Related papers: Randomized Kaczmarz Method for Single Particle X-r…
We study the problem of recovering the phase from magnitude measurements; specifically, we wish to reconstruct a complex-valued signal x of C^n about which we have phaseless samples of the form y_r = |< a_r,x >|^2, r = 1,2,...,m (knowledge…
Randomized regularized Kaczmarz algorithms have recently been proposed to solve tensor recovery models with {\it consistent} linear measurements. In this work, we propose a novel algorithm based on the randomized extended Kaczmarz algorithm…
The randomzied Kaczmarz method, along with its recently developed variants, has become a popular tool for dealing with large-scale linear systems. However, these methods usually fail to converge when the linear systems are affected by heavy…
Exploring the idea of phase retrieval has been intriguing researchers for decades, due to its appearance in a wide range of applications. The task of a phase retrieval algorithm is typically to recover a signal from linear phaseless…
The Kaczmarz method is an iterative method for solving overcomplete linear systems of equations Ax=b. The randomized version of the Kaczmarz method put forth by Strohmer and Vershynin iteratively projects onto a randomly chosen solution…
Characterizing the temporal-spectral profile of single photons is essential for quantum information protocol utilizing temporal mode for encoding. Based on the phase retrieval algorithm, we present a method to reconstruct the phase spectrum…
Kaczmarz method is one popular iterative method for solving inverse problems, especially in computed tomography. Recently, it was established that a randomized version of the method enjoys an exponential convergence for well-posed problems,…
In a computer-generated holographic projection system, the image is reconstructed via the diffraction of light from a spatial light modulator. In this process, several factors could contribute to non-linearities between the reconstruction…
Light-matter interaction is exploited in spectroscopic techniques to access information about molecular, atomic or nuclear constituents of the sample of interest. While scattered light carries both amplitude and phase information of the…
The Cryo-EM 3D particle reconstruction is essential for identifying protein and uncover the biological mechanism of the macro-molecules. In this paper, we use Kam method for reconstruction. Kam method is \textit{ab-initio}, and it assumes…
Our proposed method of random phase-free holography using virtual convergence light can obtain large reconstructed images exceeding the size of the hologram, without the assistance of random phase. The reconstructed images have low-speckle…
This paper considers the phase retrieval problem in which measurements consist of only the magnitude of several linear measurements of the unknown, e.g., spectral components of a time sequence. We develop low-complexity algorithms with…
In recent literature, a general two step procedure has been formulated for solving the problem of phase retrieval. First, a spectral technique is used to obtain a constant-error initial estimate, following which, the estimate is refined to…
Addition of random phase to the object light is required in computer-generated holograms (CGHs) to widely diffuse the object light and to avoid its concentration on the CGH; however, this addition causes considerable speckle noise in the…
We provide a complete characterization of the randomized Kaczmarz algorithm (RKA) for inconsistent linear systems. The Kaczmarz algorithm, known in some fields as the algebraic reconstruction technique, is a classical method for solving…
In recent years, phase retrieval has received much attention in statistics, applied mathematics and optical engineering. In this paper, we propose an efficient algorithm, termed Subspace Phase Retrieval (SPR), which can accurately recover…
We propose a robust and efficient approach to the problem of compressive phase retrieval in which the goal is to reconstruct a sparse vector from the magnitude of a number of its linear measurements. The proposed framework relies on…
Randomized iterative algorithms, such as the randomized Kaczmarz method, have gained considerable popularity due to their efficacy in solving matrix-vector and matrix-matrix regression problems. Our present work leverages the insights…
The Kaczmarz algorithm is a well known iterative method for solving overdetermined linear systems. Its randomized version yields provably exponential convergence in expectation. In this paper, we propose two new methods to speed up the…
X-ray phase contrast imaging significantly improves the visualization of structures with weak or uniform absorption, broadening its applications across a wide range of scientific disciplines. Propagation-based phase contrast is particularly…