My research interests span a relatively wide area, ranging from Signal Processing to Matrix Analysis, and from Algorithms to Numerical Optimization. In my work, the main focus is on deriving adaptive algorithms for efficient representations of natural signals (e.g., images, speech sound), and on investigating their theoretical properties (such as computational complexity and accuracy).

• Spike-based representations. For temporal signals, look here for details. Currently, I am studying the visual flavor of this approach, that is, I am working on the derivation of an adaptive, shiftable-kernel, highly sparse representation for images.
  
  
• Robustness and redundancy in linear representations. "Robust Coding", or "how to cope with noise in the (linear) representations by using more units". For more on this (and for nice pictures), check out our recent paper in IEEE Trans. on Image Processing.
  
  
• Speech Enhancement by Bandwidth Extension.
  
  
• Wavelets, frames, filter-banks. See how to increase coding efficiency of multiscale/multiresolution methods for a given ensemble of images, by employing statistical adaptivity of the representation. Here is a draft of our paper on Multiresolution ICA (will appear in IEEE ICASSP 2009).
  
  
• Algebraic Signal Processing Theory. For more on what that is, please see this source. If you want to see how to design alternative polynomial transforms that asymptotically approach the DTFT (their spectrum converges to the unit circle) but avoid the periodic signal extension/boundary condition, check out our recent paper.