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The theory of compressed sensing suggests that successful inversion of an image of the physical world (broadly defined to include speech signals, radar/sonar returns, vibration records, sensor array snapshot vectors, 2-D images, and so on) for its source modes and amplitudes can be achieved at measurement dimensions far lower than what might be expected… (More)

— This paper addresses canonical correlation analysis of two-channel data, when channel covariances are estimated from a limited number of samples, and are not necessarily full-rank. We show that empirical canonical correlations measure the cosines of the principal angles between the row spaces of the data matrices for the two channels. When the number of… (More)

— Detecting a sparse signal in noise is fundamentally different from reconstructing a sparse signal, as the objective is to optimize a detection performance criterion rather than to find the sparsest signal that satisfies a linear observation equation. In this paper, we consider the design of low-dimensional (compressive) measurement matrices for detecting… (More)

We consider estimating a random vector from its measurements in a fusion frame, in presence of noise and subspace erasures. A fusion frame is a collection of subspaces, for which the sum of the projection operators onto the subspaces is bounded below and above by constant multiples of the identity operator. We first consider the linear minimum mean-squared… (More)

We derive eigenvalue beamformers to resolve an unknown signal of interest whose spatial signature lies in a known subspace, but whose orientation in that subspace is otherwise unknown. The unknown orientation may be fixed, in which case the signal covariance is rank-1, or it may be random, in which case the signal covariance is multirank. We present a… (More)

The problem of two-channel constrained least squares (CLS) filtering under various sets of constraints is considered, and a general set of solutions is derived. For each set of constraints, the solution is determined by a coupled (asymmetric) generalized eigenvalue problem. This eigenvalue problem establishes a connection between two-channel CLS filtering… (More)

In this correspondence, our aim is to establish a connection between low-rank detection, low-rank estimation, and canonical coordinates. The key to this connection is the observation that Gauss-Gauss detectors and estimators share canonical coordinates in the case where the underlying model is a signal-plus-noise model. We show that in Gauss-Gauss detection… (More)

Available online xxxx Keywords: Compressive measurement design Grassmannian line packing Hypothesis testing Lexicographic optimization Sparse signal detection Uniform tight frame Worst-case coherence a b s t r a c t We consider the problem of testing for the presence (or detection) of an unknown sparse signal in additive white noise. Given a fixed… (More)

— We derive multi-rank generalizations of the MVDR beamformer to separate an unknown signal of interest in the presence of interference and noise. The spatial signature of the signal is assumed to lie in a known linear subspace, but the orientation of the signal in that subspace is otherwise unknown. The unknown orientation may be fixed for a sequence of… (More)

—We present a general method for constructing radar transmit pulse trains and receive filters for which the radar point-spread function in delay and Doppler, given by the cross-ambiguity function of the transmit pulse train and the pulse train used in the receive filter, is essentially free of range sidelobes inside a Doppler interval around the… (More)