Globally optimal smoothing functional for edge-enhancing regularized image restoration

Moon Gi Kang*, Aggelos K. Katsaggelos, Kyu T. Park

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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 languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
Number of pages9
StatePublished - Dec 1 1996
EventVisual Communications and Image Processing'96. Part 2 (of 3) - Orlando, FL, USA
Duration: Mar 17 1996Mar 20 1996


OtherVisual Communications and Image Processing'96. Part 2 (of 3)
CityOrlando, FL, USA

ASJC Scopus subject areas

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


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