Stochastic approximation in Hilbert space and the problem of detecting an object in a sequence of noisy images

Abstract

Under study is the problem of fast detection of the appearance of an object in a sequence of noisy images (using a minimal number of images once the object appears). Let the probabilistic characteristics of the images be unknown to the observer; however, two sequences of independent images are available, statistically independent of each other, containing and not containing the object of interest. In order to detect the appearance of the object it seems reasonable to use the method of cumulative summation of the values of a suitable functional of the observed images. A construction of a functional of this type is proposed by using the method of stochastic approximation in infinite dimensional Hilbert space.