A set theoretic approach to object-based image restoration

Xin Fan; Hua Huang; Chun Qi; Dequn Liang

doi:10.1117/12.587367

1 March 2005 A set theoretic approach to object-based image restoration

Xin Fan, Hua Huang, Chun Qi, Dequn Liang

Proceedings Volume 5672, Image Processing: Algorithms and Systems IV; (2005) https://doi.org/10.1117/12.587367
Event: Electronic Imaging 2005, 2005, San Jose, California, United States

Abstract

Approaches analyzing local characteristics of an image prevail in image restoration. However, they are less effective in cases of restoring images degraded by large size point spread functions (PSFs) and heavy noise. In this paper, we propose a set theoretic approach to object-based image restoration that involves the following issues: representing the common characteristics of a class of objects that images of interest contain, the formulation to combine prior knowledge of the object, and the algorithm to find the solution. The common characteristics of objects are represented as deterministic sets built on principal component analysis based models of objects. Combining these sets with those arising from observed data, object-based image restoration is formulated in a set theoretic framework. Finally, a parallel subgradient projection algorithm is applied to find the intersection of the sets. Experiments performed on frontal face images using the proposed approach show significant improvement in large size and heavy noise degradation, compared with traditional methods based on local analysis. The proposed approach opens the possibilities of introducing the more prior knowledge pertaining to objects in terms of deterministic sets and solving the problem by abundant numerical algorithms under set theoretic framework.

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Xin Fan, Hua Huang, Chun Qi, and Dequn Liang "A set theoretic approach to object-based image restoration", Proc. SPIE 5672, Image Processing: Algorithms and Systems IV, (1 March 2005); https://doi.org/10.1117/12.587367

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