A true order recursive algorithm for two-dimensional least squares error linear prediction and filtering

In this paper a novel algorithm is presented for the efficient Two-Dimensional (2-D), Least Squares (LS) FIR filtering and system identification. Causal filter masks of general boundaries are allowed. Efficient order updating recursions are developed by exploiting the spatial shift invariance property of the 2-D data set. Single step order updating recursions are developed. During each iteration, the filter coefficients set is augmented by a single new element. The single step order updating formulas allow for the development of an efficient, true order recursive algorithm for the 2-D LS causal linear prediction and filtering.