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.
Number in Series
Applied Mathematics | Mathematics | Statistics and Probability
AMS Subject Classification
Primary 62G08, Secondary 62G20.
Holdai, Veera and Korostelev, Alexander, "Image Reconstruction in Multi-Channel Model Under Gaussian Noise" (2007). Mathematics Research Reports. 54.