Constrained deconvolution by explicit correction of fourier components of the unknown distribution

The physical constraints were applied in the problem of deconvolution by explicitly correcting noise affected Fourier components of the unknown distribution. The method gives the constrained estimate optimal in the quadratic sense, i.e. the estimate closest to the exact solution in the Euclidean space of solutions. The properties of the method were theoretically examined and some practical applications in the astronomical spectroscopy have been effected. The method is compared with the similar Fourier spectrum extrapolation procedures; as a consequence application of the method is recommended particularly in the case of low signal-to-noise measurements.