This paper presents a novel class of Graph-based Transform based on 3D convolutional neural networks (GBT-CNN) within the context of block-based predictive transform coding of imaging data. The proposed GBT-CNN uses a 3D convolutional neural network (3D-CNN) to predict the graph information needed to compute the transform and its inverse, thus reducing the signalling cost to reconstruct the data after transformation. The GBT-CNN outperforms the DCT and DCT /DST, which are commonly employed in current video codecs, in terms of the percentage of energy preserved by a subset of transform coefficients, the mean squared error of the reconstructed data, and the transform coding gain according to evaluations on several video frames and medical images.

This paper introduces the GBT-NN, a novel class of Graph-based Transform within the context of block-based predictive transform coding using intra-prediction. The GBT-NNis constructed by learning a mapping function to map a graph Laplacian representing the covariance matrix of the current block. Our objective of learning such a mapping functionis to design a GBT that performs as well as the KLT without requiring to explicitly com-pute the covariance matrix for each residual block to be transformed. To avoid signallingany additional information required to compute the inverse GBT-NN, we also introduce acoding framework that uses a template-based prediction to predict residuals at the decoder. Evaluation results on several video frames and medical images, in terms of the percentageof preserved energy and mean square error, show that the GBT-NN can outperform the DST and DCT.

This paper introduces the GBT-L, a novel class of Graph-based Transform within the context of block-based predictive transform coding. The GBT-L is constructed using a 2D graph with unit edge weights and weighted self-loops in every vertex. The weighted selfloops are selected based on the residual values to be transformed. To avoid signalling any additional information required to compute the inverse GBT-L, we also introduce a coding framework that uses a template-based strategy to predict residual blocks in the pixel and residual domains. Evaluation results on several video frames and medical images, in terms of the percentage of preserved energy and mean square error, show that the GBT-L can outperform the DST, DCT and the Graph-based Separable Transform.