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It is well known that empirical mode decomposition can suffer from computational instabilities at the signal boundaries. These ``end effects'' cause two problems: 1) sifting termination issues, i.e.~convergence and 2) estimation error, i.e.~accuracy. In this paper, we propose to use linear prediction in conjunction with a previous method to address end effects, to further mitigate these problems.


Without relative motion or beam scanning, orbitalangular-momentum (OAM)-based radar is shown to be able to estimate azimuth of targets, which opens a new perspective for traditional radar techniques. However, the existing application of two-dimensional (2-D) fast Fourier transform (FFT) and multiple signal classification (MUSIC) algorithms in OAM-based radar targets detection doesn’t realize 2-D super-resolution and robust estimation.


Graph convolutional networks adapt the architecture of convolutional neural networks to learn rich representations of data supported on arbitrary graphs by replacing the convolution operations of convolutional neural networks with graph-dependent linear operations. However, these graph-dependent linear operations are developed for scalar functions supported on undirected graphs. We propose both a generalization of the underlying graph and a class of linear operations for stochastic (time-varying) processes on directed (or undirected) graphs to be used in graph convolutional networks.


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Inductive matrix completion (IMC) is a model for incorporating side information in form of “features” of the row and column entities of an unknown matrix in the matrix completion problem. As side information, features can substantially reduce the number of observed entries required for reconstructing an unknown matrix from its given entries. The IMC problem can be formulated as a low-rank matrix recovery problem where the observed entries are seen as measurements of a smaller matrix that models the interaction between the column and row features.


We extend the classical joint problem of signal demixing, blind deconvolution,
and filter identification to the realm of graphs. The model is that
each mixing signal is generated by a sparse input diffused via a graph filter.
Then, the sum of diffused signals is observed. We identify and address
two problems: 1) each sparse input is diffused in a different graph; and 2)
all signals are diffused in the same graph. These tasks amount to finding
the collections of sources and filter coefficients producing the observation.


Henze-Penrose divergence is a non-parametric divergence measure that can be used to estimate a bound on the Bayes error in a binary classification problem. In this paper, we show that a cross- match statistic based on optimal weighted matching can be used to directly estimate Henze-Penrose divergence. Unlike an earlier approach based on the Friedman-Rafsky minimal spanning tree statistic, the proposed method is dimension-independent. The new approach is evaluated using simulation and applied to real datasets to obtain Bayes error estimates.