This paper discusses predictive densities under the Kullback–Leibler loss for high-dimensional Poisson sequence models sparsity constraints. Sparsity in count data implies zero-inflation. We present a class of Bayes that attain asymptotic minimaxity sparse models. also show our with an estimator unknown level plugged-in is adaptive asymptotically minimax sense. For application, we extend result...

Minimization problems in l for Tikhonov functionals with sparsity constraints are considered. Sparsity of the solution is ensured by a weighted l penalty term. The necessary and sufficient condition for optimality is shown to be slantly differentiable (Newton differentiable), hence a semismooth Newton method is applicable. Local superlinear convergence of this method is proved. Numerical exampl...

This paper addresses the discretisation problem for sparse linear systems. Classical methods usually destroy sparsity patterns of continuous-time systems. We develop an optimisation procedure that yields the best approximation to the discrete-time dynamical matrix with a prescribed sparsity pattern and subject to stability and other constraints. By formulating this problem in an adequate manner...

Recent years have seen an increasing interest in sparseness constraints for image classification and object recognition, probably motivated by the evidence of sparse representations internal in the primate visual cortex. It is still unclear, however, whether or not sparsity helps classification. In this paper we analyze the image classification task on CIFAR-10, a very challenging dataset, and ...

Abstract: Hyperspectral unmixing aims to estimate a set of endmembers and corresponding abundances in pixels. Nonnegative matrix factorization (NMF) and its extensions with various constraints have been widely applied to hyperspectral unmixing. L1/2 and L2 regularizers can be added to NMF to enforce sparseness and evenness, respectively. In practice, a region in a hyperspectral image may posses...

Bilinear inverse problems (BIPs), the resolution of two vectors given their image under a bilinear mapping, arise in many applications. Without further constraints, BIPs are usually ill-posed. In practice, properties of natural signals are exploited to solve BIPs. For example, subspace constraints or sparsity constraints are imposed to reduce the search space. These approaches have shown some s...

Diffuse optical tomography is a novel molecular imaging technology for small animal studies. Most known reconstruction methods use the diffusion equation (DA) as forward model, although the validation of DA breaks down in certain situations. In this work, we use the radiative transfer equation as forward model which provides an accurate description of the light propagation within biological med...

Sparse representation methods have been shown to tackle adequately the inherent speed limits of magnetic resonance imaging (MRI) acquisition. Recently, learning-based techniques have been used to further accelerate the acquisition of 2D MRI. The extension of such algorithms to dynamic MRI (dMRI) requires careful examination of the signal sparsity distribution among the different dimensions of t...

A novel sparsity optimization method is proposed to select features for multi-class classification problems by directly optimizing a l2,p -norm ( 0 < p ≤ 1 ) based sparsity function subject to data-fitting inequality constraints to obtain large between-class margins. The direct sparse optimization method circumvents the empirical tuning of regularization parameters in existing feature selection...