Luis Mancera

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In recent years, Bayes least squares-Gaussian scale mixtures (BLS-GSM) has emerged as one of the most powerful methods for image restoration. Its strength relies on providing a simple and, yet, very effective local statistical description of oriented pyramid coefficient neighborhoods via a GSM vector. This can be viewed as a fine adaptation of the model to(More)
We present a simple and robust method for finding sparse representations in overcomplete transforms, based on minimization of the L0-norm. Our method is better than current solutions based on minimization of the L1-norm in terms of energy compaction. These results strongly question the equivalence of minimizing both norms in real conditions. We also show(More)
We propose two methods for sparse approximation of images under 2 error metric. First one performs an approximation error minimization given a p-norm of the representation through alternated orthogonal projections onto two sets. We study the cases p = 0 (sub-optimal) and p = 1 (optimal), and find that the 0-AP method is neatly superior, for typical images(More)
We propose a new formulation to the sparse approximation problem for the case of tight frames which allows to minimize the cost function using gradient descent. We obtain a generalized version of the iterative hard thresholding (IHT) algorithm, which provides locally optimal solutions. In addition, to avoid non-favorable minima we use an annealing technique(More)
In this paper, we propose a novel algorithm for image reconstruction from compressive measurements of wavelet coefficients. By incorporating independent Laplace priors on separate wavelet sub-bands, the inhomogeneity of wavelet coefficient distributions and therefore the structural sparsity within images are modeled effectively. We model the problem by(More)
We present a new image restoration method based on modelling the coefficients of an overcomplete wavelet response to natural images with a mixture of two Gaussian distributions, having non-zero and zero mean respectively, and reflecting the assumption that this response is close to be sparse. Including the observation model, the resulting procedure iterates(More)
We describe a method for removing quantization artifacts (de-quantizing) in the image domain, by enforcing a high degree of sparse-ness in its representation with an overcomplete oriented pyramid. For this purpose we devise a linear operator that returns the minimum L2-norm image preserving a set of significant coefficients, and estimate the original by(More)
Motivated by a recent detailed experimental study [Y. Ma et al., Phys. Chem. Chem. Phys., 2011, 13, 10741], the structure and local reactivity of PdAg/Pd(111) surface alloys were studied using periodic density functional theory calculations. As a probe of the local reactivity, CO adsorption energies were evaluated as a function of concentration and(More)
We propose a novel Bayesian formulation for the reconstruction from compressed measurements. We demonstrate that high-sparsity enforcing priors based on l p-norms, with 0 < p ≤ 1, can be used within a Bayesian framework by majorization-minimization methods. By employing a fully Bayesian analysis of the compressed sensing system and a variational Bayesian(More)
We present a theoretical framework for the computation of anharmonic vibrational frequencies for large systems, with a particular focus on determining adsorbate frequencies from first principles. We give a detailed account of our local implementation of the vibrational self-consistent field approach and its correlation corrections. We show that our approach(More)
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