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Speaker: Garvesh Raskutti (University of Wisconsin--Madison)
Title: Minimax optimal rates for photon-limited compressed sensing with Poisson noise
Abstract:
Compressed sensing is a useful paradigm for signal reconstruction with limited measurements. Past theoretical results suggest that as the number of sensors increases, the signal reconstruction error decays at a reasonable rate. However many of the past theoretical results do not account for the physical constraints of real-world systems (e.g. signal-dependent noise, intensity constraints, etc.). Recent work provides upper bounds and simulation results for the performance of photon-limited compressed sensing under Poisson noise. These results suggest that in this photon-limited Poisson noise setting, reconstruction error does not decrease and may increase as the number of sensors increase. However there exist no lower bounds on reconstruction error to ensure that the rates can not be improved. In this work, we supplement the previous upper bounds with sharp minimax lower bounds for a more general setting that includes the photon-limited case of interest. Our lower bounds confirm that as the previous upper bounds and simulations suggest, the reconstruction error does not decrease as the number of sensors increases.
This is based on joint work with Xin Jiang (Duke University, ECE), and Rebecca Willett (University of Wisconsin-Madison, ECE)
Speaker Bio:
Garvesh Raskutti is an assistant professor in the Department of Statistics and Computer Science at University of Wisconsin-Madison. He did his Ph.D. in statistics at UC Berkeley under Bin Yu and Martin Wainwright as well as a post-doc at SAMSI. His research interests include compressed sensing and high-dimensional statistical inference, non-parametric statistics, stochastic optimization, and graphical models.
