A new constrained total variational deblurring model and its fast algorithm

作者：Williams Bryan Michael; Chen Ke^*; Harding Simon P

来源：Numerical Algorithms, 2015, 69(2): 415-441.

DOI：10.1007/s11075-014-9904-2

• Total variation
• Image deblurring
• Alternating direction method of multipliers
• Box constraint
• Transforms

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.

• 出版日期2015-6