A0951
Title: Randomized Kaczmarz methods for corrupted tensor linear systems
Authors: Alejandra Castillo - Pomona College (United States) [presenting]
Jamie Haddock - Harvey Mudd College (United States)
Iryna Hartsock - H Lee Moffitt Cancer Center And Research Institute (United States)
Paulina Hoyos - University of Texas at Austin (United States)
Lara Kassab - University of California Los Angeles (United States)
Alona Kryshchenko - California State University Channel Islands (United States)
Kamila Larripa - California State Polytechnic University Humboldt (United States)
Deanna Needell - UCLA (United States)
Shambhavi Suryanarayanan - Princeton University (United States)
Karamatou Yacoubou Djima - Wellesley College (United States)
Abstract: Recovering tensor-valued signals from corrupted measurements is a central problem in various applications such as hyperspectral image reconstruction and medical imaging. The tensor linear system $A X = B$ is considered, where $A$ is a known measurement operator, $X$ is the unknown tensor signal, and $B$ contains observations potentially affected by sparse, large-magnitude corruptions. A quantile-based randomized Kaczmarz algorithm, called quantile tensor randomized Kaczmarz (qTRK), is discussed to address this challenge. By integrating quantile statistics into the iterative update process, qTRK improves robustness against adversarial errors. A variant selectively omits unreliable measurements to enhance stability further. Both algorithms offer convergence guarantees and are evaluated on synthetic and real-world examples, including a video deblurring task, showing improved performance in corrupted settings.
