In this paper, we present a non-convex ℓ₂/ℓ_q(0<q<1)-analysis method to recover a general signal that can be expressed as a block-sparse coefficient vector in a coherent tight frame, and a sufficient condition is simultaneously established to guarantee the validity of the proposed method. In addition, we also derive an efficient iterative re-weighted least square (IRLS) algorithm to solve the induced non-convex optimization problem. The proposed IRLS algorithm is tested and compared with the ℓ₂/ℓ₁-analysis and the ℓ_q(0<q≤1)-analysis methods in some experiments. All the comparisons demonstrate the superior performance of the ℓ₂/ℓ_q-analysis method with 0<q<1.

在本文中，我们提出了一种非凸ℓ ₂ / ℓ _q（0 < q <1） -分析方法来恢复可表示为在一个相干紧框架的块稀疏系数向量的一般信号，和足够的同时建立条件以保证所提出方法的有效性。此外，我们还导出了一种有效的迭代重加权最小二乘（IRLS）算法来解决诱导的非凸优化问题。所提出的算法IRLS进行测试，并与对比ℓ ₂ / ℓ ₁ -分析和ℓ _q（0 < q≤1）-某些实验中的分析方法。所有的比较展示了优越的性能ℓ ₂ / ℓ _q -分析方法与0 < q <1。