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A new iterative method for extrapolation of incomplete segmented data available in multiple separated bands is proposed and tested. The method uses the Burg algorithm to find the linear prediction parameters and an iterative procedure to improve the estimation of the linear prediction parameters and the extrapolation of the data. This method is especially effective when the spectra (Fourier transform of the observed data) are in discrete forms, in the context of radar imaging represented here, this means the objects consist of distinctly spaced scattering centers. The advantages of this algorithm are demonstrated using both numerically generated and realistic experimental data pertaining to high resolution radar imaging.