Block-sparse signal recovery via ℓ2/ℓ1 - 2 minimisation method

© 2018, The Institution of Engineering and Technology. Motivated by the recently emerged ℓ1 - 2method for sparse signal recovery, in this study, the authors make an ongoing effect to extend this methodology to the setting of block sparsity, which directly leads to the proposed ℓ2/ℓ1 - 2method for blocksparse signal recovery. Some theoretical results are induced to guarantee the validity of proposed method. In particular, the obtained recovery condition rigorously includes the one induced by Yin et al., and the obtained error estimate can be used to model both the (block-) sparse and non-sparse signals, which is more comprehensive than that induced by Yin et al. which applies only to the sparse signals. The authors also derive an alternating direction method of multipliers (ADMM)-based algorithm to tackle the induced optimisation problem. Some experimental results that are based on the synthetic block-sparse signals and the real-world foetal electrocardiogram signals further demonstrate the better performance of the ℓ2/ℓ1 - 2method when it is compared with the state-of-the-art group-lasso method and ℓ2/ℓqmethod for 0 < q < 1.