Applied Math Seminar: Alejandra Castillo (Pomona College)

Title:    Randomized Kaczmarz Methods for Corrupted Tensor Linear Systems

Abstract: Recovering tensor-valued signals from corrupted measurements is a central problem in various applications such as hyperspectral image reconstruction and medical imaging. This talk considers tensor linear systems of the form AX = B, that contain 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.