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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 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 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 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)
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