We consider linear sparse recovery problems where additional structure regarding the support of the solution is known. The form of the structure considered is non-overlapping sets of indices that each contain part of the support. An algorithm based on iterative hard thresholding is proposed to solve this problem. The convergence and error of the method are analyzed with respect to mutual coherence. Numerical simulations are examined in the context of an inverse source problem, including modifications for off-grid recovery

翻译：我们考虑的是线性稀少的回收问题,因为人们知道关于支持解决方案的额外结构。所考虑的结构的形式是非重叠的指数集,每个索引都包含部分支持。建议采用基于迭代硬阈值的算法解决这一问题。在相互一致性方面分析方法的趋同和错误。数字模拟是在反源问题的背景下研究的,包括修改离网回收。