SRI) that has fine spatial and spectral resolution. State-of-the-art methods…
We perform quantitative phase imaging using phase retrieval to implement synthetic aperture imaging. Compared to digital holography, the developed technique is simpler, less expensive, and more stable.
Super-resolution is a fundamental task in imaging, where the goal is to extract fine-grained structure from coarse-grained measurements. Here we are interested in a popular mathematical abstraction of this problem that has been widely…
In the compressive phase retrieval problem, or phaseless compressed sensing, or compressed sensing from intensity only measurements, the goal is to reconstruct a sparse or approximately $k$-sparse vector $x \in \mathbb{R}^n$ given access to…
We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…
Accurate phase extraction from sinusoidal signals is a crucial task in various signal processing applications. While prior research predominantly addresses the case of asynchronous sampling with unknown signal frequency, this study focuses…
This paper considers the problem of sampling and reconstruction of a continuous-time sparse signal without assuming the knowledge of the sampling instants or the sampling rate. This topic has its roots in the problem of recovering multiple…
Phase diffusion represents a crucial obstacle towards the implementation of high precision interferometric measurements and phase shift based communication channels. Here we present a nearly optimal interferometric scheme based on homodyne…
We give an efficient algorithm which can obtain a relative error approximation to the spectral norm of a matrix, combining the power iteration method with some techniques from matrix reconstruction which use random sampling.
Due to its significance as a subroutine, in this work, we consider the coherent version of the quantum phase estimation problem, where given an arbitrary input state and black-box access to unitaries $U$ and controlled-$U$, the goal is to…
We study an approach to solving the phase retrieval problem as it arises in a phase-less imaging modality known as ptychography. In ptychography, small overlapping sections of an unknown sample (or signal, say $x_0\in \mathbb{C}^d$) are…