PDE based Deep Learning for Geometric Image Data

Ryan Cecil and Dr. Stacey Levine, Department of Mathematics and Computer Science, Duquesne University, 600 Forbes Ave, Pittsburgh PA 15282

Image restoration is the process of estimating uncorrupted images from observations that have undergone degradations such as noise or blur. Recently, image restoration models have been proposed using the deep learning framework of convolutional neural networks (CNNs). These data-driven approaches show state of the art results with respect to performance but lack theoretical foundations, making them impractical for real-world problems where mistakes are not allowed. In addition, previous results have shown that denoising image geometry, such as level line curvature data, and then reconstructing an image estimate with the denoised curvature data yields more accurate results than denoising the image directly. This mathematically sound approach shows promise, but still lags behind CNNs with respect to performance. Furthermore, existing denoisers for natural image data do not necessarily translate to denoisers for image geometry, and this approach could benefit both from learning denoisers for image geometry as well as learning the most productive image geometries itself. In this work, we propose and analyze multiple CNNs whose architectures mimic that of a nonlinear partial differential equation for learning new higher-order geometrically motivated image features, as well as corresponding convolution filters and activation functions that can be used for image restoration, such as denoising and deblurring. Initial computational results are promising. The ultimate goal of this work is to use these learned features, filters, and nonlinear activation functions to formulate mathematically sound partial differential equation-based models for image restoration whose performances rival CNN based approaches.

Additional Abstract Information

Presenter: Ryan Cecil

Institution: Duquesne University

Type: Poster

Subject: Mathematics

Status: Approved

Time and Location

Session: Poster 8
Date/Time: Tue 5:00pm-6:00pm
Session Number: 5560