My research topics include image processing, pattern recognition, geometric signal analysis and compressed sensing. These exciting, seemingly diverse fields could be said to lie in the interstices of signal processing, machine intelligence and computational geometry.
I am particularly interested in the understanding of manifold-modeled signal and image ensembles. The assumption of geometric structure in signals has proved to be useful in data acquisition, compression, enhancement and understanding, especially when the signal data is high-dimensional (meaning: almost always!). An intriguing model for a wide range of signals - sparsity - gives rise to the paradigm of Compressed Sensing (CS), the subject of energetic research in the signal processing community over the last 3 years. Manifolds, on the other hand, serve as suitable low-dimensional models for certain naturally occuring classes of signals and images. In addition to aiding analysis of high-dimensional data, geometric models could potentially be used for building systems which need to deal with massive amounts of data, but can handle only low-dimensional signals (like, for instance, the human brain..) Understanding the inter-relationships between different signal models remains a wide-open field of study.
