Deep Neural Networks Motivated by Partial Differential Equations

• Published in: Journal of mathematical imaging and vision Vol. 62; no. 3; pp. 352 - 364
• Main Authors: Ruthotto, Lars, Haber, Eldad
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2020; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Artificial neural networks; Computer Science; Convolution; Image classification; Image processing; Image Processing and Computer Vision; Image reconstruction; Image segmentation; Machine learning; Mathematical Methods in Physics; Multivariate analysis; Neural networks; Noise reduction; Partial differential equations; Signal,Image and Speech Processing; Video data; Deep neural networks; Partial differential equations; PDE-constrained optimization; Machine learning; Image classification

Partial differential equations (PDEs) are indispensable for modeling many physical phenomena and also commonly used for solving image processing tasks. In the latter area, PDE-based approaches interpret image data as discretizations of multivariate functions and the output of image processing algori...