Optimal edge preserving restoration with efficient regularisation

Abstract

Deblurring is an ill-posed inverse problem naturally and becomes more complex if the noise is also tainting the image. Classical approaches of inverse filtering and linear algebraic restorations are now obsolete due to the additive noise, as the problem is very sensitive to the small perturbation in the data. To cater the sensitivity of solution for small perturbations, smoothness constraints are generally added in the classical approaches. Previously neural networks and gradient based approaches have widely been used for optimisation; however, due to improper regularisation and computational cost, the problem is still an active research problem. In this paper, a new simple, efficient and robust method of regularisation based on the difference of grey scale average of image and each element of the estimated image is proposed. Constrained least square error is considered for optimisation and gradient based steepest descent algorithm is designed to estimate the optimal solution for restoration iteratively. The visual results and statistical measures of the experiments are presented in the paper which shows the effectiveness of the approach as compared to the state of art and recently proposed techniques.

Keywords:

• Deblurring
• Optimisation
• Neural network
• Fuzzy logic
• Regularisation
• Smoothness constraints
• Constrained least square error
• Ill-posed inverse problems
• Blur and noise
• Gradient
• Steepest descent
• Statistical measures