A novel algorithm for finding algebraic base of singular subspace for signal information system is presented. It is based on Best Rank One Matrix (BROM) approximation for matrix representation of information system and on its subsequent matrix residua. From algebraic point of view BROM is a kind of power method for singular value problem. By attribute centering it can be used to determine principal subspace of signal information system and for this goal it is more accurate and faster than Oja’s neural algorithm for PCA while preserving its adaptivity to signal change in time and space. The concept is illustrated by an exemplary application from image processing area: adaptive computing of image energy singular trajectory which could be used for image replicas detection.