Related papers: An Augmented Lagrangian Method-Based Framework in …

In many learning tasks, structural models usually lead to better interpretability and higher generalization performance. In recent years, however, the simple structural models such as lasso are frequently proved to be insufficient.…

This paper addresses the problem of sparse phase retrieval, a fundamental inverse problem in applied mathematics, physics, and engineering, where a signal need to be reconstructed using only the magnitude of its transformation while phase…

The problem studied in this paper is ultrasound image reconstruction from frequency-domain measurements of the scattered field from an object with contrast in attenuation and sound speed. The case where the object has uniform but unknown…

We consider minimization of the sum of a large number of convex functions, and we propose an incremental aggregated version of the proximal algorithm, which bears similarity to the incremental aggregated gradient and subgradient methods…

This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel…

Multi-layered structures are widely used in the construction of metamaterial devices to realize various cutting-edge waveguide applications. This paper makes several contributions to the mathematical analysis of subwavelength resonances in…

We develop a novel wave imaging scheme for reconstructing the shape of an inhomogeneous scatterer and we consider the inverse acoustic obstacle scattering problem as a prototype model for our study. There exists a wealth of reconstruction…

We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of…

Regularization of the inverse problem is a complex issue when using Near-field Acoustic Holography (NAH) techniques to identify the vibrating sources. This paper shows that, for convex homogeneous plates with arbitrary boundary conditions,…

In this paper, we propose new methods to efficiently solve convex optimization problems encountered in sparse estimation, which include a new quasi-Newton method that avoids computing the Hessian matrix and improves efficiency, and we prove…

Our work is focused on the joint sparsity recovery problem where the common sparsity pattern is corrupted by Poisson noise. We formulate the confidence-constrained optimization problem in both least squares (LS) and maximum likelihood (ML)…

In this paper, we propose a time-frequency analysis method to obtain instantaneous frequencies and the corresponding decomposition by solving an optimization problem. In this optimization problem, the basis to decompose the signal is not…

This paper introduces a novel framework and corresponding methods for sampling and reconstruction of sparse signals in shift-invariant (SI) spaces. We reinterpret the random demodulator, a system that acquires sparse bandlimited signals, as…

We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear…

We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic…

This article considers recovery of signals that are sparse or approximately sparse in terms of a (possibly) highly overcomplete and coherent tight frame from undersampled data corrupted with additive noise. We show that the properly…

Total variation has proved its effectiveness in solving inverse problems for compressive sensing. Besides, the nonlocal means filter used as regularization preserves texture better for recovered images, but it is quite complex to implement.…

In this paper, we revisit the augmented Lagrangian method for a class of nonsmooth convex optimization. We present the Lagrange optimality system of the augmented Lagrangian associated with the problems, and establish its connections with…

Robust statistical estimators offer resilience against outliers but are often computationally challenging, particularly in high-dimensional sparse settings. Modern optimization techniques are utilized for robust sparse association…

In this paper, we present an efficient semismooth Newton method, named SSNCP, for solving a class of semidefinite programming problems. Our approach is rooted in an equivalent semismooth system derived from the saddle point problem induced…