New tool blends classic math and AI to tackle complex challenges
Researchers from the Johns Hopkins Department of Biomedical Engineering have developed an innovative tool that merges traditional mathematical methods (like variational formulations for inverse problems) with machine learning to address complex challenges in science and engineering.
This new approach, Learned Proximal Networks (LPNs), has demonstrated remarkable success in re-focusing blurry images, reconstructing medical scans, and other restoration and estimation tasks of high dimensional image data. According to the researchers, what sets LPNs apart is their ability to offer a clearer understanding of the model that is learned from data, paving the way for more precise and interpretable algorithms.
“This result is exciting because LPNs are a powerful tool for tackling complex problems with unclear or missing information,” said Jeremias Sulam, assistant professor of biomedical engineering and a member of the Johns Hopkins Mathematical Institute for Data Science (MINDS). “By combining traditional tools in variational problems and optimization with machine learning, LPNs ensure that these restoration models make precise use of a distribution learned from data via a proximal operator, leading to more reliable results and new possibilities in fields like medical imaging.”
The team’s results were published at the 2024 International Conference on Learning Representations (ICLR) this spring.
To understand the problem LPNs solve, imagine trying to figure out what a clear picture looks like when all you have is a blurry or distorted version. This issue comes up in many fields, such as medical imaging and computer vision. The tricky part is that there is no single simple answer unless some guidelines or assumptions are added—a process known as regularization.
“Regularization helps guide us to a reasonable solution,” said Zhenghan Fang, a fourth-year PhD student in biomedical engineering and lead author of this work. “Traditionally, these prior notions that reflect natural data were created by human experts, but now, with deep learning, computers can learn that from data. However, relying only on data can be risky because it’s hard to combine these data-driven tools with the precise mathematical formulations we used to enjoy with the human-designed versions.”
A tool called a proximal operator helps solve these problems by finding a balance between the data we have and what we believe natural data should look like – like whether we expect sharp edges, good contrasts, and more. While people have attempted to employ deep learning for these tasks, there’s a catch: the computer models don’t always follow the established rules, so their results may not be reliable.
“This mismatch, between traditional solvers and those found by black-box models, makes it harder for us to trust the solutions and understand how the computer is arriving at those solutions,” said Sulam.
He says that LPNs are a major advancement in this area because they’re trained to do exactly what a proximal operator does, but in a way that’s driven by data.
“The key idea here is a new training method called proximal matching,” said Fang, who is sponsored by the Kavli Neuroscience Discovery Institute at Hopkins. “This method ensures that LPNs accurately capture the important patterns in the data, leading to better and clearer results.”
The study team says that as LPNs continue to improve, they could play a crucial role in advancing fields where precise and understandable solutions are essential.
“Our LPNs help us clearly understand the rules learned from data, leading to better and more reliable results,” said Sulam. “This approach not only solves complex problems more effectively but also makes it easier to see how and why the solutions work, opening doors to new research in making models more trustworthy and understandable.”
Other contributors to the study included Sam Buchanan from the Toyota Technological Institute in Chicago.
By Dino Lencioni