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The sequential analysis of the problem of joint signal detection and signal-to-noise ratio (SNR) estimation for a linear Gaussian observation model is considered. The problem is posed as an optimization setup where the goal is to minimize the number of samples required to achieve the desired (i) type I and type II error probabilities and (ii) mean squared error performance.

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State filtering is a key problem in many signal processing applications. From a series of noisy measurement, one would like to estimate the state of some dynamic system. Existing techniques usually adopt a Gaussian noise assumption which may result in a major degradation in performance when the measurements are with the presence of outliers. A robust algorithm immune to the presence of outliers is desirable.

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One of the longstanding problems in spectral graph clustering (SGC) is the so-called model order selection problem: automated selection of the correct number of clusters. This is equivalent to the problem of finding the number of connected components or communities in an undirected graph. In this paper, we propose AMOS, an automated model order selection algorithm for SGC.

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In this work, we propose a new regularization approach for linear least-squares problems with random matrices. In
the proposed constrained perturbation regularization approach, an artificial perturbation matrix with a bounded norm is forced
into the system model matrix. This perturbation is introduced to improve the singular-value structure of the model matrix and,

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The ability to obtain accurate estimators from a set of measurements is a key factor in science and engineering. Typically, there is an inherent assumption that the measurements were taken in a sequential order, be it in space or time. However, data is increasingly irregular so this assumption of sequentially obtained measurements no longer holds. By leveraging notions of graph signal processing to account for these irregular domains, we propose an unbiased estimator for the mean of a wide sense stationary graph process based on the diffusion of a single realization.

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The recently reported Wirtinger flow (WF) algorithm has been demonstrated as a promising method for solving the problem of phase retrieval by applying a gradient descent scheme. An empirical choice of stepsize is suggested in practice. However, this heuristic stepsize selection rule is not optimal. In order to accelerate the convergence rate, we propose an improved WF with optimal stepsize. It is revealed that this optimal stepsize is the solution of a univariate cubic equation with real-valued coefficients.

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