## High-accuracy wave field reconstruction: decoupled inverse imaging with sparse modeling of phase and amplitude |

JOSA A, Vol. 29, Issue 1, pp. 44-54 (2012)

http://dx.doi.org/10.1364/JOSAA.29.000044

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### Abstract

We apply a nonlocal adaptive spectral transform for sparse modeling of phase and amplitude of a coherent wave field. The reconstruction of this wave field from complex-valued Gaussian noisy observations is considered. The problem is formulated as a multiobjective constrained optimization. The developed iterative algorithm decouples the inversion of the forward propagation operator and the filtering of phase and amplitude of the wave field. It is demonstrated by simulations that the performance of the algorithm, both visually and numerically, is the current state of the art.

© 2012 Optical Society of America

**OCIS Codes**

(100.1830) Image processing : Deconvolution

(100.3010) Image processing : Image reconstruction techniques

(100.3190) Image processing : Inverse problems

(090.1995) Holography : Digital holography

**ToC Category:**

Image Processing

**History**

Original Manuscript: March 16, 2011

Revised Manuscript: August 17, 2011

Manuscript Accepted: September 15, 2011

Published: December 6, 2011

**Citation**

Vladimir Katkovnik and Jaakko Astola, "High-accuracy wave field reconstruction: decoupled inverse imaging with sparse modeling of phase and amplitude," J. Opt. Soc. Am. A **29**, 44-54 (2012)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-1-44

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