k Block Sparse Vector Recovery via Block ℓ1-ℓ2 Minimization.

In this paper, k block sparse vectors are studied, and the block ℓ 1 - ℓ 2 model is adopted. It is proved theoretically that when the block sparsity satisfies some conditions, the k block sparse vector can be accurately recovered by the noise free block ℓ 1 - ℓ 2 model, and it can also be stably recovered by the noisy block ℓ 1 - ℓ 2 model. In the algorithm, we use the convex difference algorithm, and prove that the aggregation points of the sequence generated by the algorithm converge to the stable point of the objective function. We prove that when the parameter λ > 0 is less than a certain number λ k , the aggregation points of the sequence generated by the algorithm are block sparse. Finally, we conduct data experiments. The experiments show that when the vector is block sparse, the block ℓ 1 - ℓ 2 model can recover the unknown vector better than the traditional ℓ 1 - ℓ 2 model. [ABSTRACT FROM AUTHOR]