## Convergence properties of a quadratic approach to the inverse-scattering problem

JOSA A, Vol. 19, Issue 12, pp. 2424-2428 (2002)

http://dx.doi.org/10.1364/JOSAA.19.002424

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### Abstract

The local-minima question that arises in the framework of a quadratic approach to inverse-scattering problems is investigated. In particular, a sufficient condition for the absence of local minima is given, and some guidelines to ensure the reliability of the algorithm are outlined for the case of data not belonging to the range of the relevant quadratic operator. This is relevant also when an iterated solution procedure based on a quadratic approximation of the electromagnetic scattering at each step is considered.

© 2002 Optical Society of America

**OCIS Codes**

(100.3190) Image processing : Inverse problems

(290.3200) Scattering : Inverse scattering

**History**

Original Manuscript: March 27, 2002

Revised Manuscript: July 2, 2002

Manuscript Accepted: July 2, 2002

Published: December 1, 2002

**Citation**

Raffaele Persico, Francesco Soldovieri, and Rocco Pierri, "Convergence properties of a quadratic approach to the inverse-scattering problem," J. Opt. Soc. Am. A **19**, 2424-2428 (2002)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-19-12-2424

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- In practical cases one has at one’s disposal a finite number of data, and therefore one should indeed refer to the Euclidean norm in the space of the N-dimensional complex column vectors CN.However, the rationale remains unchanged.
- Analogously to the norm, one can refer to the scalar products in L2(Σ ⊗ S)in the general operational case and should refer to the scalar product in CNin the case with a finite number of data, but the rationale is the same.

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