site stats

Strong convexity of affine phase retrieval

WebJan 20, 2024 · We present an exact performance analysis of a recently proposed convex-optimization-formulation for this problem, known as PhaseMax. Standard convex-relaxation-based methods in phase retrieval resort to the idea of "lifting" which makes them computationally inefficient, since the number of unknowns is effectively squared. WebAug 18, 2016 · Phase Retrieval from 1D Fourier Measurements: Convexity, Uniqueness, and Algorithms Abstract: This paper considers phase retrieval from the magnitude of one …

Strong convexity of affine phase retrieval Papers With Code

WebApr 12, 2024 · 题目： Strong 3-skew commutativity preserving maps on prime ... Phase retrieval is the problem of recovering a signal from the absolute values of linear measurement coefficients, which has turned into a very active area of research. We introduce a new concept we call 2-norm phase retrieval on real Hilbert space via the area … WebThe convergence analysis is based on a form of restricted strong convexity (restricted because there is an r (r-1)/2-dimensional set of equivalent solutions along which the objective is flat). This condition also implies linear convergence of the proposed algorithm. hello another way 歌詞 https://changesretreat.com

Strong convexity of affine phase retrieval - NASA/ADS

Web2.4 Operations that preserve convexity Convexity of all sets in Section 2.2 can be veri ed directly from the de nition. Often though, to check that a set Sis convex, it is easier to start with a set of basic sets that we know are convex (such as those in Section 2.2), and recognize that our set Sof interest is given by a WebIn this paper, we prove that a natural least squares formulation for the affine phase retrieval is strongly convex on the entire space under some mild conditions, provided the measurements are complex Gaussian random vecotrs and the measurement number $m \gtrsim d \log d$ where $d$ is the dimension of signals. hello ansh

Phase Retrieval from 1D Fourier Measurements: Convexity, …

Category:Strong convexity of affine phase retrieval DeepAI

Tags:Strong convexity of affine phase retrieval

Strong convexity of affine phase retrieval

Phase retrieval from the magnitudes of affine measurements

WebSep 10, 2024 · (Phase retrieval) Phase retrieval is a common computational problem, with applications in diverse areas such as imaging, X-ray crystallography, and speech processing. For simplicity, we will focus on the version of the problem over the reals. ... RSG: beating subgradient method without smoothness and strong convexity (2016). arXiv:1512.03107 ... WebIt provides a strong support for recovering the relative phase in polarization method. Furthermore, the same amount of intensity measurements are used as in PhaseLift method. The numerical simulations also demonstrate its good effect in (affine) phase retrieval of signal and image with Fourier measurements. Declarations.

Strong convexity of affine phase retrieval

Did you know?

WebSep 8, 2024 · The classical phase retrieval problem arises in contexts ranging from speech recognition to x-ray crystallography and quantum state tomography. The generalization to matrix frames is natural in the sense that it corresponds to … http://www.pokutta.com/blog/research/2024/12/07/cheatsheet-smooth-idealized.html

WebApr 20, 2024 · In this paper, we prove that a natural least squares formulation for the affine phase retrieval is strongly convex on the entire space under some mild conditions, provided the measurements are complex Gaussian random vecotrs and the measurement number m ≳ d log d where d is the dimension of signals. WebJan 5, 2024 · More precisely, for phase retrieval in the real case, we will show that F is strongly convex at the minimizer due to the positive definiteness of the Hessian in Appendix. In the complex case, the Hessian is no long positive definite but nonnegative definite near the minimizers. For sparse phase retrieval, we are no longer able to determine θ.

http://mitliagkas.github.io/ift6085-2024/ift-6085-lecture-3-notes.pdf WebFeb 1, 2024 · In this paper, we consider the affine phase retrieval problem in which one aims to recover a signal from the magnitudes of affine measurements. Let {aj}j=1m⊂Hdand b=(b1,…,bm)⊤∈Hm, where H=Ror C. We say {aj}j=1mand bare affine phase retrievable for Hdif any x∈Hdcan be recovered from the magnitudes of the affine measurements { 〈aj,x …

WebJul 21, 2024 · This post will explain in brief details the concept of weak convexity and the methods used to solve some important weakly convex problems such as Robust Matrix Sensing and Robust Phase Retrieval. Many of the descriptions here will be very high-level and intended for non-technical readers.

WebJan 26, 2024 · Besides being able to convert into a phase retrieval problem, affine phase retrieval has its unique advantages in its solution. For example, the linear information in the observation makes it possible to solve this problem with second-order algorithms under complex measurements. hello antdownloadWebProof of convergence • Strong gradient or negative curvature =) at least a fixed reduction inf(x) at each iteration • Strong convexity near a local minimizer =) quadratic convergence ∥xk+1 x⋆∥ c∥xk x⋆∥ 2. Theorem (Very informal) For ridable-saddle functions, starting from an arbitrary initializa- lake pend oreille bathymetric mapWebThe strong convexity parameter is a measure of the curvature of f. By rearranging terms, this tells us that a -strong convex function can be lower bounded by the following inequality: f(x) f(y)r f(y)T(y x)+ 2 kx yk2 (2) The Figure 3 showcases the resulting bounds from both the smoothness and the strong convexity constraints. The lake pearl wrentham ma historyWebPhase retrieval: Given phaseless information of a complex signal, recover the signal Coherent Diffraction Imaging1. Applications: X-ray crystallography, diffraction … hello another way -それぞれの場所-WebApr 20, 2024 · being known in advance is termed as {\em affine phase retrieval}. In this paper, we prove that a natural least squares formulation for the affine phase retrieval is strongly convex on the entire space under some mild conditions, provided the measurements are complex Gaussian random vecotrs and the hello anuragWebApr 20, 2024 · In this paper, we prove that a natural least squares formulation for the affine phase retrieval is strongly convex on the entire space under some mild conditions, … lake pearl wrentham massachusettsWebApr 20, 2024 · In this paper, we prove that a natural least squares formulation for the affine phase retrieval is strongly convex on the entire space under some mild conditions, … hello another way コード