Robust deblurring random blur

The author introduces a modified technique for restoring an image that has been distorted by a linear system whose impulse response function is itself random in the presence of long-tailed noise detection. The deblurred image is obtained by calculating a robust kernel weight. The weight is chosen to optimize the combined measure of smoothness and robustness. A robust nonparametric function estimation is introduced. The estimate is motivated by the theory of M-estimation and the kernel estimation of regression functions. Consistency and asymptotic normality are shown. The estimate satisfies a minimax property, i.e. it minimizes the maximal asymptotic variance as the error distribution varies over a suitable contamination neighborhood (long-tailed noise)