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The sparse group lasso is a high-dimensional regression technique that is useful for problems whose predictors have a naturally grouped structure and where sparsity is encouraged at both the group and individual predictor level. In this…

Vector valued data appearing in concrete applications often possess sparse expansions with respect to a preassigned frame for each vector component individually. Additionally, different components may also exhibit common sparsity patterns.…

In a high-dimensional setting, sparse model has shown its power in computational and statistical efficiency. We consider variables selection problem with a broad class of simultaneous sparsity regularization, enforcing both feature-wise and…

This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…

We study the problem of corrupted sensing, a generalization of compressed sensing in which one aims to recover a signal from a collection of corrupted or unreliable measurements. While an arbitrary signal cannot be recovered in the face of…

Learned Sparse Retrieval (LSR) is an effective IR approach that exploits pre-trained language models for encoding text into a learned bag of words. Several efforts in the literature have shown that sparsity is key to enabling a good…

Compressive sensing has shown significant promise in biomedical fields. It reconstructs a signal from sub-Nyquist random linear measurements. Classical methods only exploit the sparsity in one domain. A lot of biomedical signals have…

Sparsity inducing regularization is an important part for learning over-complete visual representations. Despite the popularity of $\ell_1$ regularization, in this paper, we investigate the usage of non-convex regularizations in this…

In sparse optimization, enforcing hard constraints using the $\ell_0$ pseudo-norm offers advantages like controlled sparsity compared to convex relaxations. However, many real-world applications demand not only sparsity constraints but also…

Novel sparse reconstruction algorithms are proposed for beamspace channel estimation in massive multiple-input multiple-output systems. The proposed algorithms minimize a least-squares objective having a nonconvex regularizer. This…

In this paper, we account for approaches of sparse recovery from large underdetermined linear models with perturbation present in both the measurements and the dictionary matrix. Existing methods have high computation and low efficiency.…

We consider decision-making problems that are formulated as non-convex optimization programs where uncertainty enters the constraints through an additive term, independent of the decision variables, and robustness is imposed using a finite…

We study the problem of consistently recovering the sparsity pattern of a regression parameter vector from correlated observations governed by deterministic missing data patterns using Lasso. We consider the case in which the observed…

This paper investigates the problem of recovering the support of structured signals via adaptive compressive sensing. We examine several classes of structured support sets, and characterize the fundamental limits of accurately recovering…

This work treats the recovery of sparse, binary signals through box-constrained basis pursuit using biased measurement matrices. Using a probabilistic model, we provide conditions under which the recovery of both sparse and saturated binary…

Pairwise-constrained clustering incorporates side information through must-link (ML) and cannot-link (CL) relations between samples. While these constraints can improve cluster quality, they complicate optimization at scale and limit…

Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new…

In recent years, structured matrix recovery problems have gained considerable attention for its real world applications, such as recommender systems and computer vision. Much of the existing work has focused on matrices with low-rank…

Identifying damage of structural systems is typically characterized as an inverse problem which might be ill-conditioned due to aleatory and epistemic uncertainties induced by measurement noise and modeling error. Sparse representation can…

Sparse support recovery arises in many applications in communications and signal processing. Existing methods tackle sparse support recovery problems for a given measurement matrix, and cannot flexibly exploit the properties of sparsity…