Defence of dissertation in the field of Signal Processing Technology, M.Sc. (Tech.) Mihai Florea
In 1983, Dr. Nesterov has developed the Fast Gradient Method (FGM), a very efficient and reliable algorithm that could solve optimization problems with millions of variables. Howev-er, computer technology was limited at the time and this method did not find many applica-tions. It would be only 25 years later that a myriad of applications would emerge and FGM would become the focus of the optimization community.
Despite its strengths, FGM is poorly understood and is still regarded by many researchers to rely on "algebraic tricks". Research groups from highly ranked universities, including MIT, UC Berkeley, Caltech, and Stanford, have recently published works attempting to decipher FGMs mode of operation, but none of these works have led to major improvements.
In this thesis, using simple but powerful ideas, we give a new perspective on FGM and create a more general algorithm, the Accelerated Composite Gradient Method (ACGM), with in-creased performance that can be applied to entirely new types of problems.
One such problem is the reconstruction of ultrasound images. Ultrasound is an affordable and harmless means of screening for a variety of diseases, most importantly for cancer. By mod-eling every pixel of the image as a variable and applying ACGM, we are now able to recon-struct ultrasound images with a completely new level of detail.
Prof. Nesterov himself values this work highly and will be attending the defense as an opponent.
Opponents: Professor Yurii Nesterov, Center for Operations Research (CORE), Belgium and Professor Jean-Christophe Pesquet, University Paris-Saclay, France
Supervisor: Professor Sergey A. Vorobyov, Aalto University School of Electrical Engineering, Department of Signal Processing and Acoustics.