No icon

Alternative to Extended Block Sparse Bayesian Learning And its Relation to Pattern-Coupled Sparse Ba

Alternative to Extended Block Sparse Bayesian Learning And its Relation to Pattern-Coupled Sparse Bayesian Learning


We consider the problem of recovering block sparse signals with unknown block partition and propose a better alternative to the extended block sparse Bayesian learning (EBSBL). The underlying relationship between the proposed method, EBSBL and pattern-coupled sparse Bayesian learning (PC-SBL) is explicitly revealed. The proposed method adopts a cluster-structured prior for sparse coefficients, which encourages dependencies among neighboring coefficients by properly manipulating the hyper parameters of the neighborhood. Due to entanglement of the hyper parameters, a joint sparsely assumption is made to yield a sub-optimal analytic solution. The alternative algorithm avoids high dictionary coherence in EBSBL, reduces the unknowns of EBSBL and explains the effectiveness of EBSBL. The proposed algorithm also avoids vulnerability of parameter choice in PC-SBL. Results of comprehensive simulations demonstrate that the proposed algorithm achieves performance that is close to the best performance of PC-SBL. In addition, it outperforms EBSBL and other recently reported algorithms particularly under noisy and low sampling scenarios.


An expanded sensing matrix is firstly constructed by adding redundant columns to the original measurement matrix. And the data model is subsequently transformed into a linear combination of sub-dictionaries in the expanded sensing matrix with an augmented block-wise sparse coefficient vector.

Thereafter, the problem can be effectively solved by traditional BSBL algorithm and the original sparse coefficients can be finally computed from the augmented vector.

PC-SBL introduces a pattern coupled hierarchical Gaussian prior for each coefficient involving its own hyper parameter and those of its immediate neighbors to exert interactions between neighboring coefficients.


The proposed algorithm outperform BSBL since a rigid block structure is directly imposed on the coefficients in BSBL. PCSBL and the proposed method achieve a comparable highest success rate. Note that both the proposed method and PC-SBL outperform EBSBL when less measurements are available.

Proposed methods provide the most accurate estimates of the original sparse coefficients with less measurements, especially for those significant elements inside clusters.


Comment As:

Comment (0)