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Unsupervised Learning of Finite Mixture Models
TLDR
The novelty of the approach is that it does not use a model selection criterion to choose one among a set of preestimated candidate models; instead, it seamlessly integrate estimation and model selection in a single algorithm.
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Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems
TLDR
This paper proposes gradient projection algorithms for the bound-constrained quadratic programming (BCQP) formulation of these problems and test variants of this approach that select the line search parameters in different ways, including techniques based on the Barzilai-Borwein method.
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Sparse Reconstruction by Separable Approximation
TLDR
This work proposes iterative methods in which each step is obtained by solving an optimization subproblem involving a quadratic term with diagonal Hessian plus the original sparsity-inducing regularizer, and proves convergence of the proposed iterative algorithm to a minimum of the objective function.
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Fast Image Recovery Using Variable Splitting and Constrained Optimization
We propose a new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective…
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Sparse multinomial logistic regression: fast algorithms and generalization bounds
TLDR
This paper introduces a true multiclass formulation based on multinomial logistic regression and derives fast exact algorithms for learning sparse multiclass classifiers that scale favorably in both the number of training samples and the feature dimensionality, making them applicable even to large data sets in high-dimensional feature spaces.
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An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems
TLDR
This paper proposes a new efficient algorithm to handle one class of constrained problems (often known as basis pursuit denoising) tailored to image recovery applications and shows that the proposed algorithm is a strong contender for the state-of-the-art.
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A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration
TLDR
This paper introduces two-step 1ST (TwIST) algorithms, exhibiting much faster convergence rate than 1ST for ill-conditioned problems, and introduces a monotonic version of TwIST (MTwIST); although the convergence proof does not apply, the effectiveness of the new methods are experimentally confirmed on problems of image deconvolution and of restoration with missing samples.
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An EM algorithm for wavelet-based image restoration
TLDR
An expectation-maximization (EM) algorithm for image restoration (deconvolution) based on a penalized likelihood formulated in the wavelet domain is introduced, and it is shown that under mild conditions the algorithm converges to a globally optimal restoration.
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Alternating direction algorithms for constrained sparse regression: Application to hyperspectral unmixing
TLDR
Two new algorithms to efficiently solve convex optimization problems, based on the alternating direction method of multipliers, a method from the augmented Lagrangian family, are introduced and are shown to outperform off-the-shelf methods in terms of speed and accuracy.
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Simultaneous feature selection and clustering using mixture models
TLDR
This paper proposes the concept of feature saliency and introduces an expectation-maximization algorithm to estimate it, in the context of mixture-based clustering, and extends the criterion and algorithm to simultaneously estimate the feature saliencies and the number of clusters.
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