### Abstract

In regularized image restoration a solution is sought which preserves the fidelity to the noisy and blurred image data and also satisfies some constraints which represent our prior knowledge about the original image. A standard expression of this prior knowledge is that the original image is smooth. The regularization parameter balances these two requirements, i.e., fidelity to the data and smoothness of the solution. The smoothness requirement on the solution, however, results in a globally smooth image, i.e., no attention is paid to the preservation of the high spatial frequency information (edges). One approach towards the solution of this problem is the introduction of spatial adaptivity. A different approach is presented in this paper. According to this approach besides the constraint which bounds from above the energy of the restored image at high frequencies, a second constraint is used. With this constraint the high frequency energy of the restored image is also bounded from below. This means that very smooth solutions are not allowed, thus preserving edges and fine details in the restored image. Extending our previous work, we propose a nonlinear formulation of the regularization functional and derive an iterative algorithm for obtaining the unique minimum of this functional. The regularization parameters are evaluated simultaneously with the restored image, in an iterative fashion based on the partially restored image.

Original language | English |
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Title of host publication | Proceedings of SPIE - The International Society for Optical Engineering |

Pages | 1505-1513 |

Number of pages | 9 |

Volume | 2727 |

Edition | 3/- |

Publication status | Published - 1996 Dec 1 |

Event | Visual Communications and Image Processing'96. Part 2 (of 3) - Orlando, FL, USA Duration: 1996 Mar 17 → 1996 Mar 20 |

### Other

Other | Visual Communications and Image Processing'96. Part 2 (of 3) |
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City | Orlando, FL, USA |

Period | 96/3/17 → 96/3/20 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering

### Cite this

*Proceedings of SPIE - The International Society for Optical Engineering*(3/- ed., Vol. 2727 , pp. 1505-1513)

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*Proceedings of SPIE - The International Society for Optical Engineering.*3/- edn, vol. 2727 , pp. 1505-1513, Visual Communications and Image Processing'96. Part 2 (of 3), Orlando, FL, USA, 96/3/17.

**Globally optimal smoothing functional for edge-enhancing regularized image restoration.** / Kang, Moon Gi; Katsaggelos, Aggelos K.; Park, Kyu T.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Globally optimal smoothing functional for edge-enhancing regularized image restoration

AU - Kang, Moon Gi

AU - Katsaggelos, Aggelos K.

AU - Park, Kyu T.

PY - 1996/12/1

Y1 - 1996/12/1

N2 - In regularized image restoration a solution is sought which preserves the fidelity to the noisy and blurred image data and also satisfies some constraints which represent our prior knowledge about the original image. A standard expression of this prior knowledge is that the original image is smooth. The regularization parameter balances these two requirements, i.e., fidelity to the data and smoothness of the solution. The smoothness requirement on the solution, however, results in a globally smooth image, i.e., no attention is paid to the preservation of the high spatial frequency information (edges). One approach towards the solution of this problem is the introduction of spatial adaptivity. A different approach is presented in this paper. According to this approach besides the constraint which bounds from above the energy of the restored image at high frequencies, a second constraint is used. With this constraint the high frequency energy of the restored image is also bounded from below. This means that very smooth solutions are not allowed, thus preserving edges and fine details in the restored image. Extending our previous work, we propose a nonlinear formulation of the regularization functional and derive an iterative algorithm for obtaining the unique minimum of this functional. The regularization parameters are evaluated simultaneously with the restored image, in an iterative fashion based on the partially restored image.

AB - In regularized image restoration a solution is sought which preserves the fidelity to the noisy and blurred image data and also satisfies some constraints which represent our prior knowledge about the original image. A standard expression of this prior knowledge is that the original image is smooth. The regularization parameter balances these two requirements, i.e., fidelity to the data and smoothness of the solution. The smoothness requirement on the solution, however, results in a globally smooth image, i.e., no attention is paid to the preservation of the high spatial frequency information (edges). One approach towards the solution of this problem is the introduction of spatial adaptivity. A different approach is presented in this paper. According to this approach besides the constraint which bounds from above the energy of the restored image at high frequencies, a second constraint is used. With this constraint the high frequency energy of the restored image is also bounded from below. This means that very smooth solutions are not allowed, thus preserving edges and fine details in the restored image. Extending our previous work, we propose a nonlinear formulation of the regularization functional and derive an iterative algorithm for obtaining the unique minimum of this functional. The regularization parameters are evaluated simultaneously with the restored image, in an iterative fashion based on the partially restored image.

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M3 - Conference contribution

SN - 0819421030

SN - 9780819421036

VL - 2727

SP - 1505

EP - 1513

BT - Proceedings of SPIE - The International Society for Optical Engineering

ER -