A hierarchical sparsity-smoothness Bayesian model for ℓ0 + ℓ1 + ℓ2 regularization
Sparse signal/image recovery is a challenging topic that has captured a great interest during the last decades. To address the ill-posedness of the related inverse problem, regularization is often essential by using appropriate priors that promote the sparsity of the target signal/image. In this context, ℓ<sub>0</sub> + ℓ<sub>1</sub> regularization has been widely investigated. In this paper, we introduce a new prior accounting simultaneously for both sparsity and smoothness of restored signals. We use a Bernoulli-generalized Gauss-Laplace distribution to perform ℓ<sub>0</sub> + ℓ<sub>1</sub> + ℓ<sub>2</sub> regularization in a Bayesian framework. Our results show the potential of the proposed approach especially in restoring the non-zero coefficients of the signal/image of interest.