Privacy-Preserving Distributed Optimization via Subspace Perturbation: A General Framework

As the modern world becomes increasingly digitized and interconnected, distributed signal processing has proven to be effective in processing its large volume of data. However, a main challenge limiting the broad use of distributed signal processing techniques is the issue of privacy in handling sensitive data. To address this privacy issue, we propose a novel yet general subspace perturbation method for privacy-preserving distributed optimization, which allows each node to obtain the desired solution while protecting its private data. In particular, we show that the dual variables introduced in each distributed optimizer will not converge in a certain subspace determined by the graph topology. Additionally, the optimization variable is ensured to converge to the desired solution, because it is orthogonal to this non-convergent subspace. We therefore propose to insert noise in the non-convergent subspace through the dual variable such that the private data are protected, and the accuracy of the desired solution is completely unaffected. Moreover, the proposed method is shown to be secure under two widely-used adversary models: passive and eavesdropping. Furthermore, we consider several distributed optimizers such as ADMM and PDMM to demonstrate the general applicability of the proposed method. Finally, we test the performance through a set of applications. Numerical tests indicate that the proposed method is superior to existing methods in terms of several parameters like estimated accuracy, privacy level, communication cost and convergence rate

Light emission and finite frequency shot noise in molecular junctions: from tunneling to contact

Scanning tunneling microscope induced light emission from an atomic or molecular junction has been probed from the tunneling to contact regime in recent experiments. There, the intensity of the light emission shows strong correlation with the current/charge fluctuations at optical frequencies. We show that this is consistent with the established theory in the tunneling regime, by writing the finite-frequency shot noise as a sum of inelastic transitions between different electronic states. Based on this, we develop a practical scheme to perform calculations on realistic structures using Green's functions. The photon emission yields obtained re-produce the essential feature of the experiments.Comment: published version, Phys. Rev. B 88, 045413 (2013

Multi-Channel Maximum Likelihood Pitch Estimation

In this paper, a method for multi-channel pitch estimation is proposed. The method is a maximum likelihood estimator and is based on a parametric model where the signals in the various channels share the same fundamental frequency but can have different amplitudes, phases, and noise characteris-tics. This essentially means that the model allows for differ-ent conditions in the various channels, like different signal-to-noise ratios, microphone characteristics and reverberation. Moreover, the method does not assume that a certain array structure is used but rather relies on a more general model and is hence suited for a large class of problems. Simulations with real signals shows that the method outperforms a state-of-the-art multi-channel method in terms of gross error rate. Index Terms — Pitch estimation, microphone arrays, multi-channel audi

Optimal Filter Designs for Separating and Enhancing Periodic Signals

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