Related papers: A generalized matrix Krylov subspace method for TV…
The robust low-rank tensor completion problem addresses the challenge of recovering corrupted high-dimensional tensor data with missing entries, outliers, and sparse noise commonly found in real-world applications. Existing methodologies…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
Regularization plays a crucial role in reliably utilizing imaging systems for scientific and medical investigations. It helps to stabilize the process of computationally undoing any degradation caused by physical limitations of the imaging…
We study the qualitative properties of optimal regularisation parameters in variational models for image restoration. The parameters are solutions of bilevel optimisation problems with the image restoration problem as constraint. A general…
Total Variation (TV) and related extensions have been popular in image restoration due to their robust performance and wide applicability. While the original formulation is still relevant after two decades of extensive research, its…
Regularization by Denoising (RED) is a well-known method for solving image restoration problems by using learned image denoisers as priors. Since the regularization parameter in the traditional RED does not have any physical interpretation,…
In this paper we study the topic of signal restoration using complexity regularization, quantifying the compression bit-cost of the signal estimate. While complexity-regularized restoration is an established concept, solid practical methods…
We present a new vectorial total variation method that addresses the problem of color consistent image filtering. Our approach is inspired from the double-opponent cell representation in the human visual cortex. Existing methods of…
The main goal of this paper is to propose a new quaternion total variation regularization model for solving linear ill-posed quaternion inverse problems, which arise from three-dimensional signal filtering or color image processing. The…
Invariant risk minimization is an important general machine learning framework that has recently been interpreted as a total variation model (IRM-TV). However, how to improve out-of-distribution (OOD) generalization in the IRM-TV setting…
An optimization framework is presented for minimizing the energy functional developed around a generalized equation governing physical systems such as fluid dynamics, particle transport, phase transition, and other related systems. The…
This paper presents a regularized Newton method (RNM) with generalized regularization terms for unconstrained convex optimization problems. The generalized regularization includes quadratic, cubic, and elastic net regularizations as special…
Krylov subspace methods are a powerful tool for efficiently solving high-dimensional linear algebra problems. In this work, we study the approximation quality that a Krylov subspace provides for estimating the numerical range of a matrix.…
The goal of this paper is to further develop an approach to inverse problems with imperfect forward operators that is based on partially ordered spaces. Studying the dual problem yields useful insights into the convergence of the…
Binary optimization is a central problem in mathematical optimization and its applications are abundant. To solve this problem, we propose a new class of continuous optimization techniques which is based on Mathematical Programming with…
We apply the recently proposed superiorization methodology (SM) to the inverse planning problem in radiation therapy. The inverse planning problem is represented here as a constrained minimization problem of the total variation (TV) of the…
The problem of restoring images corrupted by Poisson noise is common in many application fields and, because of its intrinsic ill posedness, it requires regularization techniques for its solution. The effectiveness of such techniques…
Energy minimization algorithms, such as graph cuts, enable the computation of the MAP solution under certain probabilistic models such as Markov random fields. However, for many computer vision problems, the MAP solution under the model is…