Related papers: A new class of accelerated regularization methods,…
This paper investigates iterative methods for solving bi-level optimization problems where both inner and outer functions have a composite structure. We establish novel theoretical results, including the first analysis that provides…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…
Regularization is a core component of modern inverse problems, as it helps establish the well-posedness of the solution of interest. Popular regularization approaches include variational regularization and iterative regularization. The…
In this paper, we propose an acceleration framework for a class of iterative methods using the Reduced Order Method (ROM). Assuming that the underlying iterative scheme generates a rich basis for the solution space, we construct the next…
Data assisted reconstruction algorithms, incorporating trained neural networks, are a novel paradigm for solving inverse problems. One approach is to first apply a classical reconstruction method and then apply a neural network to improve…
We consider the problem of supervised learning with convex loss functions and propose a new form of iterative regularization based on the subgradient method. Unlike other regularization approaches, in iterative regularization no constraint…
In this work, we propose a high-order regularization method to solve the ill-conditioned problems in robot localization. Numerical solutions to robot localization problems are often unstable when the problems are ill-conditioned. A typical…
This paper is concerned with a novel regularisation technique for solving linear ill-posed operator equations in Hilbert spaces from data that is corrupted by white noise. We combine convex penalty functionals with extreme-value statistics…
In this paper we consider new regularization methods for linear inverse problems of dynamic type. These methods are based on dynamic programming techniques for linear quadratic optimal control problems. Two different approaches are…
In this work, we consider ill-posed inverse problems in which the forward operator is continuous and weakly closed, and the sought solution belongs to a weakly closed constraint set. We propose a regularization method based on minimizing…
Diffuse Optical Tomography (DOT) is an emerging technology in medical imaging which employs light in the NIR spectrum to estimate the distribution of optical coefficients in biological tissues for diagnostic and monitoring purposes. DOT…
We investigate the iterative methods proposed by Maz'ya and Kozlov (see [KM1], [KM2]) for solving ill-posed inverse problems modeled by partial differential equations. We consider linear evolutionary problems of elliptic, hyperbolic and…
The problem of numerical differentiation can be thought of as an inverse problem by considering it as solving a Volterra equation. It is well known that such inverse integral problems are ill-posed and one requires regularization methods to…
Nonnegative matrix factorization has been widely applied in face recognition, text mining, as well as spectral analysis. This paper proposes an alternating proximal gradient method for solving this problem. With a uniformly positive lower…
We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…
We investigate iterated Tikhonov methods coupled with a Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization method. In the…
In this paper, we investigate regularization of linear inverse problems with irregular noise. In particular, we consider the case that the noise can be preprocessed by certain adjoint embedding operators. By introducing the consequent…
We propose a variational regularization approach based on a multiscale representation called cylindrical shearlets aimed at dynamic imaging problems, especially dynamic tomography. The intuitive idea of our approach is to integrate a…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
Regularization method and Bayesian inverse method are two dominating ways for solving inverse problems generated from various fields, e.g., seismic exploration and medical imaging. The two methods are related with each other by the MAP…