相关论文: Structural Sparsity in Multiple Measurements

In this paper, we investigate jointly sparse signal recovery and jointly sparse support recovery in Multiple Measurement Vector (MMV) models for complex signals, which arise in many applications in communications and signal processing.…

One of the most prominent methods for uncertainty quantification in high-dimen-sional statistics is the desparsified LASSO that relies on unconstrained $\ell_1$-minimization. The majority of initial works focused on real (sub-)Gaussian…

The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an…

Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…

Corrupted data sets containing noisy or missing observations are prevalent in various contemporary applications such as economics, finance and bioinformatics. Despite the recent methodological and algorithmic advances in high-dimensional…

This article extends the concept of compressed sensing to signals that are not sparse in an orthonormal basis but rather in a redundant dictionary. It is shown that a matrix, which is a composition of a random matrix of certain type and a…

In a multiple measurement vector problem (MMV), where multiple signals share a common sparse support and are sampled by a common sensing matrix, we can expect joint sparsity to enable a further reduction in the number of required…

In this paper, we propose a general collaborative sparse representation framework for multi-sensor classification, which takes into account the correlations as well as complementary information between heterogeneous sensors simultaneously…

Multiple measurement vector (MMV) problem addresses the recovery of a set of sparse signal vectors that share common non-zero support, and has emerged an important topics in compressed sensing. Even though the fundamental performance limit…

The task of compressed sensing is to recover a sparse vector from a small number of linear and non-adaptive measurements, and the problem of finding a suitable measurement matrix is very important in this field. While most recent works…

Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control…

Compressive sensing is a signal acquisition framework based on the revelation that a small collection of linear projections of a sparse signal contains enough information for stable recovery. In this paper we introduce a new theory for…

Sparse coding aims to model data vectors as sparse linear combinations of basis elements, but a majority of related studies are restricted to continuous data without spatial or temporal structure. A new model-based sparse coding (MSC)…

In oversampled adaptive sensing (OAS), noisy measurements are collected in multiple subframes. The sensing basis in each subframe is adapted according to some posterior information exploited from previous measurements. The framework is…

We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon,…

Motivated by the minimax concave penalty based variable selection in high-dimensional linear regression, we introduce a simple scheme to construct structured semiconvex sparsity promoting functions from convex sparsity promoting functions…

Compressed sensing (CS) is an emerging field that has attracted considerable research interest over the past few years. Previous review articles in CS limit their scope to standard discrete-to-discrete measurement architectures using…

Optimal sensor placement is a central challenge in the design, prediction, estimation, and control of high-dimensional systems. High-dimensional states can often leverage a latent low-dimensional representation, and this inherent…

We study the performance of sparse regression methods and propose new techniques to distill the governing equations of dynamical systems from data. We first look at the generic methodology of learning interpretable equation forms from data,…

Compressive Learning is an emerging topic that combines signal acquisition via compressive sensing and machine learning to perform inference tasks directly on a small number of measurements. Many data modalities naturally have a…