相关论文: Learning optimal spatially-dependent regularizatio…

We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…

Spatially varying regularization accommodates the deformation variations that may be necessary for different anatomical regions during deformable image registration. Historically, optimization-based registration models have harnessed…

We investigate a globalized inexact semismooth Newton method applied to strongly convex optimization problems in Hilbert spaces. Here, the semismooth Newton method is appplied to the dual problem, which has a continuously differentiable…

We study Tikhonov regularization for possibly nonlinear inverse problems with weighted $\ell^1$-penalization. The forward operator, mapping from a sequence space to an arbitrary Banach space, typically an $L^2$-space, is assumed to satisfy…

Recovering corrupted images is one of the most challenging problems in image processing. Among various restoration tasks, blind image deblurring has been extensively studied due to its practical importance and inherent difficulty. In this…

Image segmentation techniques are predominately based on parameter-laden optimization. The objective function typically involves weights for balancing competing image fidelity and segmentation regularization cost terms. Setting these…

Regularization techniques are necessary to compute meaningful solutions to discrete ill-posed inverse problems. The well-known 2-norm Tikhonov regularization method equipped with a discretization of the gradient operator as regularization…

We propose a new space-variant regularization term for variational image restoration based on the assumption that the gradient magnitudes of the target image distribute locally according to a half-Generalized Gaussian distribution. This…

In this paper we present a spatially-adaptive method for image reconstruction that is based on the concept of statistical multiresolution estimation as introduced in [Frick K, Marnitz P, and Munk A. "Statistical multiresolution Dantzig…

In this work, we study first-order algorithms for solving Bilevel Optimization (BO) where the objective functions are smooth but possibly nonconvex in both levels and the variables are restricted to closed convex sets. As a first step, we…

Recent work in CT imaging has seen increased interest in the use of total variation (TV) and related penalties to regularize problems involving reconstruction from undersampled or incomplete data. Superiorization is a recently proposed…

We study the numerical integration problem for functions with infinitely many variables. The function spaces of integrands we consider are weighted reproducing kernel Hilbert spaces with norms related to the ANOVA decomposition of the…

Denoising of coefficients in a sparse domain (e.g. wavelet) has been researched extensively because of its simplicity and effectiveness. Literature mainly has focused on designing the best global threshold. However, this paper proposes a…

Total variation (TV) regularization is a popular reconstruction method for ill-posed imaging problems, and particularly useful for applications with piecewise constant targets. However, using TV for medical cone-beam computed X-ray…

We present a novel variational approach to image restoration (e.g., denoising, inpainting, labeling) that enables to complement established variational approaches with a histogram-based prior enforcing closeness of the solution to some…

In this paper, we consider a large class of nonlinear equations derived from first-order type methods for solving composite optimization problems. Traditional approaches to establishing superlinear convergence rates of semismooth…

In this work we derive a second-order approach to bilevel optimization, a type of mathematical programming in which the solution to a parameterized optimization problem (the "lower" problem) is itself to be optimized (in the "upper"…

Second-order optimality conditions of the bilevel programming problems are dependent on the second-order directional derivatives of the value functions or the solution mappings of the lower level problems under some regular conditions,…

In this paper, we consider linear ill-posed problems in Hilbert spaces and their regularization via frame decompositions, which are generalizations of the singular-value decomposition. In particular, we prove convergence for a general class…

We consider composite linear inverse problems where the signal to recover is modeled as a sum of two functions. We study a variational framework formulated as an optimization problem over the pairs of components using two regularization…