Convergence properties of a constrained 2-D adaptive digital filter

A novel adaptive 2-D digital filter is presented in which the filter is determined by a 1-D FIR (finite impulse response) prototype, and hence the computational complexity of the coefficient up date algorithm has an order of complexity O{M}, rather than O{M²}. The price paid for the improved performance is that the adaptive filter is 'preconstrained' according to the contours which are established by fixing the mapping parameters A, B, C, D, and E. This implies that some a priori information about the symmetry of an unknown system characteristic must be known before this structure can be used effectively. This adaptive 2-D filter is particularly attractive for applications in real-time image processing for robotics and computer vision where constrained adaptive filters may be quite useful, and where reduced computational complexity is essential for real-time operation.