In this paper, we propose a neural implementation of a companded quantization scheme allowing to train and implement optimal scalar quantization in data compression systems based on neural networks. The advantage of companded quantization lies in the fact that it allows to implement optimal non-linear quantization in a simpler form based on uniform quantization. In our work, we consider two different models of uniform quantization. Further on, in order to verify the effectiveness of the proposed approach, we made a series of experiments on natural grayscale images. The results for the proposed scheme were compared to the results obtained with uniform quantization and optimal non-linear quantization calculated with approximate Lloyd-Max algorithm. The results of experiments showed that the proposed approach allowed to obtain the best results.