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Sparse solutions to linear inverse problems with multiple measurement vectors

This work considers in depth the extension of two classes of algorithms-Matching Pursuit and FOCal Underdetermined System Solver-to the multiple measurement case so that they may be used in applications such as neuromagnetic imaging, where multiple measurement vectors are available, and solutions with a common sparsity structure must be computed.
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An affine scaling methodology for best basis selection

A methodology is developed to derive algorithms for optimal basis selection by minimizing diversity measures proposed by Wickerhauser (1994) and Donoho (1994). These measures include the p-norm-like…
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Dictionary Learning Algorithms for Sparse Representation

Algorithms for data-driven learning of domain-specific overcomplete dictionaries are developed to obtain maximum likelihood and maximum a posteriori dictionary estimates based on the use of Bayesian models with concave/Schur-concave negative log priors, showing improved performance over other independent component analysis methods.
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ICLabel: An automated electroencephalographic independent component classifier, dataset, and website

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Subset selection in noise based on diversity measure minimization

A Bayesian framework is used to account for noise in the data and a maximum a posteriori (MAP) estimation procedure leads to an iterative procedure which is a regularized version of the focal underdetermined system solver (FOCUSS) algorithm that is superior to the OMP in noisy environments.
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The Complex Gradient Operator and the CR-Calculus ECE275A - Lecture Supplement - Fall 2005

A thorough discussion and development of the calculus of real-valued functions of complex-valued vectors is given using the framework of the Wirtinger Calculus, filling a gap in the pedagogic literature.
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Machine Learning Methods for Predicting Failures in Hard Drives: A Multiple-Instance Application

A new algorithm based on the multiple-instance learning framework and the naive Bayesian classifier (mi-NB) is developed which is specifically designed for the low false-alarm case, and is shown to have promising performance.
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The attitude control problem

A general framework for the analysis of the attitude tracking control problem for a rigid body is presented. A large family of globally stable control laws is obtained by using the globally…
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AMICA : An Adaptive Mixture of Independent Component Analyzers with Shared Components

An asymptotic Newton algorithm is derived for Quasi Maximum Likelihood estimation of the ICA mixture model, using the ordinary gradient and Hessian, and it is proved asymPTotic stability when the source models match the true sources.

Variational EM Algorithms for Non-Gaussian Latent Variable Models

A general equivalence is established among convex bounding methods, evidence based methods, and ensemble learning/Variational Bayes methods, which has previously been demonstrated only for particular cases.
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