Robust Identification of 2-D Periodic Systems with Applications to Texture Synthesis and Classification

In this paper we address the problem of robust identification of separable in denominator 2-dimensional (2D) discrete LTI systems that have a periodic impulse response. These systems arise in the context of many applications ranging from image processing to sensor arrays. The main result of the paper shows that a nominal plant that interpolates the experimental data as well as worst case bounds on the identification error can be obtained by performing a singular value decomposition on two Hankel matrices obtained from the experimental data. These results are illustrated with two practical examples arising in the context of image processing: texture synthesis and texture classification