Complex Function Estimation Using a Stochastic Classification/Regression Framework: Specific Applications to Image Superresolution

A stochastic framework combining classification with nonlinear regression is proposed. The performance evaluation is tested in terms of a patch-based image superresolution problem. Assuming a multi-variate Gaussian mixture model for the distribution of all image content, unsupervised probabilistic clustering via expectation maximization allows segmentation of the domain. Subsequently, for the regression component of the algorithm, a modified support vector regression provides per class nonlinear regression while appropriately weighting the relevancy of training points during training. Relevancy is determined by probabilistic values from clustering. Support vector machines, an established convex optimization problem, provide the foundation for additional formulations of learning the kernel matrix via semi-definite programming problems and quadratically constrained quadratic programming problems.