An image may be disturbed by impulse noise during transmission or acquisition. To effectively restore the disturbed image is important for the applications of image processing. This study aims at enhancing the disturbed images by using the convolutional neural network (CNN) to identify similar patterns for the restoration of noisy pixels. In the training phase, each noisy pixel is analysed and compared with the noise-free image to find the closest neighbouring pixels. The pixels in a local window form a micro-pattern. All the captured micro-patterns, whose centre pixel is noisy, become a dataset for the training of a position CNN. The closest neighbouring pixel of a noisy image to the centre one of the noise-free image at the same position of each micro-pattern is selected to be the target. In the enhancement phase, a noisy micro-pattern, where the centre pixel is noisy, is input into the trained position CNN. The top N pixels are recognised and averaged to replace the grey level of the centre pixel. An enhanced pixel is obtained. The experimental results show that the position CNN can well recognise the similar neighbouring pixels and effectively enhance the noisy pixels in an image disturbed by salt-and-pepper noise.