A true order recursive algorithm for two-dimensional mean squared error linear prediction and filtering

In this paper a novel algorithm is presented for the efficient two-dimensional (2-D), mean squared error (MSE), FIR filtering and system identification. 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 MSE linear prediction and filtering. In contrast to the existing column(row)wise 2-D recursive schemes based on the Levinson–Wiggins–Robinson multichannel algorithm, the proposed technique offers the greatest maneuverability in the 2-D index space in a computational efficient way. This flexibility can be taken into advantage if the shape of the 2-D mask is not a priori known and has to be dynamically configured. The recursive character of the algorithm allows for a continuous reshaping of the filter mask. Search for the optimal filter mask, essentially reconfigures the filter mask to achieve an optimal match. The optimum determination of the mask shape offers important advantages in 2-D system modeling, filtering and image restoration. An illustrative example from 2-D autoregressive spectrum estimation is also supplied.