Name
Abstract | ||
|---|---|---|
We consider an $ell_2$-regularized non-convex optimization problem for recovering signals from their noisy phaseless observations. We design and study the performance of a message passing algorithm that aims to solve this optimization problem. We consider the asymptotic setting $m,n rightarrow infty$, $m/n rightarrow delta$ and obtain sharp performance bounds, where $m$ is the number of measurements and $n$ is the signal dimension. We show that for complex signals the algorithm can perform accurate recovery with only $m=left ( frac{64}{pi^2}-4right)napprox 2.5n$ measurements. Also, we provide sharp analysis on the sensitivity of the algorithm to noise. We highlight the following facts about our message passing algorithm: (i) Adding $ell_2$ regularization to the non-convex loss function can be beneficial even in the noiseless setting; (ii) spectral initialization has marginal impact on the performance of the algorithm. |
Year | Venue | DocType |
|---|---|---|
2018 | ICML | Journal |
Volume | Citations | PageRank |
abs/1806.03276 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Junjie Ma | 1 | 148 | 15.24 |
| Xu, Ji | 2 | 20 | 3.37 |
| Arian Maleki | 3 | 803 | 57.52 |