Strong convexity of affine phase retrieval
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 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
Strong convexity of affine phase retrieval
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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 …
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}. ... 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 ...
WebIntuitively speaking, strong convexity means that there exists a quadratic lower bound on the growth of the function. This directly implies that a strong convex function is strictly convex since the quadratic lower bound growth is of course strictly grater than the linear growth. Although the definition in (1) is commonly used, it would be ... 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.
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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. nancy conservatoryWebFeb 1, 2024 · A number of recent methods for phase retrieval are based on least squares (LS) formulations which assume errors in the quadratic measurements. We extend this … nancy constructionWebApr 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, … nancy continental walletWebThe 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. nancy constantineWebJan 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. nancy convenience inc beaconWebAug 18, 2016 · Phase Retrieval from 1D Fourier Measurements: Convexity, Uniqueness, and Algorithms Abstract: This paper considers phase retrieval from the magnitude of one … nancy conver powellWebMay 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 … nancy construction houdemont