Physical Sciences and Mathematics Commons^™

Image Reconstruction In Multi-Channel Model Under Gaussian Noise, Veera Holdai, Alexander Korostelev

Mathematics Research Reports

The image reconstruction from noisy data is studied. A nonparametric boundary function is estimated from observations in N independent channels in Gaussian white noise. In each channel the image and the background intensities are unknown. They define a non-identifiable nuisance "parameter" that slows down the typical minimax rate of convergence. The large sample asymptotics of the minimax risk is found and an asymptotically optimal estimator for boundary function is suggested.