_{c}, Donoho [2] shows that exact recovery is possible if Δ > l/f

_{c}, but does not...

A parallel algorithm for low-rank tensor decomposition that is especially well-suited for big tensors is proposed. The new algorithm is based on parallel processing of a set of randomly compressed, reduced-size ‘replicas’ of the big tensor. Each replica is independently decomposed, and the results are joined via a master linear equation per tensor mode. The approach enables massive parallelism with...

Independent component analysis (ICA) is a widely used technique for extracting latent (unobserved) source signals from observed multidimensional measurements. In this paper we construct a fast and robust bootstrap (FRB) method for testing hypotheses on elements of the mixing matrix in the ICA model. The FRB method can be devised for estimators which are solutions to fixed-point (FP) equations. In...

Persistent homology has become one of the most popular tools used in topological data analysis for analyzing big data sets. In an effort to minimize the computational complexity of finding the persistent homology of a data set, we develop a simplicial collapse algorithm called the selective collapse. This algorithm works by representing the previously developed strong collapse as a forest and uses...

Applications involving large-scale dictionary learning tasks motivate well online optimization algorithms for generally non-convex and non-smooth problems. In this big data context, the present paper develops an online learning framework by jointly leveraging the stochastic approximation paradigm with first-order acceleration schemes. The generally non-convex objective evaluated online at the resultant...

Choosing a distance preserving measure or metric is fundamental to many signal processing algorithms, such as k-means, nearest neighbor searches, hashing, and compressive sensing. In virtually all these applications, the efficiency of the signal processing algorithm depends on how fast we can evaluate the learned metric. Moreover, storing the chosen metric can create space bottlenecks in high dimensional...

Canonical Polyadic Decomposition (CPD), also known as PARAFAC, is a useful tool for tensor factorization. It has found application in several domains including signal processing and data mining. With the deluge of data faced in our societies, large-scale matrix and tensor factorizations become a crucial issue. Few works have been devoted to large-scale tensor factorizations. In this paper, we introduce...

In this paper we consider a diffusion field induced by multiple point sources and address the problem of reconstructing the field from its spatio-temporal samples obtained using a sensor network. We begin by formulating the problem as a multi-source estimation problem — so estimating source locations, activation times and intensities given samples of the induced field. Next a two-step algorithm is...

While spike trains are obviously not band-limited, the theory of super-resolution tells us that perfect recovery of unknown spike locations and weights from low-pass Fourier transform measurements is possible provided that the minimum spacing, Δ, between spikes is not too small. Specifically, for a cutoff frequency of f_{c}, Donoho [2] shows that exact recovery is possible if Δ > l/f_{c}, but does not...

We introduce a new cyclic spectrum estimation method for wide-sense cyclostationary (WSCS) signals sampled at sub-Nyquist rate using non-uniform sampling. We exploit the block Toeplitz structure of the WSCS signal correlation matrix and write the linear relationship between this matrix and the correlations of the sub-Nyquist rate samples as an overdetermined system. We find the condition under which...

This paper considers the problem of signal recovery from magnitude measurements for signals in modulation invariant spaces. It proposes a measurement setup such that almost every signal in such a signal space can be reconstructed from its amplitude measurements up to a global constant phase and with a sampling rate of four times the rate of innovation of the signal space. The applicability of the...

Recently, classical sampling theory has been broadened to include a class of non-bandlimited signals that possess finite rate of innovation (FRI). In this paper we consider the reconstruction of a periodic stream of Diracs from noisy samples. We demonstrate that its noiseless FRI samples can be represented as a ratio of two polynomials. Using this structure as a model, we propose recovering the FRI...

The approximation of linear time-invariant (LTI) systems by sampling series is an important topic in signal processing. However, the convergence of the approximation process is not guaranteed. In this paper we prove that for every sampling pattern that is a complete interpolating sequence there exists a universal stable LTI system such that for every oversampling factor there exists a bandlimited...

In this work we propose an adaptive receiver with enhanced range estimation capabilities, which jointly exploits the over-sampling of the noisy returns and the spillover of target energy to adjacent range samples. To this end, a proper discrete-time model for the received signal is introduced. Then, the Generalized Likelihood Ratio Test (GLRT) is derived and assessed. The performance analysis highlights...

In the context of an heterogeneous disturbance with a Low Rank (LR) structure (called clutter), one may use the LR approximation for filtering and detection process. These methods are based on the projector onto the clutter subspace instead of the noise covariance matrix. In such context, adaptive LR schemes have been shown to require less secondary data to reach equivalent performances as classical...

In this paper, we study the joint design of Doppler robust transmit sequence and receive filter to improve the performance of an active sensing system dealing with signal-dependent interference. The signal-to-interference-plus-noise ratio (SINR) of the filter output is considered as the performance measure of the system. The design problem is cast as a max-min optimization problem to robustify the...

This paper concerns the use of wideband RF backscatter from semi-passive RF tags for energy-efficient wireless telemetry. Using LFM (Linear Frequency Modulated) signals from a radar basestation, we present a method for joint ranging and communications with a distributed set of sensor nodes. Backscatter signaling from each node results in modulation on a sub-carrier frequency determined by the node...

Compressed Sensing is a new signal processing methodology that allows to reconstruct sparse signals using a relatively small number of samples in the form of random projections. These samples are collected at a much lower rate than Nyquist rate. This paper focuses on the application of Compressed Sensing in Cognitive Radar systems that use wide operating frequency bandwidths for spectrum sensing and...

The statistical angular resolution limit (RL) of two closely-spaced point sources in array processing is analyzed based on the framework of hypothesis test. For the first time, the general case where neither the source signals nor the parameters of interest are known under both the null hypothesis and the alternative is considered. Using the theory of misspecified model, the asymptotic distribution...

In this paper, we investigate the variational Bayes based I-vector method for speaker diarization of telephone conversations. The motivation of the proposed algorithm is to utilize variational Bayesian framework and exploit potential channel effect of total variability modeling for diarization of conversation side. Other three well-known techniques are compared as follows: K-means clustering for eigenvoices...