A fourth-order partial differential equation denoising model with an adaptive relaxation method

Abstract

In this paper, an adaptive relaxation method and a discontinuity treatment of edges are proposed to improve the digital image denoising process by using the fourth-order partial differential equation (known as the YK model) first proposed by You and Kaveh. Since the YK model would generate some speckles into the denoised image, a relaxation method is incorporated into the model to reduce the formation of isolated speckles. An additional improvement is employed to handle the discontinuity on the edges of the image. In order to stop the iteration automatically, a control of the iteration is integrated into the denoising process. Numerical results demonstrate that such modifications not only make the denoised image look more natural, but also achieve a higher value of peak signal noise ratio (PSNR).

Keywords:

• image denoising
• fourth-order PDE
• relaxation method

2014 AMS Subject Classifications:

• 65K05
• 65K10
• 49M37
• 49M25
• 68U10