Related papers: Iterative regularization for low complexity regula…
A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that…
Inspired by several recent developments in regularization theory, optimization, and signal processing, we present and analyze a numerical approach to multi-penalty regularization in spaces of sparsely represented functions. The sparsity…
Recently, the $\l_{p}$-norm regularization minimization problem $(P_{p}^{\lambda})$ has attracted great attention in compressed sensing. However, the $\l_{p}$-norm $\|x\|_{p}^{p}$ in problem $(P_{p}^{\lambda})$ is nonconvex and…
Image restoration refers to the process of reconstructing noisy, destroyed, or missing parts of an image, which is an ill-posed inverse problem. A specific regularization term and image degradation are typically assumed to achieve…
Sparse model selection is ubiquitous from linear regression to graphical models where regularization paths, as a family of estimators upon the regularization parameter varying, are computed when the regularization parameter is unknown or…
Many inverse problems are concerned with the estimation of non-negative parameter functions. In this paper, in order to obtain non-negative stable approximate solutions to ill-posed linear operator equations in a Hilbert space setting, we…
We develop a novel primal-dual algorithm to solve a class of nonsmooth and nonlinear compositional convex minimization problems, which covers many existing and brand-new models as special cases. Our approach relies on a combination of a new…
In this paper we provide a detailed analysis of the iteration complexity of dual first order methods for solving conic convex problems. When it is difficult to project on the primal feasible set described by convex constraints, we use the…
In this paper, we propose a double iteratively reweighted algorithm to solve nonconvex and nonsmooth optimization problems, where both the objectives and constraint functions are formulated by concave compositions to promote group-sparse…
In this paper, we establish universal approximation theorems for neural networks applied to general nonlinear ill-posed operator equations. In addition to the approximation error, the measurement error is also taken into account in our…
We address the optimization problem in a data-driven variational reconstruction framework, where the regularizer is parameterized by an input-convex neural network (ICNN). While gradient-based methods are commonly used to solve such…
In the context of sparse recovery, it is known that most of existing regularizers such as $\ell_1$ suffer from some bias incurred by some leading entries (in magnitude) of the associated vector. To neutralize this bias, we propose a class…
Optimization problems constrained by partial differential equations (PDEs) naturally arise in scientific computing, as those constraints often model physical systems or the simulation thereof. In an implicitly constrained approach, the…
This paper considers a large class of problems where we seek to recover a low rank matrix and/or sparse vector from some set of measurements. While methods based on convex relaxations suffer from a (possibly large) estimator bias, and other…
Convex regularizers are often used for sparse learning. They are easy to optimize, but can lead to inferior prediction performance. The difference of $\ell_1$ and $\ell_2$ ($\ell_{1-2}$) regularizer has been recently proposed as a nonconvex…
Image reconstruction of EIT mathematically is a typical nonlinear and severely ill-posed inverse problem. Appropriate priors or penalties are required to enable the reconstruction. The commonly used L2-norm can enforce the stability to…
Iteratively reweighted $\ell_1$ algorithm is a popular algorithm for solving a large class of optimization problems whose objective is the sum of a Lipschitz differentiable loss function and a possibly nonconvex sparsity inducing…
In this article we develop and analyze novel iterative regularization techniques for the solution of systems of nonlinear ill--posed operator equations. The basic idea consists in considering separately each equation of this system and…
We consider a regularized least squares problem, with regularization by structured sparsity-inducing norms, which extend the usual $\ell_1$ and the group lasso penalty, by allowing the subsets to overlap. Such regularizations lead to…
In this work, we consider a class of differentiable criteria for sparse image computing problems, where a nonconvex regularization is applied to an arbitrary linear transform of the target image. As special cases, it includes…