FIELD OF EXPERTS: OPTIMAL STRUCTURED BAYESIAN COMPRESSED SENSING

Exploiting signal structure can improve Compressed Sensing reconstruction performance. In this paper, we propose an optimal structured Bayesian Compressed Sensing (BCS) reconstruction framework. Constructed to capture signal structure precisely, this framework employs Field of Experts (FoE) to fuse Hidden Markov Random Fields with Gaussian Scale Mixtures as prior distributions. This approach optimizes the parameters of FoE by minimizing KL-divergence via Contrastive Divergence learning method. An analytical posterior inference via auxiliary-variable Gibbs sampler is then constituted to reconstruct the signal. Simulations show that this proposed method, named Optimal Structured BCS based on FoE (OS-BCS-FoE), outperforms previous CS recovery methods used for image restoration applications.