  Deep convolutional neural networks (DCNN) have enjoyed great successes in
many signal processing applications because they can learn complex, non-linear
causal relationships from input to output. In this light, DCNNs are well suited
for the task of sequential prediction of multidimensional signals, such as
images, and have the potential of improving the performance of traditional
linear predictors. In this research we investigate how far DCNNs can push the
envelop in terms of prediction precision. We propose, in a case study, a
two-stage deep regression DCNN framework for nonlinear prediction of
two-dimensional image signals. In the first-stage regression, the proposed deep
prediction network (PredNet) takes the causal context as input and emits a
prediction of the present pixel. Three PredNets are trained with the regression
objectives of minimizing $\ell_1$, $\ell_2$ and $\ell_\infty$ norms of
prediction residuals, respectively. The second-stage regression combines the
outputs of the three PredNets to generate an even more precise and robust
prediction. The proposed deep regression model is applied to lossless
predictive image coding, and it outperforms the state-of-the-art linear
predictors by appreciable margin.
