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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… (More)

The problem of recovering a structured signal x ∈ C p from a set of dimensionality-reduced linear measurements b = Ax arises in a variety of applications, such as medical imaging, spectroscopy, Fourier optics, and computerized tomography. Due to computational and storage complexity or physical constraints imposed by the problem, the measurement matrix A ∈ C… (More)

—We consider the minimum variance distor-tionless response (MVDR) beamforming problems where the array covariance matrix is rank deficient. The conventional approach handles such rank-deficiencies via diagonal loading on the covariance matrix. In this setting, we show that the array weights for optimal signal estimation can admit a sparse representation on… (More)

Effectively solving many inverse problems in engineering requires to leverage all possible prior information about the structure of the signal to be estimated. This often leads to tackling constrained optimization problems with mixtures of regularizers. Providing a general purpose optimization algorithm for these cases, with both guaranteed convergence rate… (More)

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