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A new constrained total variational deblurring model and its fast algorithm

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<mark>Journal publication date</mark>29/06/2015
<mark>Journal</mark>Numerical Algorithms
Issue number2
Volume69
Number of pages27
Pages (from-to)415-441
Publication StatusPublished
<mark>Original language</mark>English

Abstract

Although image intensities are non-negative quantities, imposing positivity is not always considered in restoration models due to a lack of simple and robust methods of imposing the constraint. This paper proposes a suitable exponential type transform and applies it to the commonly-used total variation model to achieve implicitly constrained solution (positivity at its lower bound and a prescribed intensity value at the upper bound). Further to establish convergence, a convex model is proposed through a relaxation of the transformed functional. Numerical algorithms are presented to solve the resulting non-linear partial differential equations. Test results show that the proposed method is competitive when compared with existing methods in simple cases and more superior in other cases.