## Improved success rate and stability for phase retrieval by including randomized overrelaxation in the hybrid input output algorithm |

Optics Express, Vol. 20, Issue 15, pp. 17093-17106 (2012)

http://dx.doi.org/10.1364/OE.20.017093

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### Abstract

In this paper, we study the success rate of the reconstruction of objects of finite extent given the magnitude of its Fourier transform and its geometrical shape. We demonstrate that the commonly used combination of the hybrid input output and error reduction algorithm is significantly outperformed by an extension of this algorithm based on randomized overrelaxation. In most cases, this extension tremendously enhances the success rate of reconstructions for a fixed number of iterations as compared to reconstructions solely based on the traditional algorithm. The good scaling properties in terms of computational time and memory requirements of the original algorithm are not influenced by this extension.

© 2012 OSA

**OCIS Codes**

(100.3190) Image processing : Inverse problems

(100.5070) Image processing : Phase retrieval

(290.3200) Scattering : Inverse scattering

(100.3200) Image processing : Inverse scattering

(110.3200) Imaging systems : Inverse scattering

**ToC Category:**

Image Processing

**History**

Original Manuscript: June 18, 2012

Manuscript Accepted: June 25, 2012

Published: July 11, 2012

**Citation**

Martin Köhl, A. A. Minkevich, and Tilo Baumbach, "Improved success rate and stability for phase retrieval by including randomized overrelaxation in the hybrid input output algorithm," Opt. Express **20**, 17093-17106 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-15-17093

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