  This work examines the compressed sensor caching problem in wireless sensor
networks and devises efficient distributed sparse data recovery algorithms to
enable collaboration among multiple caches. In this problem, each cache is only
allowed to access measurements from a small subset of sensors within its
vicinity to reduce both cache size and data acquisition overhead. To enable
reliable data recovery with limited access to measurements, we propose a
distributed sparse data recovery method, called the collaborative sparse
recovery by anchor alignment (CoSR-AA) algorithm, where collaboration among
caches is enabled by aligning their locally recovered data at a few anchor
nodes. The proposed algorithm is based on the consensus alternating direction
method of multipliers (ADMM) algorithm but with message exchange that is
reduced by considering the proposed anchor alignment strategy. Then, by the
deep unfolding of the ADMM iterations, we further propose the Deep CoSR-AA
algorithm that can be used to significantly reduce the number of iterations. We
obtain a graph neural network architecture where message exchange is done more
efficiently by an embedded autoencoder. Simulations are provided to demonstrate
the effectiveness of the proposed collaborative recovery algorithms in terms of
the improved reconstruction quality and the reduced communication overhead due
to anchor alignment.
