Seminario - Accelerated Optimization in the PDE Framework

Where: Aula Magna – Dipartimento di Matematica e Informatica
Date: 6 december 2021
Time: 11:00 am
Speaker: Prof. Anthony Yezzi
Title: Accelerated Optimization in the PDE Framework
Abstract: Following the seminal work of Nesterov, accelerated optimization methods (sometimes referred to as momentum methods) have been used to powerfully  Boost the performance of first-order, gradient-based parameter estimation in  Scenarios where second-order optimization strategies are either inapplicable or impractical. Not only does accelerated gradient descent converge  considerably faster than traditional gradient descent, but it performs a more robust  local search of the parameter space by initially overshooting and then oscillating back as it settles into a final configuration, thereby selecting only local minimizers with a attraction basin large enough to accommodate the initial overshoot. This behavior has made accelerated search methods particularly popular within the machine learning community where stochastic variants have been proposed as well. So far, however, accelerated optimization methods  have been applied to searches over finite parameter spaces. We show how a  variational setting for these finite dimensional methods (published by Wibisono,  Wilson and Jordan in 2016) can be extended to the infinite dimensional  setting, both in linear functional spaces as well as to the more complicated manifold of 2D curves and 3D surfaces. Moreover, we also show how extremely simple explicit discretizaion schemes can be used to efficiently solve the resulting  class of high dimensional optimization problems. We will illustrate applications of this strategy to problems in image restortation, image segmentation, 3D reconsrution, and (time permitting) will conclude with some recent  preliminary results related to the training of deep convolutional neural networks.

Speaker Bio: Professor Yezzi was born in Gainsville, Florida and grew up in Minneapolis, Minnesota. He obtained both his Bachelor's degree and his Ph.D. in the Department of Electrical Engineering at the University of Minnesota with minors in mathematics and music. After completing his Ph.D., he continued his research as a post-Doctoral Research Associate at the Laboratory for Information and Decision Systems at Massachusetts Institute of Technology in Boston, MA. His research interests fall broadly within the fields of image processing and computer vision. In particular, he is interested in curve and surface evolution theory and partial differential equation techniques as they apply to topics within these fields (such as segmentation, image smoothing and enhancement, optical flow, stereo disparity, shape from shading, object recognition, and visual tracking). Much of Dr. Yezzi's work is particularly tailored to problems in medical imaging, including cardiac ultrasound, MRI, and CT. He joined the Georgia Tech faculty in the fall of 1999 where he has taught courses in DSP and is working to develop advanced courses in computer vision and medical image processing. Professor Yezzi consults with industry in the areas of visual inspection and medical imaging. His hobbies include classical guitar, opera, and martial arts.

Research interests: 

• Image Processing (particularly medical imaging applications)
• Computer Vision
• Estimation and Control
• Computation and algorithms
• Applied differential geometry