Phase Retrieval by the Inverse Power Method
Phase retrieval is to recover signals from phaseless linear measurements. The most efficient methods to tackle this problem are nonconvex gradient approaches, which however generally need an elaborate initialized guess to ensure successful reconstruction. The inverse power method is proposed to provide a more accurate initialization. Numerical experiments illustrate the higher accuracy of the proposed method over other initialization methods. And we further demonstrate the iterative use of the initialization method can obtain an even better estimate.
KeywordsPhase retrieval Spectral method Inverse power method
- 4.Fienup, C., Dainty, J.: Phase retrieval and image reconstruction for astronomy. Image Recovery Theory Appl. 231, 275 (1987)Google Scholar
- 8.Netrapalli, P., Jain, P., Sanghavi, S.: Phase retrieval using alternating minimization. In: Advances in Neural Information Processing Systems, pp. 2796–2804 (2013)Google Scholar
- 11.Zhang, H., Liang, Y.: Reshaped wirtinger flow for solving quadratic system of equations. In: Advances in Neural Information Processing Systems, pp. 2622–2630 (2016)Google Scholar
- 13.Wang, G., Giannakis, G., Saad, Y., Chen, J.: Solving most systems of random quadratic equations. In: Advances in Neural Information Processing Systems, pp. 1865–1875 (2017)Google Scholar
- 14.Chen, Y., Candes, E.: Solving random quadratic systems of equations is nearly as easy as solving linear systems. In: Advances in Neural Information Processing Systems, pp. 739–747 (2015)Google Scholar