Networks for Nonlinear Diffusion Problems in Imaging.

Area of Science:

• Computer Vision
• Deep Learning
• Image Processing

Background:

• Deep learning, particularly convolutional neural networks (CNNs), has revolutionized imaging and vision tasks.
• CNNs achieve high performance even in applications where their suitability for capturing underlying physics is not obvious.
• Classical CNN architectures may lack interpretability and generalizability in certain scientific imaging domains.

Purpose of the Study:

• To develop a novel deep learning network architecture, DiffNet, specifically designed for diffusion-related problems in imaging.
• To create a nonlinear network architecture that explicitly models physical processes.
• To enhance interpretability and generalizability compared to traditional CNNs.

Main Methods:

• Developed DiffNet, a network architecture based on nonlinear diffusion processes.
• Designed explicit update rules within the DiffNet architecture.
• Evaluated DiffNet on the inverse problem of nonlinear diffusion using the Perona-Malik filter.
• Tested performance on the STL-10 image dataset.

Main Results:

• DiffNet demonstrated competitive performance against the established U-Net architecture.
• DiffNet required a fraction of the parameters compared to U-Net.
• DiffNet necessitated significantly less training data than U-Net.
• The explicit updates in DiffNet led to better interpretability and generalizability.

Conclusions:

• DiffNet presents a viable and efficient alternative to CNNs for specific imaging tasks, particularly those involving diffusion.
• The network's design based on physical processes enhances its understanding and application in scientific imaging.
• DiffNet offers a promising direction for developing more interpretable and data-efficient deep learning models for image processing.