Finite horizon model reduction of a class of neutrally stable systems with applications to texture synthesis and recognition

In this paper we address the problem of finite-horizon model reduction for a class of neutrally stable discrete-time systems. The main result of the paper shows that this problem can be solved by considering suitable defined Hankel operators and Grammians, leading to an algorithm similar to the well known balanced truncation. However, in this case the structure of the problem can be exploited to obtain tighter truncation error bounds. These results are illustrated with a non-trivial practical example arising in the context of image processing: texture synthesis and recognition.