Strong convexity of affine phase retrieval
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 … WebSep 1, 2024 · In this paper, we consider DWSAFT phase retrieval. The paper is organized as follows. In Section 2, we provide some basis notations and definitions. Under some …
Strong convexity of affine phase retrieval
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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. 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, …
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 WebSep 1, 2024 · Due to its strong connections with compressed sensing and matrix completion, phase retrieval has become a research hot spot recently. For more survey of phase retrieval, see [9] . Phase retrieval for one dimensional signals is an ill-posed problem, unless one imposes additional information on signals to be reconstructed [10] .
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, … 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 …
WebThese results show an essential difference between the affine phase retrieval and the classical phase retrieval, where the least squares formulations for the classical phase retrieval are non-convex. The recovery of a signal from the intensity measurements with some entries being known in advance is termed as {\em affine phase retrieval}. ...
WebMay 21, 2024 · This highlights a notable difference between generalized affine phase retrieval and generalized phase retrieval. Furthermore, using tools of algebraic geometry, we show that m≥ 2d (resp. m≥ 4d-1) generic measurements A={(M_j,b_j)}_j=1^m have the generalized phase retrieval property for F= R (resp. F= C). READ FULL TEXT farmers pick australiaWebMay 21, 2024 · We develop a framework for generalized affine phase retrieval with presenting necessary and sufficient conditions for {(M_j, b_j)}_j=1^m having generalized … farmers pick auhttp://www.pokutta.com/blog/research/2024/12/07/cheatsheet-smooth-idealized.html farmers phone number customer serviceWebDefinitions: Convexity, Examples & Views 2. Conditions of Optimality 1. First Order Condition 2. Second Order Condition 3. Operations that Preserve the Convexity 1. Pointwise Maximum ... Examples 1. Norm 2. Entropy 3. Affine 4. Determinant 5. Maximum 3. Views of Functions and Related Hyperplanes 3. 1. Definitions: Convex Function vs Convex Set ... farmers photo framesWebApr 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 farmers pickles enumclawWebJul 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. free people levi\u0027s cropped taper jumpsuitWebIn 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. farmers phone number claims