Machine learning is a new topic of increasing interest in scientific research, involving many practical engineering applications besides mathematical analysis of algorithms. It is known that many common optimisation problems exist in machine learning, such as algorithm choices, and model solutions. Although there have been notable achievements in the fields of machine learning and optimisation, many challenging problems remain, such as large-scale optimisation problems, fast algorithms for machine learning, and applications of machine learning to image denoising, which is a hard-to-solve inverse problem.

Images are often corrupted by impulse noise, one of the most common types of noise. Impulse noise has a short duration but degrades the quality of images. Impulse noise has two common types: salt-and-pepper noise and random-valued noise. There exist many established methods to remove impulse noise while preserving the integrity of edges and image details. Among these methods, two have attracted intensive attention from researchers. One is the median filter method (along with some important variants) – this method restores the noise pixels poorly when the noise ratio is high, and the recovered image may lose its details and be distorted. The other method is the variational approach, which may change the grey level of every pixel, including the uncorrupted ones.

The aim of this Special Issue is to encourage contributions of original research articles as well as review articles on new developments in machine learning, novel optimisation algorithms, and their applications to image restoration.

Potential topics include but are not limited to the following:

• Machine learning, cloud computing, and their applications in image restoration
• Large-scale deep model, black box machine learning algorithms
• Nonlinear eigenvalue problems, tensor analysis, and their applications in compressive sensing
• Nonlinear analysis for image restoration and machine learning
• Training data, data analysis, and complexity in machine learning