CIF: Efficient Distributed Solutions for Problems in Computational Imaging and AI

This project develops faster and more communication-efficient methods for solving large-scale data analysis problems that arise in computational imaging and artificial intelligence. In many modern applications, data are collected or processed across multiple machines or devices, making it important to design methods that reduce both computation and communication costs. Examples include dynamic magnetic resonance imaging, image and video compression, detection and tracking of moving objects for driverless cars, multi-target tracking in robotics, and efficient adaptation of large language models for specialized uses. A central challenge in these applications is to recover useful information from incomplete, corrupted, or distributed data while keeping the algorithms fast, reliable, and broadly usable across different data sets and measurement settings. The project will advance the foundations of efficient distributed learning and may enable practical improvements in areas such as near-real-time dynamic medical imaging and reliable artificial intelligence systems. The project will also support education and workforce development through the CyMath K-12 Math program which provides mathematics tutoring and mentoring. During this project, CyMath will be expanded into a multi-tier mathematics mentoring program that supports K-12 students, undergraduate tutors, and graduate student mentors, while also producing pilot evaluations of the program's educational impact. The project studies fast distributed algorithms for two classes of robust low-rank matrix and tensor learning problems. The first class is low-rank plus sparse matrix recovery from missing or otherwise undersampled observed data, often called the low-rank plus sparse model. The second class is low-rank recovery from shuffled, column-wise undersampled measurements. These models are motivated by computational imaging, tracking, video analysis, and parameter-efficient adaptation of large language models, where changes in model parameters can often be represented using low-rank or low-rank plus sparse structures. The research will develop a generalized multi-block alternating gradient descent and minimization framework, called Multi-AltGDmin, for partly decoupled optimization problems. In such problems, some groups of variables can be updated very efficiently when the other variables are fixed, while other groups are more computationally expensive. The goal is to design algorithms that retain the low per-iteration cost of gradient descent while approaching the faster convergence behavior of alternating minimization. The project will analyze sample complexity, iteration complexity, communication efficiency, and resilience to Byzantine attacks in distributed settings. It will also address new algorithmic and proof challenges caused by multiple variable blocks, including the need to choose update sequences that respect problem assumptions and to design distributed updates when different blocks depend on differently partitioned data. If successful, the project will provide the first provably correct, efficient, and attack-resilient distributed Multi-AltGDmin methods for robust principal component analysis and related problems, as well as for shuffled low-rank column-wise sensing. The resulting proof techniques are expected to be useful for other distributed learning and optimization problems. 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.