A new variational approach for restoring images with multiplicative noise

• Published in: Computers & mathematics with applications (1987) Vol. 71; no. 10; pp. 2034 - 2050
• Main Authors: Ullah, Asmat, Chen, Wen, Khan, Mushtaq Ahmad
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.05.2016
• Subjects: Blocking; Fractional-order total variation; High-order PDE norm; Mathematical models; Maximum a posteriori (MAP); Multiplicative noise; Noise; Norms; Preserves; Strategy; Synthetic aperture radar; Visual; Multiplicative noise; High-order PDE norm; Maximum a posteriori (MAP); Fractional-order total variation; Synthetic aperture radar
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2016.03.024

This paper proposes a novel variational model for restoration of images corrupted with multiplicative noise. It combines a fractional-order total variational filter with a high-order PDE (Laplacian) norm. The combined approach is able to preserve edges while avoiding the blocky-effect in smooth regions. This strategy minimizes a certain energy subject to a fitting term derived from a maximum a posteriori (MAP). Semi-implicit gradient descent scheme is applied to efficiently finding the minimizer of the proposed functional. To improve the numerical results, we opt for an adaptive regularization parameter selection procedure for the proposed model by using the trial-and-error method. The existence and uniqueness of a solution to the proposed variational model is established. In this study parameter dependence is also discussed. Experimental results demonstrate the effectiveness of the proposed model in visual improvement as well as an increase in the peak signal-to-noise ratio comparing to corresponding PDE methods.