Williams BM, Chen K, Harding SP. A new constrained total variational deblurring model and its fast algorithm. Numerical Algorithms. 2015 Jun;69:415-41.
https://link.springer.com/article/10.1007/s11075-014-9904-2
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.
