Efficient Iterative Reconstruction Algorithms for Magnetic Resonance Imaging

• Grant number: 25/06013-4
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: September 01, 2026
• End date: August 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Ernesto Julián Goldberg Birgin
• Grantee: Gabriel Rodrigues Silva Grillo
• Supervisor: Marcelo Victor Wust Zibetti
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Institution abroad: NYU Langone Medical Center, United States
• Associated to the scholarship: 23/15603-4 - Incremental Methods with Acceleration and Exact Smoothing of Convex Optimization Problems: A Unified Approach Through First-Order Inexact Methods, BP.DR

Abstract

Magnetic Resonance Imaging is a linear inverse problem that can be modeled by Bayesian inference. Assuming the noise and solution's distribution leads to variational regularization problems, for which appropriate optimization methods are known. With machine learning techniques, such as diffusion and score-based models, one can estimate the solution's distribution from data. However, the variational regularization problem emerging in this scenario is more challenging. In this project, we aim to develop an appropriate method for this situation. (AU)