MULTIDIMENSIONAL SPECTRAL ESTIMATION: New enhanced algorithms for Spectral Power Estimation with theorical demonstrations and simulations over real Synthetic Aperture Radar signals.

We study the theory and the application for a multiple of methods in the domain of spectral power estimation. In the 2D case, and the general ND case new methods are proposed for spectral power estimation following the criteria of an associated positive definite ND correlation matrix extension, and the Maximum of Entropy spectral power measure. The ND-Toeplitz correlation matrix structure is studied under two conditions. The first is the infinite positive extension support with an approximate matching property. The second is a positive extension with a Maximum of Entropy property. These two conditions, or two approaches, have allowed, respectively, the development of two new methods for spectral power estimation SMSE, and SMCE. Newly presented methods were submitted to a numerical comparative study which included other methods; like Capon, Quarter Plan, etc... Numerical tests were run over artificially generated data and also real Synthetic Aperture Radar signal. For seriously engaged researchers, the executables programs, of all presented algorithms, are available for download from the web.