In the last decade, some very effective frameworks for image restoration have been proposed that (a) exploit non-locality (long-distance correlations) in natural images, and (b) use patched instead of pixels to robustly compare photometric similarities (called patch-based methods). In the first talk, we will present a simple yet effective idea of incorporating regression into the framework of patch-based restoration. We will present some results on synthetic and natural images, which show the proposed method consistently performs better than traditional patch-based methods beyond a moderate noise level, and significantly so when p is close to zero. We will present some insights into these findings (following the well-known connection between “sparsity” and “robustness”), and relate it to some recent theoretical results on the optimality of patch-based methods. We will also analyze the convergence and stability of the numerical algorithms for the regression, particulary for the non-convex regime
Kunal Chaudhury is a postdoctoral research associate at Princeton University, in the Program in Applied and Computational Mathematics. Kunal did his PhD in Computers, Communications, and Information Systems from the Ecole Polytechnique Federale de Lausanne (EPFL) in Switzerland, with a thesis titled "Optimally Localized Wavelets and Smoothing Kernels''. He has a Bachelors in Electrical Engineering (Jadavpur University, 2003), and a Masters in System Science and Automation (Indian Institute of Science, 2005). Kunal has research interests in computational harmonic analysis and its applications to signal and image processing, in the design of fast algorithms for signal and image processing, and also in spectral and convex relaxations, distributed graph localization, and dimensionality reduction. His broad interest is in the development and analysis of mathematical models and algorithms for the above mentioned areas.