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Future wireless systems are trending towards higher carrier frequencies that offer larger communication bandwidth but necessitate the use of large antenna arrays. Signal processing techniques for channel estimation currently deployed in wireless devices do not scale well to this “high-dimensional” regime in terms of performance and pilot overhead.

Graph prediction problems prevail in data analysis and machine learning. The inverse prediction problem, namely to infer input data from given output labels, is of emerging interest in various applications. In this work, we develop invertible graph neural network (iGNN), a deep generative model to tackle the inverse prediction problem on graphs by casting it as a conditional generative task.

Countless signal processing applications include the reconstruction of signals from few indirect linear measurements. The design of effective measurement operators is typically constrained by the underlying hardware and physics, posing a challenging and often even discrete optimization task. While the potential of gradient-based learning via the unrolling of iterative recovery algorithms has been demonstrated, it has remained unclear how to leverage this technique when the set of admissible measurement operators is structured and discrete.

We study the problem of reconstructing a high-dimensional signal $\mathrm {x} \in \mathbb {R}^{n}$ from a low-dimensional noisy linear measurement $\mathrm {y}=\mathrm {M}\mathrm {x}+\mathrm {e} \in \mathbb {R}^{\ell }$ , assuming x admits a certain structure.

In Bora et al. (2017), a mathematical framework was developed for compressed sensing guarantees in the setting where the measurement matrix is Gaussian and the signal structure is the range of a generative neural network (GNN). The problem of compressed sensing with GNNs has since been extensively analyzed when the measurement matrix and/or network weights follow a subgaussian distribution.

There is a growing interest in deep model-based architectures (DMBAs) for solving imaging inverse problems by combining physical measurement models and learned image priors specified using convolutional neural nets (CNNs). For example, well-known frameworks for systematically designing DMBAs include plug-and-play priors (PnP), deep unfolding (DU), and deep equilibrium models (DEQ).