Application of stochastic approximation in the Hilbert space to solving the problem of detecting the instant of arrival of an object in a sequence of noisy images

Abstract

Application of stochastic approximation in an infinite-dimensional Hilbert space to the problem of object detection on one observed image distorted by noise and to the problem of fast detection of object arrival in a sequence of noisy images is considered. No a priori information is assumed to be available. The observer is supposed to have two stochastically independent sequences of independent “exact” noisy images, one containing and one not containing the object that has to be (repeatedly) detected by the observer in the nearest time.