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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)

Watermarking allows robust and unobtrusive insertion of information in a digital document. During the last few years, techniques have been proposed for watermarking relational databases or Xml documents, where information insertion must preserve a specific measure on data (for example the mean and variance of numerical attributes).
In this article we… (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)

Compressed sensing is the art of reconstructing a sparse vector from its inner products with respect to a small set of randomly chosen measurement vectors. It is usually assumed that the ensemble of measurement vectors is in isotropic position in the sense that the associated covariance matrix is proportional to the identity matrix. In this paper, we… (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)

Received (received date) Revised (revised date) We present a simple way to quantize the well-known Margulis expander map. The result is a quantum expander which acts on discrete Wigner functions in the same way the classical Margulis expander acts on probability distributions. The quantum version shares all essential properties of the classical counterpart,… (More)

Xml streams are valuable, continuous, high-throughput sources of information whose owners must be protected against illegal redistributions. Watermarking is a known technique for hiding copyrights marks within documents, thus preventing redistributions. Here, we introduce a watermarking algorithm for Xml streams so that (i) the watermark embedding and… (More)