Professor Balzano and her students investigate problems in statistical signal processing and optimization, particularly dealing with large and messy data. Her applications typically have missing, corrupted, and uncalibrated data as well as heterogeneous data in terms of sensors, sensor quality, and scale in both time and space. Her theoretical interests involve classes of non-convex problems that include Principal Components Analysis (or the Singular Value Decomposition) and many interesting variants such as PCA with sparse or structured principal components, orthogonality and non-negativity constraints, nonlinear variants such as low-dimensional algebraic variety models, and even categorical data or human preference data. She concentrates on fast gradient methods and related optimization methods that are scalable to real-time operation and massive data. Her work provides algorithmic and statistical guarantees for these algorithms on the aforementioned non-convex problems, and she focuses carefully on assumptions that are realistic for the relevant applications. She has worked in the areas of online algorithms, real-time computer vision, compressed sensing and matrix completion, network inference, and sensor networks.
Real-time dynamic background tracking and foreground separation. At time t = 101, the virtual camera slightly pans to right 20 pixels. We show how GRASTA quickly adapts to the new subspace by t = 125. The first row is the original video frame; the middle row is the tracked background; the bottom row is the separated foreground.