Decentralized Jointly Sparse Optimization by Reweighted Lq Minimization
A set of vectors (or signals) are jointly sparse if their nonzero entries are commonly supported on a small subset of locations. Consider a network of agents which collaborative recover a set of joint sparse vectors. This paper proposes novel decentralized algorithms to recover these vectors in a way that every agent runs a recovery algorithm while neighbor agents exchange only their estimates of the joint support but not their data. The agents will obtain their solutions by taking advantages of the joint sparse structure while keeping their data private. As such, the proposed approach finds applications in distributed (compressive) sensing, decentralized event detection, as well as collaborative data mining. We use a non-convex minimization model and propose algorithms that alternate between support estimate consensus and signal estimate update. The latter step is based on reweighted Lq iterations, where q can be 1 or 2. We numerically compare the proposed decentralized algorithms with existing centralized and decentralized algorithms. Simulation results demonstrate that the proposed decentralized approaches have strong recovery performance and converge reasonably fast.
Citable link to this pagehttps://hdl.handle.net/1911/102196
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- CAAM Technical Reports