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Affine rank minimization algorithms typically rely on calculating thegradient of a data error followed by a singular value decomposition at everyiteration. Because these two steps are expensive, heuristic approximations areoften used to reduce computational burden. To this end, we propose a recoveryscheme that merges the two steps with randomized approximations, and as aresult, operates on space proportional to the degrees of freedom in theproblem. We theoretically establish the estimation guarantees of the algorithmas a function of approximation tolerance. While the theoretical approximationrequirements are overly pessimistic, we demonstrate that in practice thealgorithm performs well on the quantum tomography recovery problem.

Randomized Low-Memory Singular Value Projection