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Hessian-Based Regularization for 3-D Microscopy Image Restoration

S. Lefkimmiatis, A. Bourquard, M. Unser

Proceedings of the Ninth IEEE International Symposium on Biomedical Imaging: From Nano to Macro (ISBI'12), Barcelona, Kingdom of Spain, May 2-5, 2012, pp. 1731-1734.



We investigate a non quadratic regularizer that is based on the Hessian operator for dealing with the restoration of 3-D images in a variational framework. We show that the regularizer under study is a valid extension of the total-variation (TV) functional, in the sense that it retains its favorable properties while following a similar underlying principle. We argue that the new functional is well suited for the restoration of 3-D biological images since it does not suffer from the well-known staircase effect of TV. Furthermore, we present an efficient 3-D algorithm for the minimization of the corresponding objective function. Finally, we validate the overall proposed regularization framework through image deblurring experiments on simulated and real biological data.


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