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—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)

We consider the problem of testing for the presence (or detection) of an unknown sparse signal in additive white noise. Given a fixed measurement budget, much smaller than the dimension of the signal, we consider the general problem of designing compressive measurements to maximize the measurement signal-to-noise ratio (SNR), as increasing SNR improves the… (More)

—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)

Over the last decade, considerable progress has been made towards developing new signal processing methods to manage the deluge of data caused by advances in sensing, imaging, storage, and computing technologies. Most of these methods are based on a simple but fundamental observation. That is, high-dimensional data sets are typically highly redundant and… (More)

—We describe a method of constructing a sequence (pulse train) of phase-coded waveforms, for which the ambiguity function is free of range sidelobes along modest Doppler shifts. The constituent waveforms are Golay complementary waveforms which have ideal ambiguity along the zero Doppler axis but are sensitive to nonzero Doppler shifts. We extend this… (More)

We study the detection error probability associated with a balanced binary relay tree, where the leaves of the tree correspond to N identical and independent sensors. The root of the tree represents a fusion center that makes the overall detection decision. Each of the other nodes in the tree are relay nodes that combine two binary messages to form a single… (More)

Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame can be regarded as a frame-like collection of subspaces in a Hilbert Communicated by Qiyu Sun. for sponsoring the workshop on " Frames for the finite world: Sampling, coding and quantization " in August 2008,… (More)

—In [1]–[4], we considered the question of basis mis-match in compressive sensing. Our motivation was to study the effect of mismatch between the mathematical basis (or frame) in which a signal was assumed to be sparse and the physical basis in which the signal was actually sparse. We were motivated by the problem of inverting a complex space-time radar… (More)

In this paper, we analyze the impact of compressed sensing with random matrices on Fisher information and the CRB for estimating unknown parameters in the mean value function of a multivariate normal distribution. We consider the class of random compression matrices that satisfy a version of the Johnson-Lindenstrauss lemma, and we derive analytical lower… (More)