Collaborative Research: Algorithms for Learning Regularizations of Inverse Problems with High Data Heterogeneity

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In today's era of big data, massive amount of data are being collected in various acquisition settings and different formats from diverse sources. Such high heterogeneity has posed serious challenges in many aspects of analysis, inference, and computation involving big data. This project aims at developing novel modeling and computational methods, including highly structured deep neural networks and novel training algorithms, to effectively address this challenging issue. Results of this project will provide powerful computational tools to a broad range of important fields involving large heterogenous data sets, such as signal processing, medical imaging, computer vision, and bioinformatics.The research in this project includes three major components: (1) Development of learnable optimization algorithms (LOAs) which induce highly efficient schemes for solving nonconvex and nonsmooth inverse problems. These LOAs effectively integrate residual learning architectures into exact and inexact descent-type algorithms, which not only have outstanding efficiency compared to the state-of-the-art methods in practice but are also supported by rigorous convergence guarantees in theory; (2) Novel training strategies based on bi-level optimization to learn the parameters of the LOAs, which can explore the underlying common features across a variety of tasks in heterogeneous data sets as well as the task-specific features; and (3) Efficient methods to solve the bi-level optimization problems of parameter training with comprehensive computation and sampling complexity analysis.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.