Clarkson University Assistant Professor of Mathematics Guohui Song recently received a National Science Foundation (NSF) award for research on convex optimization algorithms.

Song will receive a total of $140,501 for his project "Collaborative Research: An Integrated Approach to Convex Optimization Algorithms."

Image reconstruction and feature extraction have been important aspects in various applications such as medical resonance imaging (MRI) and synthetic aperture radar (SAR), Song explains.

These procedures involve challenges, however as many of the current methods in MRI and SAR formulate the problem as various convex optimization models.

"This project could lead to new ideas and techniques in designing the MRI scan machine in both the way of collecting the data and the way of reconstructing the images from them," Song said.

"It is aiming to have a systematic study of evaluating such models and also develop novel models based on the evaluation."

Because different applications may vary in sampling domains, levels of detail required and processing domains for the features of interest, the sampling domains or processing domains may not be well suited for the underlying question.

For example, Song said, the MRI scanner might collect the data in a spiral way. This is a fast and smooth way to collect the data, but it may not be a good way to represent the image. While the spiral way might be good as a sampling domain, it might not be as good as a processing domain.

These factors make the problems ill-posed, and various regularization techniques are necessary to study the problems by formulating them as convex optimization models.

The NSF award will support graduate and undergraduate student work on this project as well as other researchers in the group.

The project will provide students with opportunities for training through research and will prepare them for careers in science and engineering.