  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.
