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A new approach to permittivity profile reconstruction based on impulse reflection response processing is considered. The impulse response data is examined to be obtained with use of microwave reflection coefficient data extrapolation technique completed with discrete Fourier transform. The extrapolation is carried through special functional minimization procedure providing minimum of quasiduration of impulse response (method of minimum of duration, MMD). Results of numerical data processing using Gelpsilafand-Levitan iterative scheme for permittivity profile reconstruction are presented.