Least squares order statistic filter for signal restoration

The fundamental theory for restoring discrete waveforms immersed in independent noise using order-statistic (OS) filters, with the least-squares criterion as a fidelity measure, is developed. Nondynamical least-squares OS filter design methods are extended to the case of arbitrary discrete waveforms immersed in independent noise. A method for incorporating local structural constraints into the optimization process is introduced. A small number of these constraints can ensure that the filter designed is sensitive to local high-information signal structures. This is accomplished within a natural framework by appending the constraints into the objective function to be minimized using a Lagrangian approach. The principal drawback of OS filter design remains the complexity of computing the temporal/spatial correlations of the OS. A suboptimal approximation technique that yields good results when it is applied to the image restoration problem is developed. Some directions for future research are explored