Abstract:

This talk explores sparse coding of natural images in the highly overcomplete regime. Dr. Bruno Olshausen shows that as the overcompleteness ratio approaches 10x, new types of dictionary elements emerge beyond the classical Gabor function shape obtained from complete or only modestly overcomplete sparse coding. These more diverse dictionaries allow images to be approximated with lower L1 norm (for a fixed SNR), and the coefficients exhibit steeper decay.  He also evaluates the learned dictionaries in a denoising task, showing that higher degrees of overcompleteness yield modest gains in performance.  These results are of relevance to neuroscience, because the neural representation of images in cortical area V1 is also highly overcomplete.  Possible advantages of overcompleteness in image representation will be discussed.

Speaker Bio:

Bruno Olshausen received B.S. and M.S. degrees in Electrical Engineering from Stanford University and a Ph.D. in Computation and Neural Systems from the California Institute of Technology.  He was a postdoctoral fellow in the Department of Psychology at Cornell University, and at the Center for Biological and Computational Learning at the Massachusetts Institute of Technology.  He joined the faculty at the University of California at Davis in 1996, and in 2005 moved to UC Berkeley, where he is currently Professor of Neuroscience and Optometry.  He also directs the Redwood Center for Theoretical Neuroscience, a multidisciplinary group focusing on building mathematical and computational models of brain function.  Olshausen's research focuses on understanding the information processing strategies employed by the visual system for tasks such as object recognition and scene analysis.  He is specifically interested in how visual representations are adapted to statistics of the natural environment.