ABSTRACT
This chapter proposes new algorithms for finding discontinuity surface of a signal specified with random errors at a regular grid. The standard deviation of random errors is finite. Two variants of the general problem of finding discontinuities of a signal from its noisy measurements are considered. The problem of finding discontinuities of a function is very important in many applications. This chapter describes the edge detector and the thin line detector. The spot detection problem is considered as an example. The chapter provides a justification of the edge detector algorithm. The asymptotic consistency of the edge detection algorithm is proved. The chapter provides a set of numerical experiments based on specific assumptions of the multidimensional algorithm.
