Two-dimensional spectral estimation method with data extension and its improvement

This paper considers the application of the two-dimensional (2-D) spectral estimation for estimating the frequency of the 2-D sinusoidal signal from a small number of data arrays. Comparing the 2-D autocorrelation method, which is a typical 2-D method of linear prediction, and the data extension method proposed by Frost et al., it is shown that the data extension method gives a better result of spectral estimation. It is noted that the estimation accuracy is deteriorated when an additive noise is mixed. From such a viewpoint, this paper considers first the noise-compensation method, where the noise power is subtracted from the diagonal elements of the correlation matrix in the Yule-Walker equation in the one-dimensional (1-D) processing. Then, a simple and efficient noise-compensated autoregression (AR) parameter estimation method is derived, which can solve at the same time the problems of the accurate estimation of the noise power and the deterioration of the AR parameter estimation accuracy due to the oversubtraction of the estimated noise power, which have been considered unsolved. Applying the idea to the data extension method, an improved data extension method is derived. It is shown that by this improvement, the accuracy of the data prediction is improved and the estimation of the 2-D spectrum is improved greatly.