Phaseless Rcovery using Gauss-Newton Method

Abstract

In this paper, we develop a concrete algorithm for phase retrieval, which we refer to as Gauss-Newton algorithm. In short, this algorithm starts with a good initial estimation, which is obtained by a modified spectral method, and then update the iteration point by a Gauss-Newton iteration step. We prove that a re-sampled version of this algorithm quadratically converges to the solution for the real case with the number of random measurements being nearly minimal. Numerical experiments also show that Gauss-Newton method has better performance over the other algorithms.

16 pages

References in corpus (5)

• Phase Retrieval via Wirtinger Flow: Theory and Algorithms
• GESPAR: Efficient Phase Retrieval of Sparse Signals
• Solving Systems of Random Quadratic Equations via Truncated Amplitude Flow
• Stable Signal Recovery from Phaseless Measurements
• Phase Retrieval with One or Two Diffraction Patterns by Alternating Projection with Null Initialization

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• Recursive Importance Sketching for Rank Constrained Least Squares: Algorithms and High-order Convergence
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• Spectral Method for Phase Retrieval: an Expectation Propagation Perspective
• Solving Systems of Quadratic Equations via Exponential-type Gradient Descent Algorithm
• The estimation performance of nonlinear least squares for phase retrieval
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• Performance bound of the intensity-based model for noisy phase retrieval
• Sharp global convergence guarantees for iterative nonconvex optimization: A Gaussian process perspective
• The recovery of complex sparse signals from few phaseless measurements