Uniqueness conditions for 1D signal reconstruction from power spectrum with additional data term information

Signal reconstruction from its power spectrum is an important technique widely useful in different application fields. However, uniqueness is generally hard to be guaranteed by usual approaches due to nonlinearity of the power spectrum measurement models. In this paper a very general structure of the 1-dimensonal signal with given power spectrum is established and some conditions are introduced to guarantee the uniqueness of solution in signal reconstruction on basis of this formulism. Such conditions are about one or more additional information of the signal component and two algorithms are established for signal construction. One of the algorithms is exact and another one is iterative and approximate, both can reach the real signal under the introduced conditions.