Related papers: Primal-dual method to the minimized surface regula…
In this paper we investigate the convergence behavior of a primal-dual splitting method for solving monotone inclusions involving mixtures of composite, Lipschitzian and parallel sum type operators proposed by Combettes and Pesquet in [7].…
We consider the problem of finding the minimization of the sum of a convex function and the composition of another convex function with a continuous linear operator from the view of fixed point algorithms based on proximity operators. We…
We propose a model-based image reconstruction method for photoacoustic tomography(PAT) involving a novel form of regularization and demonstrate its ability to recover good quality images from significantly reduced size datasets. The…
In this paper, we propose a global framework that includes a detailed model of the photo-switching and acoustic processes for photo-switching optoacoustic mesoscopy, based on the underlying physics. We efficiently implement two forward…
Image restoration remains a challenging task in image processing. Numerous methods tackle this problem, often solved by minimizing a non-smooth penalized co-log-likelihood function. Although the solution is easily interpretable with…
Conventional image reconstruction models for lensless cameras often assume that each measurement results from convolving a given scene with a single experimentally measured point-spread function. These image reconstruction models fall short…
In this paper we combine the stochastic variance reduced gradient (SVRG) method [17] with the primal dual fixed point method (PDFP) proposed in [7] to solve a sum of two convex functions and one of which is linearly composite. This type of…
In this paper we propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex optimization problems. The complicating constraints are moved into the…
We consider the problem of minimizing the sum of an average function of a large number of smooth convex components and a general, possibly non-differentiable, convex function. Although many methods have been proposed to solve this problem…
Composite minimization involves a collection of smooth functions which are aggregated in a nonsmooth manner. In the convex setting, we design an algorithm by linearizing each smooth component in accordance with its main curvature. The…
Regularized empirical risk minimization problem with linear predictor appears frequently in machine learning. In this paper, we propose a new stochastic primal-dual method to solve this class of problems. Different from existing methods,…
The objective of this paper is to develop methods for solving image recovery problems subject to constraints on the solution. More precisely, we will be interested in problems which can be formulated as the minimization over a closed convex…
This paper associates a dual problem to the minimization of an arbitrary linear perturbation of the robust sum function introduced in DOI 10.1007/s11228-019-00515-2. It provides an existence theorem for primal optimal solutions and, under…
Primal-Dual Interior-Point methods are capable of solving constrained convex optimization problems to tight tolerances in a fast and robust manner. The derivatives of the primal-dual solution with respect to the problem matrices can be…
Lagrangian duality in mixed integer optimization is a useful framework for problems decomposition and for producing tight lower bounds to the optimal objective, but in contrast to the convex counterpart, it is generally unable to produce…
The primal-dual optimization algorithm developed in Chambolle and Pock (CP), 2011 is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping…
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 digital images, the performance of optical aberration is a multivariate degradation, where the spectral of the scene, the lens imperfections, and the field of view together contribute to the results. Besides eliminating it at the…
We conduct a study and comparison of superiorization and optimization approaches for the reconstruction problem of superiorized/regularized least-squares solutions of underdetermined linear equations with nonnegativity variable bounds.…
In this work we present a novel optimization strategy for image reconstruction tasks under analysis-based image regularization, which promotes sparse and/or low-rank solutions in some learned transform domain. We parameterize such…