Learning Graph Signal Representations with Narrowband Spectral Kernels

In this work, we study the problem of learning graph dictionary models from partially observed graph signals. We represent graph signals in terms of atoms generated by narrowband graph kernels. We formulate an optimization problem where the kernel parameters are learnt jointly with the signal representations under a triple regularization scheme: While the first regularization term aims to control the spectrum of the narrowband kernels, the second term encourages the reconstructed graph signals to vary smoothly on the graph, and the third term enforces that similar graph signals have similar representations over the learnt dictionaries. Once the graph kernels and signal representations are learnt, the initially unknown values of the signals are estimated based on the computed model. Experimental results show that the proposed method gives significant improvements in the estimation performance compared to reference approaches.