Gibbs Artifacts Removal with Nonlinearity

Gibbs artifacts, appearing as oscillations or ringing around sharp edges or boundaries, are frequently encountered in image processing. They arise when the image's frequency components are adjusted, such as in image deblurring and sharpening. Linear methods are ineffective in reducing Gibbs artifacts; nonlinear methods may be more effective.

One such nonlinear method is the use of neural networks. This paper applies a simple convolutional neural network (CNN) to an image sharpening task and observes the effects of Gibbs artifacts. This network has only one convolutional layer, which consists of four channels. The well-known rectified linear unit (ReLU) is used as the nonlinear activation function.

For simple one-dimensional (1D) and two-dimensional (2D), unrealistic case studies, the Gibbs artifacts are completely removed. The reason why the artifacts can be removed is explained.

This simple case study illustrates the power of nonlinear functions and the use of multiple channels. In fact, this task can be achieved without using a neural network.