Distributed Compressed Sensing With Personalized Variational Auto-Encoders

This paper proposes an efficient distributed learning algorithm for compressed sensing recovery over a multi-sensor network, by exploiting the personalization technique to capture both the correlation and discrepancy characteristics among different sensors. In particular, a specific joint sparsity model is considered, in which each sensor makes observations to a sparse vector that is a linear combination of a common vector and a private innovative one. A variational auto-encoder (VAE) based generative model is designed, with its architecture personalized for each of the sensors. The personalized architecture separates the generator into two parallel counterparts: a common part among sensors corresponding to the sparse common vector and a node-specific one for the innovation. Then we develop a two-stage distributed learning algorithm. At the first stage, the sensors collaboratively train their personalized VAEs with a modified loss function to learn the priors of the two constituent vectors. At the second stage, they jointly recover the vectors from their measurements, through distributed optimization with a consensus constraint on the common vector. Numerical simulations validate the effectiveness and efficiency of the proposed algorithm, especially when the number of measurements is small.