In this paper, we present modifications of the iterative hard thresholding (IHT) method for recovery of jointly row-sparse and low-rank matrices. In particular a Riemannian version of IHT is considered which significantly reduces computational cost of the gradient projection in the case of rank-one measurement operators, which have concrete applications in blind deconvolution. Experimental results are reported that show near-optimal recovery for Gaussian and rank-one measurements, and that adaptive stepsizes give crucial improvement. A Riemannian proximal gradient method is derived for the special case of unknown sparsity.

翻译：在本文中,我们介绍了对迭代硬阈值(IHT)方法的修改,以回收联合行片状和低位矩阵。特别是,考虑到里曼尼版的IHT可大幅降低一级测量操作员的梯度预测的计算成本,这些操作员在盲目分解中具有具体应用。据报告,实验结果显示,高斯和一级测量的恢复接近最佳,适应性分级具有关键的改进作用。 一种里曼尼级准度梯度方法是针对未知的气候的特例制定的。