Multi-valued neurons are the neural processing elements with complex-valued weights, huge functionality (it is possible to implement on the single neuron arbitrary mapping described by partially defined multiple-valued function), quickly converged learning algorithms. Such features of the multi-valued neurons may be used for solution of the different kinds of problems.Neural network with multi-valued neurons for image recognition will be considered in the paper. Such a network with original architecture analyzes the phases of the Fourier spectral coefficients corresponding to the low frequencies. Quickly converged learning algorithm and huge functionality of multi-valued neurons allow getting 100% successful recognition of the different classes of images including the blurred and corrupted ones. Simulation results are presented on the example of face recognition.