Mário A. T. Figueiredo

TL;DR: 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.

TL;DR: 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.

TL;DR: 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.

TL;DR: 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.

TL;DR: 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.