The field of image processing has grown immensely in the past few decades. There is a great demand for an increase in efficient processing of images, especially for multimedia, biology, and medicine, such as enhancing the quality of electron microscope and MRI (Magnetic Resonance Imaging) images. In addition, there is also a great need to develop ways to store more and more information, and especially how to transmit and process the information using computers and networks.

All of these things require the use of several mathematical techniques. Overall, there is no one mathematical theory of image processing. Instead, mathematicians and scientists use several areas of mathematics, including applied, partial differential equations, statistics, etc. to solve image processing needs. As computers and processing becomes even more powerful, these mathematical tools will become even more important.