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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)

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)

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)

* 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)

This paper presents a walermarking/fingerprinting system for relational databases. It features a built-in declarative language to specify usability constraints that watermarked data sets must comply with. For a subset of these constraints, namely, weight-independent constraints, we propose a novel watermarking strategy that consists of translating them into… (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)

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)

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)

Relational databases watermarking aims at protecting the intellectual or industrial property of a dataset, by applying secret and slight alterations on it. When critical usability constraints of this dataset must be preserved, finding such alterations (watermarks) is a difficult computational task, which is not optimized by the current watermarking systems.… (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)