Stability analysis of multichannel, linear predictive systems

In this study we have attempted to investigate the stability problems observed in multichannel multidimensional linear predictive modeling of images. Morf et al.[3] have shown that based on a positive definite autocorrelation matrix, singular values of the matrix H??q+ 1. HERM (?q+ 1) must lie inside the unit circle for a stable solution, where ?q+1 is the normalized partial correlation matrix and HERM(.) denotes the Hermitian operator. We have employed this stability method to modify the multichannel Levinson algorithm [1,2] for obtaining stable linear prediction coefficients. Since the procedure involved block-by-block processing of image intensity values, blocks of 32×32 pixels were defined as analysis windows. A two-step stabilization method has been developed for these windows and it is applied to the multichannel multidimensional linear prediction of monochromatic imagery. The first step is based on heuristic notions and employed for obtaining strictly positive definite multichannel autocorrelation matrices R[q]. The second step is based on forcing singular values of H to reside inside the unit circle for satisfying the stability criterion reported in [3].