  A novel algorithm for the recovery of low-rank matrices acquired via
compressive linear measurements is proposed and analyzed. The algorithm, a
variation on the iterative hard thresholding algorithm for low-rank recovery,
is designed to succeed in situations where the standard rank-restricted
isometry property fails, e.g. in case of subexponential unstructured
measurements or of subgaussian rank-one measurements. The stability and
robustness of the algorithm are established based on distinctive
matrix-analytic ingredients and its performance is substantiated numerically.
