Related papers: A generalized matrix Krylov subspace method for TV…
Despite the popularity and practical success of total variation (TV) regularization for function estimation, surprisingly little is known about its theoretical performance in a statistical setting. While TV regularization has been known for…
In this paper we present deflation and augmentation techniques that have been designed to accelerate the convergence of Krylov subspace methods for the solution of linear systems of equations. We review numerical approaches both for linear…
In this paper, we propose a regularization technique for noisy-image super-resolution and image denoising. Total variation (TV) regularization is adopted in many image processing applications to preserve the local smoothness. However, TV…
The augmented Lagrangian (AL) method that solves convex optimization problems with linear constraints has drawn more attention recently in imaging applications due to its decomposable structure for composite cost functions and empirical…
Many scientific applications require the evaluation of the action of the matrix function over a vector and the most common methods for this task are those based on the Krylov subspace. Since the orthogonalization cost and memory requirement…
Many practical imaging systems suffer from uncertainty in acquisition geometry -- such as projection angles in computed tomography or sensor positions in photoacoustic tomography -- leading to nonlinear inverse problems that require joint…
In this paper, we consider a primal-dual domain decomposition method for total variation regularized problems appearing in mathematical image processing. The model problem is transformed into an equivalent constrained minimization problem…
Second-order optimization methods, such as cubic regularized Newton methods, are known for their rapid convergence rates; nevertheless, they become impractical in high-dimensional problems due to their substantial memory requirements and…
We propose the use of the Kantorovich-Rubinstein norm from optimal transport in imaging problems. In particular, we discuss a variational regularisation model endowed with a Kantorovich-Rubinstein discrepancy term and total variation…
We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…
In this paper, we consider an inverse space-dependent source problem for a time-fractional diffusion equation. To deal with the ill-posedness of the problem, we transform the problem into an optimal control problem with total variational…
We introduce a method for fast estimation of data-adapted, spatio-temporally dependent regularization parameter-maps for variational image reconstruction, focusing on total variation (TV)-minimization. Our approach is inspired by recent…
Even after over two decades, the total variation (TV) remains one of the most popular regularizations for image processing problems and has sparked a tremendous amount of research, particularly to move from scalar to vector-valued…
We present a numerical method for the minimization of constrained optimization problems where the objective is augmented with large quadratic penalties of inconsistent equality constraints. Such objectives arise from quadratic integral…
This paper introduces new solvers for efficiently computing solutions to large-scale inverse problems with group sparsity regularization, including both non-overlapping and overlapping groups. Group sparsity regularization refers to a type…
In this paper, we propose a penalty dual-primal augmented lagrangian method for solving convex minimization problems under linear equality or inequality constraints. The proposed method combines a novel penalty technique with updates the…
This paper surveys an important class of methods that combine iterative projection methods and variational regularization methods for large-scale inverse problems. Iterative methods such as Krylov subspace methods are invaluable in the…
Hyperspectral analysis has gained popularity over recent years as a way to infer what materials are displayed on a picture whose pixels consist of a mixture of spectral signatures. Computing both signatures and mixture coefficients is known…
We develop and analyze an inexact regularized alternating projection method for nonconvex feasibility problems. Such a method employs inexact projections on one of the two sets, according to a set of well-defined conditions. We prove the…
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…