BDoG-Net: Algorithm Unrolling for Blind Deconvolution on Graphs

Starting from first graph signal processing (GSP) principles, we present a novel model-based deep learning approach to blind deconvolution of sparse graph signals. Despite the bilinear nature of the observations, by requiring invertibility of the unknown (diffusion graph filter) forward operator we can formulate a convex optimization problem and solve it using the alternating-direction method of multipliers (ADMM). We then unroll and truncate the novel ADMM iterations to arrive at a parameterized neural network architecture for blind deconvolution on graphs (BDoG-Net), which we train in an end-to-end fashion using labeled data. This supervised learning approach offers several advantages, such as interpretability, parameter efficiency, and controllable complexity during inference. Our reproducible numerical experiments corroborate that BDoG-Net exhibits performance on par with the iterative ADMM baseline, but with markedly faster inference times and without the need to manually adjust the step-size or penalty parameters. The application of BDoG-Net to a simplified instance of source localization over networks is also discussed. Overall, our approach combines the best of both worlds by incorporating the inductive biases of a GSP model-based solution within a data-driven, trainable deep learning architecture for blind deconvolution on graphs.