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This letter addresses the blind signal estimation problem in the so-called conjugate signal model, where the observed signal is a linear combination of the desired signal and its complex conjugate. It will be shown that blind signal recovery in this kind of signal model is feasible using only the second-order statistics of the observed signal, under the assumption of circular or proper complex signals. Furthermore, one practical example application in the field of communications receiver signal processing will be given, where the image signal interference caused by amplitude and phase mismatches of the receiver analog branches is digitally attenuated. In addition to the analytical results and practical implementation algorithms, the efficiency of the proposed estimation concepts in the digital image rejection application is evaluated using computer simulations, showing impressive performance results.