相关论文: A Low-rank Projected Proximal Gradient Method for …

Existing results for low-rank matrix recovery largely focus on quadratic loss, which enjoys favorable properties such as restricted strong convexity/smoothness (RSC/RSM) and well conditioning over all low rank matrices. However, many…

Optimization algorithms are pivotal in advancing various scientific and industrial fields but often encounter obstacles such as trapping in local minima, saddle points, and plateaus (flat regions), which makes the convergence to reasonable…

This paper presents an algorithm tailored for the efficient recovery of sparse probability measures incorporating $\ell_0$-sparse regularization within the probability simplex constraint. Employing the Bregman proximal gradient method, our…

Low-rank matrix estimation under heavy-tailed noise is challenging, both computationally and statistically. Convex approaches have been proven statistically optimal but suffer from high computational costs, especially since robust loss…

In this paper, we present a convergence analysis of the Group Projected Subspace Pursuit (GPSP) algorithm proposed by He et al. [HKL+23] (Group Projected subspace pursuit for IDENTification of variable coefficient differential equations…

In this paper, utilizing techniques in compressed sensing, parallel optimization and deep learning, we propose a model-driven approach to jointly design the common measurement matrix and GROUP LASSO-based jointly sparse signal recovery…

Compressed sensing has a wide range of applications that include error correction, imaging, radar and many more. Given a sparse signal in a high dimensional space, one wishes to reconstruct that signal accurately and efficiently from a…

Compressive Sensing (CS) stipulates that a sparse signal can be recovered from a small number of linear measurements, and that this recovery can be performed efficiently in polynomial time. The framework of model-based compressive sensing…

Sparse subspace clustering (SSC) relies on sparse regression for accurate neighbor identification. Inspired by recent progress in compressive sensing, this paper proposes a new sparse regression scheme for SSC via two-step reweighted…

This article proposes an efficient numerical method for solving nonlinear partial differential equations (PDEs) based on sparse Gaussian processes (SGPs). Gaussian processes (GPs) have been extensively studied for solving PDEs by…

Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be…

Accurate signal recovery or image reconstruction from indirect and possibly undersampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by…

This paper presents a geometric analysis of the simultaneous blind deconvolution and phase retrieval (BDPR) problem via a structured low-rank tensor recovery framework. Due to the highly complicated structure of the associated sensing…

We present and analyze a novel sparse polynomial technique for approximating high-dimensional Hilbert-valued functions, with application to parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our…

In this paper, we propose a proximal stochasitc gradient algorithm (PSGA) for solving composite optimization problems by incorporating variance reduction techniques and an adaptive step-size strategy. In the PSGA method, the objective…

We present a novel class of projected gradient (PG) methods for minimizing a smooth but not necessarily convex function over a convex compact set. We first provide a novel analysis of the constant-stepsize PG method, achieving the…

We consider the problem of recovering signals from their power spectral density. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In…

Limitations on bandwidth and power consumption impose strict bounds on data rates of diagnostic imaging systems. Consequently, the design of suitable (i.e. task- and data-aware) compression and reconstruction techniques has attracted…

Low-rank matrix estimation is a canonical problem that finds numerous applications in signal processing, machine learning and imaging science. A popular approach in practice is to factorize the matrix into two compact low-rank factors, and…

Proximal algorithms have gained popularity in recent years in large-scale and distributed optimization problems. One such problem is the phase retrieval problem, for which proximal operators have been proposed recently. The phase retrieval…