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This work proposes a new recurrent polynomial neural network that utilises both the temporal dynamics of the image formation process and the multi-linear interactions between the pixels for 1D/2D predictive image coding. The network consists of a layer of summing units followed by a product unit and incorporates a feedback link from the output to the input layer. It is trained using a small size training set through dynamic backpropagation. Its performance is evaluated on a database of 15 images and compared to the higher-order neural network, the feedforward pi-sigma neural network, and the standard linear predictor.