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—We present novel techniques for analyzing the problem of low-rank matrix recovery. The methods are both considerably simpler and more general than previous approaches. It is shown that an unknown n × n matrix of rank r can be efficiently reconstructed from only O(nrν ln 2 n) randomly sampled expansion coefficients with respect to any given matrix basis.(More)
* This technical note supplies an affirmative answer to a question raised in a recent pre-print in the context of a " matrix recovery " problem. Assume one samples m Hermitian matrices X1,. .. , Xm with replacement from a finite collection. The deviation of the sum X1 + · · · + Xm from its expected value in terms of the operator norm can be estimated by an(More)
In this work we analyze the problem of phase retrieval from Fourier measurements with random diffraction patterns. To this end, we consider the recently introduced PhaseLift algorithm, which expresses the problem in the language of convex optimization. We provide recovery guarantees which require O(log 2 d) different diffraction patterns, thus improving on(More)
The problem of retrieving phase information from amplitude measurements alone has appeared in many scientific disciplines over the last century. PhaseLift is a recently introduced algorithm for phase recovery that is computationally efficient, numerically stable, and comes with rigorous performance guarantees. PhaseLift is optimal in the sense that the(More)
In this paper, we study watermarking methods to prove the ownership of an ontology. Different from existing approaches, we propose to watermark not by altering existing statements, but by removing them. Thereby, our approach does not introduce false statements into the ontology. We show how ownership of ontologies can be established with provably tight(More)