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Distribution agnostic Bayesian compressive sensing with incremental support estimation

Abstract

In most compressive sensing algorithms, such as L1-optimization and greedy family techniques, the only a priori information utilized in the reconstruction procedure is the sparsity information. Meanwhile, there exists another family of techniques based on the Bayesian strategy, which considers comprehensive a priori statistical knowledge of the sparse data. This feature resulted in more increased attention to this category of algorithms. One member of the Bayesian-based family of compressive sensing reconstruction algorithms is the support Agnostic Bayesian Matching Pursuit, which is agnostic to support distribution.However, its high computation complexity in determining the set of dominant supports makes this algorithm unfeasible for practical applications such as wireless sensor networks (WSNs). Due to the special conditions of WSNs, consists of limited-power sensors, developed algorithms for them must have the least possible amount of computations. Given this, in this paper, we propose a Bayesian-based method with incremental support detection for distributed sparse signal recovery, which considerably reduces computational complexity. In the proposed method, in a network of sensors, sparse signal reconstruction from noisy measurements is done distributively and in the form of incremental cooperation. So, the number of required computations will be significantly reduced, which will result in a fast approach. The computer simulations show the superior performance of the proposed incremental Bayesian recovery method.

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Correspondence to Ghanbar Azarnia.

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Azarnia, G. Distribution agnostic Bayesian compressive sensing with incremental support estimation. Multidim Syst Sign Process (2021). https://doi.org/10.1007/s11045-021-00804-w

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Keywords

  • Wireless sensor networks
  • Compressed sensing
  • Sparse signal
  • Incremental topology
  • Bayesian approach