Digital image processing is the demand of the common development of computer science, mathematics, and social applications. Mathematics plays an essential role in the development of digital image processing as the field is involved in all branches of image processing. Over the years, the practical requirements and engineering background of digital image processing also promote the development of the branch of applied mathematics. The application of partial differential equation methods to digital image processing has been an important direction in the field of applied mathematics in the past 20 years. There are constantly new challenges in studying digital image processing based on the partial differential equation method.

Partial differential equation (PDE) method shows better performance than traditional image processing methods, and some new ideas have never been considered in traditional image processing, such as affine invariant feature extraction, image structure and texture decomposition, etc. Partial differential equation method aims to establish the mathematical model of a partial differential equation, and then make the image change according to the partial differential equation, and finally achieve the desired effect. The results obtained by processing images with partial differential equations are beyond the reach of traditional methods.

The aim of this Special Issue is to bring together original research articles and review articles in the field of digital image processing (e.g., image filtering, restoration, segmentation, magnification, image enhancement, colour enhancement, etc.) based on partial differential equation methods. We highly encourage submissions discussing partial differential equation methods for digital image processing. Research can include image processing, signal and information processing, pattern recognition, applied mathematics, and equations of mathematical physics.

Potential topics include but are not limited to the following:

• Nonlinear image enhancement method based on PDE
• Application of PDE in image denoising
• Image restoration based on PDE
• Fuzzy video image processing based on PDE
• Image segmentation algorithm based on PDE
• Digital video repair method based on PDE
• Image filtering based on PDE
• Colour enhancement based on PDE
• Image restoration based on PDE
• Image magnification based on PDE
• Pattern recognition based on PDE
• Signal and information processing based on PDE