SEQUENTIAL AND PARALLEL SCHEMES FOR ADAPTIVE 2-D PARAMETER-ESTIMATION WITH APPLICATION TO IMAGE ESTIMATION

In this paper, the non-causal quarter plane 2-D Recursive Least Squares (2D-RLS) algorithm for adaptive processing is developed. The complexity of this algorithm turns out to be O(L6) per iteration, for an L x L window. With the aim of reducing this complexity, the matrix gains appearing in the algorithm are replaced by scalar gains. This approach yields the Approximate 2-D Recursive Least Squares (A2D-RLS) algorithm, which is shown to have a complexity of O(L2). With the objective of reducing the computation time even further, a parallel scheme is developed for the A2D-RLS algorithm. Since the algorithm is inherently sequential, its parallelization involves some more approximations. The desired accuracy of the estimated parameters is shown to place an upper bound on the number of processors. The parallel scheme is suitable for implementation on shared memory as well as distributed memory machines. The algorithm is applied to the problem of image estimation. Simulation results giving speed-up, efficiency, and the accuracy of the estimated image are presented.