## Reconstruction of an Object From Its Noisy Fourier Modulus: Ideal Estimate of the Object to Be Reconstructed and a Method That Attempts to Find That Estimate

Applied Optics, Vol. 38, Issue 26, pp. 5568-5576 (1999)

http://dx.doi.org/10.1364/AO.38.005568

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### Abstract

In general, the problem of reconstructing an object from its Fourier modulus has no solution when the Fourier modulus is contaminated by noise. Therefore a quasi solution, which we call the ideal estimate of the object to be reconstructed, is defined here based on the concept of territories of the convergence objects of the error-reduction algorithm, and a method that attempts to find that solution is presented. Keeping in mind that the ideal estimate is one of the output-stagnation objects of the hybrid input–output algorithm, we modify the hybrid input–output algorithm so that the output-stagnation objects can be located even when the value of the feedback parameter is not infinitesimally small, and this modified algorithm is combined with the hybrid input–output algorithm itself. The results of computer simulations carried out to test the performance of the proposed method are shown.

© 1999 Optical Society of America

**OCIS Codes**

(070.2590) Fourier optics and signal processing : ABCD transforms

(100.2000) Image processing : Digital image processing

(100.3010) Image processing : Image reconstruction techniques

(100.5070) Image processing : Phase retrieval

**Citation**

Hiroaki Takajo, Takao Shizuma, Tohru Takahashi, and Seiji Takahata, "Reconstruction of an Object From Its Noisy Fourier Modulus: Ideal Estimate of the Object to Be Reconstructed and a Method That Attempts to Find That Estimate," Appl. Opt. **38**, 5568-5576 (1999)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-38-26-5568

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