References

Nonparametric regression is a standard tool to uncover statistical relationships between pairs of random variables. Unfortunately, implementation of fully nonparametric smoothers are negatively impacted by the curse of dimensionality, which is why until now, these tool have been had limited success in image analysis. Recent advances in nonparametric smoothing [1] have shown that a simple iterative bias correction scheme can adapt to the underlying smoothness of the true regression function, and as a result can partially mitigate the curse of dimensionality. Practically, one can get good multivariate smoothers in dimensions of up to 20 to 50 dimensions (when the true regression is smooth). This makes it now possible to explore casting the problem of image denoising and image inpainting as a nonparametric smoothing problem. The first part of the talk will discuss the theory underlying the iterative bias reduction smoothing approach (as implemented in R [2]). The second half present some recent results on applying that method to image data and comparison with existing procedures