Side information provides a pivotal role for message delivery in many communication scenarios to accommodate increasingly large data sets, e.g., caching networks. Although index coding provides a fundamental modeling framework to exploit the benefits of side information, the index coding problem itself still remains open and only a few instances have been solved. In this paper, we propose a nov...

We examine nonstationary signals within the framework of compressive sensing and sparse reconstruction. Most of these signals, which arise in numerous applications, exhibit small relative occupancy in the time-frequency domain, casting them as sparse in a joint-variable representation. We present two general approaches to incorporate sparsity into time-frequency analysis, leading to what we ref...

This paper surveys the significance of sparsity for the Support Vector Machine (SVM) method. The SVM method is a machine learning technique with a wide range of applications, e.g. medical diagnosis, pattern recognition, and clustering. The method is fairly recent; Vapnik is credited with originating it in 1979. We present a general introduction to SVMs in the context of data classification and ...

This article explores the homogeneity of coefficients in high-dimensional regression, which extends the sparsity concept and is more general and suitable for many applications. Homogeneity arises when regression coefficients corresponding to neighboring geographical regions or a similar cluster of covariates are expected to be approximately the same. Sparsity corresponds to a special case of ho...

Sparsity-based models have proven to be very effective in most image processing applications. The notion of sparsity has recently been extended to structured sparsity models where not only the number of components but also their support is important. This paper goes one step further and proposes a new model where signals are composed of a small number of molecules, which are each linear combina...

The wavelet coefficients of a 2D natural image are not only approximately sparse with a large number of coefficients tend to be zeros, but also yield a quadtree structure. According to structured sparsity theory, the required measurement bounds for compressive sensing reconstruction can be reduced to O(K+log(N/K)) by exploiting the tree structure rather than O(K+Klog(N/K)) for standard K-sparse...

We consider the problem of learning a distance metric from a limited amount of pairwise information as effectively as possible. The proposed SERAPH (SEmi-supervised metRic leArning Paradigm with Hyper sparsity) is a direct and substantially more natural approach for semi-supervised metric learning, since the supervised and unsupervised parts are based on a unified information theoretic framewor...

We develop an algorithm for reconstructing magnetic resonance images (MRI) from highly undersampled k-space data. While existing methods focus on either image-level or patch-level sparse regularization strategies, we present a regularization framework that uses both image and patch-level sparsity constraints. The proposed regularization enforces image-level sparsity in terms of spatial finite d...

Seismic data comprise many traces that provide a spatiotemporal sampling of the reflected wavefield. However, such informationmay suffer from ambient and random noise during acquisition, which could possibly limit the use of seismic data in reservoir locating. Traditionally, fixed transforms are used to separate the noise from the data by exploiting their different characteristics in a transfor...