Bayesian Structured-Sparse Modeling Using a Bernoulli–Laplacian Prior

Recently, sparse signal and image recovery have shown significant promise in different biomedical fields. In this paper, we introduce a novel method to recover structured-sparse biomedical signals and images in a hierarchical Bayesian framework. The proposed method promoted sparse distribution using a Bernoulli–Laplace prior. In addition to sparse prior, we consider cluster prior on sparsity patterns. To implement the Bayesian inference, we use an MCMC technique to sample the target posterior distribution. Using generated samples, the model parameters and hyperparameters are estimated in an unsupervised scheme. Finally, the estimation procedure has been completed using the MAP estimator. Our method solves the inverse problem automatically without needing to alter the parameters manually. We have used synthetic data sets with several sparsity scenarios to explore the proposed algorithm, which outperforms the existing recovery methods, e.g., CoSaMP, BCS, EBSBL, and Cluss. Finally, through experiments using different real-life biomedical data (EMG and ECG signals and MR images), the superiority of the proposed method is demonstrated. This study demonstrates that using a combination of Bernoulli–Laplace and structured prior on sparsity patterns can recover structured-sparse biomedical signals and images precisely. Graphical Abstract: (Figure presented.)