Distributed Adaptive Networks: A Graphical Evolutionary Game-Theoretic View

Distributed adaptive filtering has been considered as an effective approach for data processing and estimation over distributed networks. Most existing distributed adaptive filtering algorithms focus on designing different information diffusion rules, regardless of the nature evolutionary characteristic of a distributed network. In this paper, we study the adaptive network from the game theoretic perspective and formulate the distributed adaptive filtering problem as a graphical evolutionary game. With the proposed formulation, the nodes in the network are regarded as players and the local combiner of estimation information from different neighbors is regarded as different strategies selection. We show that this graphical evolutionary game framework is very general and can unify the existing adaptive network algorithms. Based on this framework, as examples, we further propose two error-aware adaptive filtering algorithms. Moreover, we use graphical evolutionary game theory to analyze the information diffusion process over the adaptive networks and evolutionarily stable strategy of the system. Finally, simulation results are shown to verify the effectiveness of our analysis and proposed methods.Comment: Accepted by IEEE Transactions on Signal Processin

Adaptive Optical Phase Estimation Using Time-Symmetric Quantum Smoothing

Quantum parameter estimation has many applications, from gravitational wave detection to quantum key distribution. We present the first experimental demonstration of the time-symmetric technique of quantum smoothing. We consider both adaptive and non-adaptive quantum smoothing, and show that both are better than their well-known time-asymmetric counterparts (quantum filtering). For the problem of estimating a stochastically varying phase shift on a coherent beam, our theory predicts that adaptive quantum smoothing (the best scheme) gives an estimate with a mean-square error up to $2\sqrt{2}$ times smaller than that from non-adaptive quantum filtering (the standard quantum limit). The experimentally measured improvement is $2.24 \pm 0.14$

Spectral filtering for the reduction of the Gibbs phenomenon of polynomial approximation methods on Lissajous curves with applications in MPI

Polynomial interpolation and approximation methods on sampling points along Lissajous curves using Chebyshev series is an effective way for a fast image reconstruction in Magnetic Particle Imaging. Due to the nature of spectral methods, a Gibbs phenomenon occurs in the reconstructed image if the underlying function has discontinuities. A possible solution for this problem are spectral filtering methods acting on the coefficients of the approximating polynomial. In this work, after a description of the Gibbs phenomenon and classical filtering techniques in one and several dimensions, we present an adaptive spectral filtering process for the resolution of this phenomenon and for an improved approximation of the underlying function or image. In this adaptive filtering technique, the spectral filter depends on the distance of a spatial point to the nearest discontinuity. We show the effectiveness of this filtering approach in theory, in numerical simulations as well as in the application in Magnetic Particle Imaging

Spectral filtering for the resolution of the Gibbs phenomenon in MPI applications

open3Polynomial interpolation on the node points of Lissajous curves using Chebyshev series is an e effective way for a fast image reconstruction in Magnetic Particle Imaging. Due to the nature of spectral methods, a Gibbs phenomenon occurs in the reconstructed image if the underlying function has discontinuities. A possible solution for this problem are spectral filtering methods acting on the coefficients of the interpolating polynomial. In this work, after a description of the Gibbs phenomenon in two dimensions, we present an adaptive spectral filtering process for the resolution of this phenomenon and for an improved approximation of the underlying function or image. In this adaptive filtering technique, the spectral filter depends on the distance of a spatial point to the nearest discontinuity. We show the effectiveness of this filtering approach in theory, in numerical simulations as well as in the application in Magnetic Particle Imaging.openDe Marchi, Stefano; Erb, Wolfgang; Marchetti, Francesco.DE MARCHI, Stefano; Erb, Wolfgang; Marchetti, Francesc

A kepstrum approach to filtering, smoothing and prediction

The kepstrum (or complex cepstrum) method is revisited and applied to the problem of spectral factorization where the spectrum is directly estimated from observations. The solution to this problem in turn leads to a new approach to optimal filtering, smoothing and prediction using the Wiener theory. Unlike previous approaches to adaptive and self-tuning filtering, the technique, when implemented, does not require a priori information on the type or order of the signal generating model. And unlike other approaches - with the exception of spectral subtraction - no state-space or polynomial model is necessary. In this first paper results are restricted to stationary signal and additive white noise

Effects of Multirate Systems on the Statistical Properties of Random Signals

In multirate digital signal processing, we often encounter time-varying linear systems such as decimators, interpolators, and modulators. In many applications, these building blocks are interconnected with linear filters to form more complicated systems. It is often necessary to understand the way in which the statistical behavior of a signal changes as it passes through such systems. While some issues in this context have an obvious answer, the analysis becomes more involved with complicated interconnections. For example, consider this question: if we pass a cyclostationary signal with period K through a fractional sampling rate-changing device (implemented with an interpolator, a nonideal low-pass filter and a decimator), what can we say about the statistical properties of the output? How does the behavior change if the filter is replaced by an ideal low-pass filter? In this paper, we answer questions of this nature. As an application, we consider a new adaptive filtering structure, which is well suited for the identification of band-limited channels. This structure exploits the band-limited nature of the channel, and embeds the adaptive filter into a multirate system. The advantages are that the adaptive filter has a smaller length, and the adaptation as well as the filtering are performed at a lower rate. Using the theory developed in this paper, we show that a matrix adaptive filter (dimension determined by the decimator and interpolator) gives better performance in terms of lower error energy at convergence than a traditional adaptive filter. Even though matrix adaptive filters are, in general, computationally more expensive, they offer a performance bound that can be used as a yardstick to judge more practical "scalar multirate adaptation" schemes

Adaptive spectral identification techniques in presence of undetected non linearities

The standard procedure for detection of gravitational wave coalescing binaries signals is based on Wiener filtering with an appropriate bank of template filters. This is the optimal procedure in the hypothesis of addictive Gaussian and stationary noise. We study the possibility of improving the detection efficiency with a class of adaptive spectral identification techniques, analyzing their effect in presence of non stationarities and undetected non linearities in the noiseComment: 4 pages, 2 figures, uses ws-procs9x6.cls Proceedings of "Non linear physics: theory and experiment. II", Gallipoli (Lecce), 200