In the context of signal processing for information-measurement systems (IMS), we consider the case  when the detected signals are linear combinations of original signals acting (with different efficiency) on each of IMS sensors. In certain problems (processing radar signal data arrays and information for medical-biology IMS, gain equalization and adaptive noise cancellation for communication channels), both the form of original signals and the proportion of their mixing at the output of the measuring system sensors are unknown. The problem at reconstruction of original signals is complicated by the necessity to identify the mixing structure. For stationary and independent original signals, the problem of their reconstruction is solved using neural network (NN) algorithms. Two NN structures, models for their construction and learning algorithms are considered. The lack of a priori information on the signal form and mixing structure allows one to fulfil only signal reconstruction with a precision of signal generalized permutation.