Related papers: Second Order Differences of Cyclic Data and Applic…
Steganography schemes are designed with the objective of minimizing a defined distortion function. In most existing state of the art approaches, this distortion function is based on image feature preservation. Since smooth regions or clean…
Total variation (TV) denoising is a nonparametric smoothing method that has good properties for preserving sharp edges and contours in objects with spatial structures like natural images. The estimate is sparse in the sense that TV…
The difference-of-convex (DC) program is an important model in nonconvex optimization due to its structure, which encompasses a wide range of practical applications. In this paper, we aim to tackle a generalized class of DC programs, where…
In this paper, we propose a Dimension-Reduced Second-Order Method (DRSOM) for convex and nonconvex (unconstrained) optimization. Under a trust-region-like framework, our method preserves the convergence of the second-order method while…
Image registration is a fundamental task in medical image analysis. Recently, deep learning based image registration methods have been extensively investigated due to their excellent performance despite the ultra-fast computational time.…
The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…
This paper addresses the optimization problem of minimizing non-convex continuous functions, which is relevant in the context of high-dimensional machine learning applications characterized by over-parametrization. We analyze a randomized…
We investigate a well-known phenomenon of variational approaches in image processing, where typically the best image quality is achieved when the gradient flow process is stopped before converging to a stationary point. This paradox…
We consider the problem of denoising with the help of prior information taken from a database of clean signals or images. Denoising with variational methods is very efficient if a regularizer well adapted to the nature of the data is…
This paper focuses on regularisation methods using models up to the third order to search for up to second-order critical points of a finite-sum minimisation problem. The variant presented belongs to the framework of [3]: it employs random…
While first-order optimization methods such as stochastic gradient descent (SGD) are popular in machine learning (ML), they come with well-known deficiencies, including relatively-slow convergence, sensitivity to the settings of…
Owing to the edge preserving ability and low computational cost of the total variation (TV), variational models with the TV regularization have been widely investigated in the field of multiplicative noise removal. The key points of the…
2D Total Variation Denoising (TVD) is a widely used technique for image denoising. It is also an important nonparametric regression method for estimating functions with heterogenous smoothness. Recent results have shown the TVD estimator to…
Three-dimensional (3D) imaging is popular in medical applications, however, anisotropic 3D volumes with thick, low-spatial-resolution slices are often acquired to reduce scan times. Deep learning (DL) offers a solution to recover…
Total Generalized Variation (TGV) has recently been proven certainly successful in image processing for preserving sharp features as well as smooth transition variations. However, none of the existing works aims at numerically calculating…
Variational wave function ansatze are an invaluable tool to study the properties of strongly correlated systems. We propose such a wave function, based on the theory of auxiliary fields and combining aspects of auxiliary-field quantum Monte…
Natural images tend to mostly consist of smooth regions with individual pixels having highly correlated spectra. This information can be exploited to recover hyperspectral images of natural scenes from their incomplete and noisy…
Regularization approaches have demonstrated their effectiveness for solving ill-posed problems. However, in the context of variational restoration methods, a challenging question remains, which is how to find a good regularizer. While total…
Variational regularization techniques are dominant in the field of mathematical imaging. A drawback of these techniques is that they are dependent on a number of parameters which have to be set by the user. A by now common strategy to…
We propose and analyze several inexact regularized Newton-type methods for finding a global saddle point of convex-concave unconstrained min-max optimization problems. Compared to first-order methods, our understanding of second-order…