### Abstract

An important consideration in regularized image restoration is the evaluation of the regularization parameter. Various techniques exist in the literature for the evaluation of this parameter, which depend on the assumed prior knowledge about the problem. These techniques evaluate the regularization parameter either at a separate preprocessing step or by iterating based on the completely restored image, therefore requiring many restorations of the image with different values of the regularization parameter. The authors propose a nonlinear frequency-domain adaptive regularized iterative image restoration algorithm. According to this algorithm a regularization circulant matrix is used that corresponds to the assignment of a regularization parameter to each discrete frequency. Therefore, each frequency component is appropriately regularized. The resulting algorithm produces more accurate results and converges considerably faster than the algorithm that uses one regularization parameter for all frequencies. The regularization matrix is updated at each iteration step, based on the partially restored image. No prior knowledge about the image or the noise is required. The development of the algorithm is based on a set-theoretic regularization approach, where bounds on the weighted error residual and stabilizing functional are updated in the frequency domain at each iteration step. The proposed algorithm is analyzed theoretically and tested experimentally. Sufficient conditions for convergence are obtained in terms of a control parameter, which is specified by the conditions for convergence and optimality of the regularization parameters at each discrete frequency location. Finally the proposed algorithm is compared experimentally with other related algorithms.

Original language | English |
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Pages (from-to) | 3222-3232 |

Number of pages | 11 |

Journal | Optical Engineering |

Volume | 33 |

Issue number | 10 |

DOIs | |

Publication status | Published - 1994 Jan 1 |

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### All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics
- Engineering(all)

### Cite this

*Optical Engineering*,

*33*(10), 3222-3232. https://doi.org/10.1117/12.181245