Acoustical Scene Analysis and Fast Solution of Wave Propagation Problems

My research is driven by a desire to solve problems using all computer science and math tools at our disposal. Previous research has focused on building vision systems for the blind; joint audiovisual tracking and surveillance systems; creating auditory virtual reality; inventing a camera for sound and others. In this talk I will speak about two different but complementary research efforts that are ongoing in my group. Sound scene analysis: Humans and other animals are extremely good at paying attention to one sound of interest among many, in complex reverberative environments with many sources. Our early research established the physical and psyhophysical basis of how humans perceive scenes, which I will review. A newly funded project focuses on understanding how underwater acoustic scene analysis is performed by animals such as dolphins, and how it can be used to create autonomous underwater robots. Fast solvers for Acoustic and Electromagnetic Wave Propagation: A fundamental bottleneck in the solution of many classical problems of mathematical physics is the time and memory complexity of the solver. A theme of our research has been the development of efficient integral equation solvers for the Laplace, Poisson, Helmholtz and Maxwell equations. We solve a number of problems associated with numerical quadrature in these problems via new algorithms. Another issue is that these formulations lead to dense linear algebra systems, with O(N2) memory and O(N3) time complexity. A long standing theme of our work has been the use and development of the Fast Multipole Method, associated data structures, extensions to machine learning and statistics. I will discuss some of these as well.