A Tour of Modern "Image Processing"

Recent developments in computational imaging and restoration have heralded the arrival and convergence of several powerful methods for adaptive processing of multidimensional data. Examples include Moving Least Square (from Graphics), the Bilateral Filter and Anisotropic Diffusion (from Vision), Boosting and Spectral Methods (from Machine Learning), Non-local Means (from Signal Processing), Bregman Iterations (from Applied Math), Kernel Regression and Iterative Scaling (from Statistics). While these approaches found their inspirations in diverse fields of nascence, they are deeply connected. In this talk, I will present a practical and unified framework for understanding some common underpinnings of these methods. This leads to new insights and a broad understanding of how these diverse methods interrelate. I will also discuss several applications, and the statistical performance of the resulting algorithms. Finally I briefly illustrate connections between these techniques and classical Bayesian approaches.