Globally optimal smoothing functional for edge-enhancing regularized image restoration

Moon Gi Kang; Aggelos K. Katsaggelos; Kyu Tae Park

doi:10.1117/12.233226

27 February 1996 Globally optimal smoothing functional for edge-enhancing regularized image restoration

Moon Gi Kang, Aggelos K. Katsaggelos, Kyu Tae Park

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Proceedings Volume 2727, Visual Communications and Image Processing '96; (1996) https://doi.org/10.1117/12.233226
Event: Visual Communications and Image Processing '96, 1996, Orlando, FL, United States

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.

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Moon Gi Kang, Aggelos K. Katsaggelos, and Kyu Tae Park "Globally optimal smoothing functional for edge-enhancing regularized image restoration", Proc. SPIE 2727, Visual Communications and Image Processing '96, (27 February 1996); https://doi.org/10.1117/12.233226

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KEYWORDS

Image restoration

Image enhancement

Image processing

Matrices

Spatial frequencies

Algorithm development

Computer engineering

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