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Hessian-based norm regularization for image restoration with biomedical applications
Stamatios Lefkimmiatis1, Aurélien Bourquard, Michael Unser
1École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland. stamatis.lefkimmiatis@epfl.ch
Summary
We introduce novel Hessian-based regularization methods for image restoration, extending total-variation (TV) to reduce staircase effects. These methods offer improved image quality and efficient computation for large-scale applications.
Area of Science:
- Image Processing
- Computer Vision
- Applied Mathematics
Background:
- Total-variation (TV) regularization is successful for image restoration but can cause staircase artifacts.
- Existing methods often struggle with balancing noise reduction and detail preservation.
Purpose of the Study:
- To develop advanced regularization techniques for image restoration using nonquadratic Hessian-based functionals.
- To overcome limitations of traditional TV methods, specifically the staircase effect.
Main Methods:
- Derivation of second-order regularizers based on matrix norms of the Hessian operator.
- Interpretation of TV using mixed norms of directional derivatives.
- Development of an efficient iteratively reweighted least-square algorithm with a preconditioned conjugate gradient method.
Main Results:
- The proposed regularizers maintain desirable properties of TV, including convexity and invariance.
- Effective reduction of the staircase effect in restored images.
- Efficient and scalable minimization scheme applicable to large images.
Conclusions:
- Nonquadratic Hessian-based regularization offers a powerful framework for image restoration.
- The developed methods provide a superior alternative to TV for mitigating staircase artifacts.
- The efficient algorithm enables practical application to complex, large-scale image restoration tasks.