Image reconstruction with smoothed mixtures of regressions

This work builds upon the kernel regression framework for solving the general image processing problem of denoising, deblurring and interpolating from scattered image samples. A competitive expectation-maximization method estimates globally all parameters of a generative image model, accounting for missing samples. One 2D footprint kernel and a local linear regression plane are estimated per data sample. Kernels can shift and their prior probabilities are estimated as well, unlike in nonparametric models. Missing data yields an underdetermined problem that is regularized by smoothing the marginal mixture density. At each iteration, a balloon estimator computes numerically the spatial 'territory' associated to each data samples. Results of these numerical diffusion operations are used to convolve adaptively each kernel in the forward model. Finally, the complete image is reconstructed by smoothing regression for combining conditional means of local linear regressors. Experiments apply this iterative Bayesian technique in image restoration.