Per-channel autoregressive linear prediction padding in tiled CNN processing of 2D spatial data

We present linear prediction as a differentiable padding method. For each channel, a stochastic autoregressive linear model is fitted to the padding input by minimizing its noise terms in the least-squares sense. The padding is formed from the expected values of the autoregressive model given the known pixels. We trained the convolutional RVSR super-resolution model from scratch on satellite image data, using different padding methods. Linear prediction padding slightly reduced the mean square super-resolution error compared to zero and replication padding, with a moderate increase in time cost. Linear prediction padding better approximated satellite image data and RVSR feature map data. With zero padding, RVSR appeared to use more of its capacity to compensate for the high approximation error. Cropping the network output by a few pixels reduced the super-resolution error and the effect of the choice of padding method on the error, favoring output cropping with the faster replication and zero padding methods, for the studied workload.