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Titlebook: Coherence; In Signal Processing David Ramírez,Ignacio Santamaría,Louis Scharf Book 2022 The Editor(s) (if applicable) and The Author(s), un

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Some Nonlinear Evolution Equations,del, model order determination, and total least squares. A section on oblique projections addresses the problem of resolving a few modes in the presence of many. Sections on multidimensional scaling and the Johnson-Lindenstrauss lemma introduce two topics in ambient dimension reduction that are loos
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Spectral Properties and Regularity,principal angles and with canonical correlations. The study of factorizations of two-channel covariance matrices leads to filtering formulas for MMSE filters and their error covariances. When covariance matrices are estimated from measurements, then the filter and error covariance are random matrice
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https://doi.org/10.1007/978-1-4612-5561-1on. The probability distribution for the measurements may carry the signal in a parameterization of the mean or in a parameterization of the covariance matrix. Likelihood ratio detectors are derived, their invariances are revealed, and their null distributions are derived where tractable. The result
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Spectral Properties and Regularity,n noise covariance matrices by constructing covariance estimates from a secondary channel of signal-free measurements. Then the Kelly and Should we say ACE (adaptive coherence estimator) detectors, and their generalizations, are derived as generalized likelihood ratio detectors. These detectors use
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Spectral Properties and Regularity,n. We study second-order detectors where the unknown transmitted signal is modeled as a zero-mean Gaussian and averaged out or marginalized and first-order detectors where the unknown transmitted signal appears in the mean of the observations with no prior distribution assigned to it. The signal sub
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Spectral Properties and Regularity,ween pairs of subspaces. In this chapter, we first review the geometry of the Grassmann and Stiefel manifolds, in which .-dimensional subspaces and .-dimensional frames live, respectively. Then, we assign probability distributions to these manifolds. We pay particular attention to the problem of sub
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Alfonso Castro,Ratnasingham Shivajirnel methods, and time-frequency modeling. The concept of coherence in compressed sensing and matrix completion is made clear by the restricted isometry property and the concept of coherence index, which are discussed in the chapter. We also consider in this chapter multiview learning, in which the
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