In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Q: In many applications spanning from sensor to social networks, transportation systems, gene regulatory networks or big data, the signals of interest are defined over the vertices of a graph. The aim of this paper is to propose a least mean square (LMS) strategy for adaptive estimation of signals defined over graphs. Assuming the graph signal to be band-limited, over a known bandwidth, the method enables reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of observations over a subset of vertices. A detailed mean square analysis provides the performance of the proposed method, and leads to several insights for designing useful sampling strategies for graph signals. Numerical results validate our theoretical findings, and illustrate the performance of the proposed method. Furthermore, to cope with the case where the bandwidth is not known beforehand, we propose a method that performs a sparse online estimation of the signal support in the (graph) frequency domain, which enables online adaptation of the graph sampling strategy. Finally, we apply the proposed method to build the power spatial density cartography of a given operational region in a cognitive network environment.

A: Least Mean Squares Estimation of Graph Signals
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Q: Distortion of the underlying speech is a common problem for single-channel speech enhancement algorithms, and hinders such methods from being used more extensively. A dictionary based speech enhancement method that emphasizes preserving the underlying speech is proposed. Spectral patches of clean speech are sampled and clustered to train a dictionary. Given a noisy speech spectral patch, the best matching dictionary entry is selected and used to estimate the noise power at each time-frequency bin. The noise estimation step is formulated as an outlier detection problem, where the noise at each bin is assumed present only if it is an outlier to the corresponding bin of the best matching dictionary entry. This framework assigns higher priority in removing spectral elements that strongly deviate from a typical spoken unit stored in the trained dictionary. Even without the aid of a separate noise model, this method can achieve significant noise reduction for various non-stationary noises, while effectively preserving the underlying speech in more challenging noisy environments.

A: SINGLE CHANNEL SPEECH ENHANCEMENT USING OUTLIER DETECTION
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Q: The Frank-Wolfe method (a.k.a. conditional gradient algorithm) for smooth optimization has regained much interest in recent years in the context of large scale optimization and machine learning. A key advantage of the method is that it avoids projections the computational bottleneck in many applications replacing it by a linear optimization step. Despite this advantage, the known convergence rates of the FW method fall behind standard first order methods for most settings of interest. It is an active line of research to derive faster linear optimization-based algorithms for various settings of convex optimization. In this paper we consider the special case of optimization over strongly convex sets, for which we prove that the vanila FW method converges at a rate of 1 t2 . This gives a quadratic improvement in convergence rate compared to the general case, in which convergence is of the order 1t , and known to be tight. We show that various balls induced by `p norms, Schatten norms and group norms are strongly convex on one hand and on the other hand, linear optimization over these sets is straightforward and admits a closed-form solution. We further show how several previous fastrate results for the FW method follow easily from our analysis.

A:
Faster Rates for the Frank-Wolfe Method over Strongly-Convex Sets
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