Parallel-form realization of 2-D adaptive separable-denominator state-space filters

This paper treats the parallel-form realization of two-dimensional (2-D) adaptive state-space filters whose transfer functions are separable in the denominator. The adaptive filters are described by the Roesser local state-space (LSS) model and the least mean squares (LMS) method is used here to adjust the filter parameters. First, the Roesser LSS model with separable denominator is realized in a parallel form. The stability condition of the filter is then shown. Next, the LMS method is employed to adjust the filter parameters in the parallel form. In addition, the computational time required for the realization is investigated. Finally, the adaptive filter is applied in numerical examples to the 2-D spatial-domain filter design and to the noise reduction of an image.