Parameter estimation for linear multichannel multidimensional models of non-Gaussian discrete random fields

This paper is concerned with the problem of estimating the multichannel impulse response function of a 2-D multiple-input multiple-output (MIMO) system given only the measurements of the vector output of the system. Such models arise in a variety of situations such as color images (textures), or image data from multiple frequency bands, multiple sensors or multiple time frames. We extend the approach of Tugnait (see IEEE Trans. Image Processing, vol.TP-3, p.109-27, 1994) (which deals with SISO 2-D systems) to MIMO 2-D systems. The paper is focused on certain theoretical aspects of the problem: estimation criteria, existence of a solution, and parameter identifiability. An iterative, inverse filter criteria based approach is developed using the third-order and/or fourth-order normalized cumulants of the inverse filtered data at zero-lag. The approach is input-iterative, i.e., the input sequences are extracted and removed one-by-one. The matrix impulse response is then obtained by cross-correlating the extracted inputs with the observed outputs.