Interpolation of signals with missing data using PCA

A non-iterative methodology for the interpolation of sampled signals with missing data resorting to Principal Component Analysis is introduced. Based on unbiased estimators for the mean and covariance of signals, corrupted by zero-mean noise, the Principal Component Analysis is performed and the signal is interpolated given the optimal solution of a weighted least squares minimization problem. Upper and lower bounds for the mean square interpolation error are also provided in the interval of validity of the method. A preliminary performance assessment, with 1-D and 2-D signals, is included based on the results of a series of Monte Carlo experiments.